Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.8% → 43.7%

Time: 33.0s

Alternatives: 39

Speedup: 4.1×

• 88.1% 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: 30.8% 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: 43.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ t_2 := y \cdot x - t \cdot z\\ t_3 := y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-105}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-296}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, a, \mathsf{fma}\left(j \cdot t - k \cdot y, y4, \left(-y0\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot b\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(y4, y1, \left(-y0\right) \cdot y5\right), k, \mathsf{fma}\left(\mathsf{fma}\left(y0, c, \left(-a\right) \cdot y1\right), x, \left(-t\right) \cdot \mathsf{fma}\left(y4, c, \left(-a\right) \cdot y5\right)\right)\right) \cdot y2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, y1, \mathsf{fma}\left(t\_2, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+258}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          (fma
           (- (* b a) (* i c))
           y
           (fma (- (* y0 c) (* y1 a)) y2 (* (- j) (- (* y0 b) (* y1 i)))))
          x))
        (t_2 (- (* y x) (* t z)))
        (t_3
         (*
          y0
          (fma
           (- y5)
           (fma k y2 (* (- j) y3))
           (fma c (fma x y2 (* (- y3) z)) (* (- b) (fma j x (* (- k) z))))))))
   (if (<= x -4.1e-60)
     t_1
     (if (<= x -7.8e-105)
       t_3
       (if (<= x -5.3e-296)
         (*
          (fma
           t_2
           a
           (fma (- (* j t) (* k y)) y4 (* (- y0) (- (* j x) (* k z)))))
          b)
         (if (<= x 1.45e-247)
           t_3
           (if (<= x 1.02e-42)
             (*
              (fma
               (fma y4 y1 (* (- y0) y5))
               k
               (fma
                (fma y0 c (* (- a) y1))
                x
                (* (- t) (fma y4 c (* (- a) y5)))))
              y2)
             (if (<= x 8.5e+41)
               (*
                (fma
                 (+ (* (- y2) x) (* y3 z))
                 y1
                 (fma t_2 b (* (- (* y2 t) (* y3 y)) y5)))
                a)
               (if (<= x 3.8e+258)
                 t_1
                 (* (* x (fma a b (* (- c) i))) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = fma(((b * a) - (i * c)), y, fma(((y0 * c) - (y1 * a)), y2, (-j * ((y0 * b) - (y1 * i))))) * x;
	double t_2 = (y * x) - (t * z);
	double t_3 = y0 * fma(-y5, fma(k, y2, (-j * y3)), fma(c, fma(x, y2, (-y3 * z)), (-b * fma(j, x, (-k * z)))));
	double tmp;
	if (x <= -4.1e-60) {
		tmp = t_1;
	} else if (x <= -7.8e-105) {
		tmp = t_3;
	} else if (x <= -5.3e-296) {
		tmp = fma(t_2, a, fma(((j * t) - (k * y)), y4, (-y0 * ((j * x) - (k * z))))) * b;
	} else if (x <= 1.45e-247) {
		tmp = t_3;
	} else if (x <= 1.02e-42) {
		tmp = fma(fma(y4, y1, (-y0 * y5)), k, fma(fma(y0, c, (-a * y1)), x, (-t * fma(y4, c, (-a * y5))))) * y2;
	} else if (x <= 8.5e+41) {
		tmp = fma(((-y2 * x) + (y3 * z)), y1, fma(t_2, b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (x <= 3.8e+258) {
		tmp = t_1;
	} else {
		tmp = (x * fma(a, b, (-c * i))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(fma(Float64(Float64(b * a) - Float64(i * c)), y, fma(Float64(Float64(y0 * c) - Float64(y1 * a)), y2, Float64(Float64(-j) * Float64(Float64(y0 * b) - Float64(y1 * i))))) * x)
	t_2 = Float64(Float64(y * x) - Float64(t * z))
	t_3 = Float64(y0 * fma(Float64(-y5), fma(k, y2, Float64(Float64(-j) * y3)), fma(c, fma(x, y2, Float64(Float64(-y3) * z)), Float64(Float64(-b) * fma(j, x, Float64(Float64(-k) * z))))))
	tmp = 0.0
	if (x <= -4.1e-60)
		tmp = t_1;
	elseif (x <= -7.8e-105)
		tmp = t_3;
	elseif (x <= -5.3e-296)
		tmp = Float64(fma(t_2, a, fma(Float64(Float64(j * t) - Float64(k * y)), y4, Float64(Float64(-y0) * Float64(Float64(j * x) - Float64(k * z))))) * b);
	elseif (x <= 1.45e-247)
		tmp = t_3;
	elseif (x <= 1.02e-42)
		tmp = Float64(fma(fma(y4, y1, Float64(Float64(-y0) * y5)), k, fma(fma(y0, c, Float64(Float64(-a) * y1)), x, Float64(Float64(-t) * fma(y4, c, Float64(Float64(-a) * y5))))) * y2);
	elseif (x <= 8.5e+41)
		tmp = Float64(fma(Float64(Float64(Float64(-y2) * x) + Float64(y3 * z)), y1, fma(t_2, b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (x <= 3.8e+258)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	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[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * y + N[(N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision] * y2 + N[((-j) * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[((-y5) * N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2 + N[((-y3) * z), $MachinePrecision]), $MachinePrecision] + N[((-b) * N[(j * x + N[((-k) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e-60], t$95$1, If[LessEqual[x, -7.8e-105], t$95$3, If[LessEqual[x, -5.3e-296], N[(N[(t$95$2 * a + N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * y4 + N[((-y0) * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 1.45e-247], t$95$3, If[LessEqual[x, 1.02e-42], N[(N[(N[(y4 * y1 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k + N[(N[(y0 * c + N[((-a) * y1), $MachinePrecision]), $MachinePrecision] * x + N[((-t) * N[(y4 * c + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[x, 8.5e+41], N[(N[(N[(N[((-y2) * x), $MachinePrecision] + N[(y3 * z), $MachinePrecision]), $MachinePrecision] * y1 + N[(t$95$2 * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[x, 3.8e+258], t$95$1, N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.10000000000000013e-60 or 8.49999999999999938e41 < x < 3.80000000000000009e258

   1. Initial program 23.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 60.6%

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

   if -4.10000000000000013e-60 < x < -7.8e-105 or -5.2999999999999995e-296 < x < 1.45e-247

   1. Initial program 38.4%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 25.0%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 69.3%

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

   if -7.8e-105 < x < -5.2999999999999995e-296

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.7%

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

   if 1.45e-247 < x < 1.0199999999999999e-42

   1. Initial program 33.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 37.6%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 34.5%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 40.9%

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

   12. Taylor expanded in y2 around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

   14. Applied rewrites 57.3%

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

   if 1.0199999999999999e-42 < x < 8.49999999999999938e41

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 67.0%

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

   if 3.80000000000000009e258 < x

   1. Initial program 11.1%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-296}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot x - t \cdot z, a, \mathsf{fma}\left(j \cdot t - k \cdot y, y4, \left(-y0\right) \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot b\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-247}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(y4, y1, \left(-y0\right) \cdot y5\right), k, \mathsf{fma}\left(\mathsf{fma}\left(y0, c, \left(-a\right) \cdot y1\right), x, \left(-t\right) \cdot \mathsf{fma}\left(y4, c, \left(-a\right) \cdot y5\right)\right)\right) \cdot y2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+258}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 56.2% accurate, 0.5× speedup

Math

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

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 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)) t_1))
          (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))
   (if (<= t_2 INFINITY)
     t_2
     (*
      (fma (+ (* y4 (- b)) (* y5 i)) k (fma (- (* b a) (* i c)) x (* t_1 y3)))
      y))))

C

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = 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)) * t_1)) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(fma(Float64(Float64(y4 * Float64(-b)) + Float64(y5 * i)), k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(t_1 * y3))) * y);
	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[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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] * t$95$1), $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]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(N[(N[(y4 * (-b)), $MachinePrecision] + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(t$95$1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $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 91.2%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 44.8%

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

4. Final simplification 58.6%

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

Alternative 3: 40.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot c - y1 \cdot a\\ t_2 := y0 \cdot b - y1 \cdot i\\ \mathbf{if}\;y3 \leq -3.2 \cdot 10^{+199}:\\ \;\;\;\;\left(-c\right) \cdot \left(z \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -4 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-y1\right) + y5 \cdot y0, j, \mathsf{fma}\left(-z, t\_1, \left(y4 \cdot c - y5 \cdot a\right) \cdot y\right)\right) \cdot y3\\ \mathbf{elif}\;y3 \leq -1.35 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq -3.5 \cdot 10^{-276}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(t\_1, y2, \left(-j\right) \cdot t\_2\right)\right) \cdot x\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, t, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y3, t\_2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 c) (* y1 a))) (t_2 (- (* y0 b) (* y1 i))))
   (if (<= y3 -3.2e+199)
     (* (- c) (* z (fma (- i) t (* y0 y3))))
     (if (<= y3 -4e+70)
       (*
        (fma
         (+ (* y4 (- y1)) (* y5 y0))
         j
         (fma (- z) t_1 (* (- (* y4 c) (* y5 a)) y)))
        y3)
       (if (<= y3 -1.35e-219)
         (*
          (fma
           (+ (* (- y2) x) (* y3 z))
           a
           (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
          y1)
         (if (<= y3 -3.5e-276)
           (* (- i) (* z (fma (- c) t (* k y1))))
           (if (<= y3 2.3e+86)
             (* (fma (- (* b a) (* i c)) y (fma t_1 y2 (* (- j) t_2))) x)
             (if (<= y3 2.05e+239)
               (*
                (- j)
                (fma
                 (+ (* y4 (- b)) (* y5 i))
                 t
                 (fma (- (* y4 y1) (* y5 y0)) y3 (* t_2 x))))
               (* (* y5 (fma (- a) y3 (* i k))) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * c) - (y1 * a);
	double t_2 = (y0 * b) - (y1 * i);
	double tmp;
	if (y3 <= -3.2e+199) {
		tmp = -c * (z * fma(-i, t, (y0 * y3)));
	} else if (y3 <= -4e+70) {
		tmp = fma(((y4 * -y1) + (y5 * y0)), j, fma(-z, t_1, (((y4 * c) - (y5 * a)) * y))) * y3;
	} else if (y3 <= -1.35e-219) {
		tmp = fma(((-y2 * x) + (y3 * z)), a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (y3 <= -3.5e-276) {
		tmp = -i * (z * fma(-c, t, (k * y1)));
	} else if (y3 <= 2.3e+86) {
		tmp = fma(((b * a) - (i * c)), y, fma(t_1, y2, (-j * t_2))) * x;
	} else if (y3 <= 2.05e+239) {
		tmp = -j * fma(((y4 * -b) + (y5 * i)), t, fma(((y4 * y1) - (y5 * y0)), y3, (t_2 * x)));
	} else {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * c) - Float64(y1 * a))
	t_2 = Float64(Float64(y0 * b) - Float64(y1 * i))
	tmp = 0.0
	if (y3 <= -3.2e+199)
		tmp = Float64(Float64(-c) * Float64(z * fma(Float64(-i), t, Float64(y0 * y3))));
	elseif (y3 <= -4e+70)
		tmp = Float64(fma(Float64(Float64(y4 * Float64(-y1)) + Float64(y5 * y0)), j, fma(Float64(-z), t_1, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y))) * y3);
	elseif (y3 <= -1.35e-219)
		tmp = Float64(fma(Float64(Float64(Float64(-y2) * x) + Float64(y3 * z)), a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (y3 <= -3.5e-276)
		tmp = Float64(Float64(-i) * Float64(z * fma(Float64(-c), t, Float64(k * y1))));
	elseif (y3 <= 2.3e+86)
		tmp = Float64(fma(Float64(Float64(b * a) - Float64(i * c)), y, fma(t_1, y2, Float64(Float64(-j) * t_2))) * x);
	elseif (y3 <= 2.05e+239)
		tmp = Float64(Float64(-j) * fma(Float64(Float64(y4 * Float64(-b)) + Float64(y5 * i)), t, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y3, Float64(t_2 * x))));
	else
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	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[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3.2e+199], N[((-c) * N[(z * N[((-i) * t + N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4e+70], N[(N[(N[(N[(y4 * (-y1)), $MachinePrecision] + N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * j + N[((-z) * t$95$1 + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision], If[LessEqual[y3, -1.35e-219], N[(N[(N[(N[((-y2) * x), $MachinePrecision] + N[(y3 * z), $MachinePrecision]), $MachinePrecision] * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y3, -3.5e-276], N[((-i) * N[(z * N[((-c) * t + N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.3e+86], N[(N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * y + N[(t$95$1 * y2 + N[((-j) * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y3, 2.05e+239], N[((-j) * N[(N[(N[(y4 * (-b)), $MachinePrecision] + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * t + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y3 + N[(t$95$2 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -3.20000000000000006e199

   1. Initial program 8.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.1%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 63.4%

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

   if -3.20000000000000006e199 < y3 < -4.00000000000000029e70

   1. Initial program 28.9%

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

   3. Taylor expanded in y3 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 77.2%

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

   if -4.00000000000000029e70 < y3 < -1.35e-219

   1. Initial program 25.1%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.8%

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

   if -1.35e-219 < y3 < -3.49999999999999993e-276

   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 z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 36.6%

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

   6. Taylor expanded in i around -inf

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

   8. Applied rewrites 66.5%

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

   if -3.49999999999999993e-276 < y3 < 2.2999999999999999e86

   1. Initial program 35.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 54.6%

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

   if 2.2999999999999999e86 < y3 < 2.0500000000000001e239

   1. Initial program 35.7%

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

   3. Taylor expanded in j around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. neg-mul-1 N/A

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

      4. lower-neg.f64 N/A

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

      5. associate--l+ N/A

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

      6. mul-1-neg N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

   5. Applied rewrites 61.0%

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

   if 2.0500000000000001e239 < y3

   1. Initial program 10.5%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]
3. Recombined 7 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.2 \cdot 10^{+199}:\\ \;\;\;\;\left(-c\right) \cdot \left(z \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -4 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-y1\right) + y5 \cdot y0, j, \mathsf{fma}\left(-z, y0 \cdot c - y1 \cdot a, \left(y4 \cdot c - y5 \cdot a\right) \cdot y\right)\right) \cdot y3\\ \mathbf{elif}\;y3 \leq -1.35 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq -3.5 \cdot 10^{-276}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, t, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y3, \left(y0 \cdot b - y1 \cdot i\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot b - y1 \cdot i\\ t_2 := \mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot t\_1\right)\right) \cdot x\\ t_3 := \mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, t\_1 \cdot z\right)\right) \cdot k\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-301}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 b) (* y1 i)))
        (t_2
         (*
          (fma
           (- (* b a) (* i c))
           y
           (fma (- (* y0 c) (* y1 a)) y2 (* (- j) t_1)))
          x))
        (t_3
         (*
          (fma
           (+ (* y4 (- b)) (* y5 i))
           y
           (fma (- (* y4 y1) (* y5 y0)) y2 (* t_1 z)))
          k)))
   (if (<= x -1.5e-30)
     t_2
     (if (<= x -3e-95)
       t_3
       (if (<= x -4.2e-301)
         (*
          (*
           (- b)
           (fma c (/ (fma (- y) y3 (* t y2)) b) (- (fma (- k) y (* j t)))))
          y4)
         (if (<= x 6e-34)
           t_3
           (if (<= x 8.5e+41)
             (*
              (fma
               (+ (* (- y2) x) (* y3 z))
               y1
               (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
              a)
             (if (<= x 3.8e+258) t_2 (* (* x (fma a b (* (- c) i))) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * b) - (y1 * i);
	double t_2 = fma(((b * a) - (i * c)), y, fma(((y0 * c) - (y1 * a)), y2, (-j * t_1))) * x;
	double t_3 = fma(((y4 * -b) + (y5 * i)), y, fma(((y4 * y1) - (y5 * y0)), y2, (t_1 * z))) * k;
	double tmp;
	if (x <= -1.5e-30) {
		tmp = t_2;
	} else if (x <= -3e-95) {
		tmp = t_3;
	} else if (x <= -4.2e-301) {
		tmp = (-b * fma(c, (fma(-y, y3, (t * y2)) / b), -fma(-k, y, (j * t)))) * y4;
	} else if (x <= 6e-34) {
		tmp = t_3;
	} else if (x <= 8.5e+41) {
		tmp = fma(((-y2 * x) + (y3 * z)), y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	} else if (x <= 3.8e+258) {
		tmp = t_2;
	} else {
		tmp = (x * fma(a, b, (-c * i))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * b) - Float64(y1 * i))
	t_2 = Float64(fma(Float64(Float64(b * a) - Float64(i * c)), y, fma(Float64(Float64(y0 * c) - Float64(y1 * a)), y2, Float64(Float64(-j) * t_1))) * x)
	t_3 = Float64(fma(Float64(Float64(y4 * Float64(-b)) + Float64(y5 * i)), y, fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), y2, Float64(t_1 * z))) * k)
	tmp = 0.0
	if (x <= -1.5e-30)
		tmp = t_2;
	elseif (x <= -3e-95)
		tmp = t_3;
	elseif (x <= -4.2e-301)
		tmp = Float64(Float64(Float64(-b) * fma(c, Float64(fma(Float64(-y), y3, Float64(t * y2)) / b), Float64(-fma(Float64(-k), y, Float64(j * t))))) * y4);
	elseif (x <= 6e-34)
		tmp = t_3;
	elseif (x <= 8.5e+41)
		tmp = Float64(fma(Float64(Float64(Float64(-y2) * x) + Float64(y3 * z)), y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	elseif (x <= 3.8e+258)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	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[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * y + N[(N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision] * y2 + N[((-j) * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(y4 * (-b)), $MachinePrecision] + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * y + N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * y2 + N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -1.5e-30], t$95$2, If[LessEqual[x, -3e-95], t$95$3, If[LessEqual[x, -4.2e-301], N[(N[((-b) * N[(c * N[(N[((-y) * y3 + N[(t * y2), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + (-N[((-k) * y + N[(j * t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[x, 6e-34], t$95$3, If[LessEqual[x, 8.5e+41], N[(N[(N[(N[((-y2) * x), $MachinePrecision] + N[(y3 * z), $MachinePrecision]), $MachinePrecision] * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[x, 3.8e+258], t$95$2, N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.49999999999999995e-30 or 8.49999999999999938e41 < x < 3.80000000000000009e258

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 60.6%

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

   if -1.49999999999999995e-30 < x < -3e-95 or -4.1999999999999997e-301 < x < 6e-34

   1. Initial program 35.2%

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

   3. Taylor expanded in k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 53.3%

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

   if -3e-95 < x < -4.1999999999999997e-301

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 47.2%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 51.9%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 61.2%

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

   if 6e-34 < x < 8.49999999999999938e41

   1. Initial program 31.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 75.4%

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

   if 3.80000000000000009e258 < x

   1. Initial program 11.1%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-95}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-301}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, y, \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2, \left(y0 \cdot b - y1 \cdot i\right) \cdot z\right)\right) \cdot k\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+258}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y2\right) \cdot x + y3 \cdot z\\ \mathbf{if}\;y2 \leq -9 \cdot 10^{+215}:\\ \;\;\;\;\left(-\mathsf{fma}\left(c, \frac{y2 \cdot t}{b}, \left(-j\right) \cdot t\right) \cdot b\right) \cdot y4\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(\left(y \cdot y3\right) \cdot y4\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (+ (* (- y2) x) (* y3 z))))
   (if (<= y2 -9e+215)
     (* (- (* (fma c (/ (* y2 t) b) (* (- j) t)) b)) y4)
     (if (<= y2 -6.5e+126)
       (* y0 (* y2 (fma (- k) y5 (* c x))))
       (if (<= y2 -2.6e+95)
         (+
          (* c (* (* y y3) y4))
          (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
         (if (<= y2 -4.8e-52)
           (*
            (*
             (- b)
             (fma c (/ (fma (- y) y3 (* t y2)) b) (- (fma (- k) y (* j t)))))
            y4)
           (if (<= y2 7.5e+65)
             (*
              (fma
               (+ (* y4 (- b)) (* y5 i))
               k
               (fma (- (* b a) (* i c)) x (* (- (* y4 c) (* y5 a)) y3)))
              y)
             (if (<= y2 8e+122)
               (*
                (fma
                 t_1
                 a
                 (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
                y1)
               (*
                (fma
                 t_1
                 y1
                 (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
                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 t_1 = (-y2 * x) + (y3 * z);
	double tmp;
	if (y2 <= -9e+215) {
		tmp = -(fma(c, ((y2 * t) / b), (-j * t)) * b) * y4;
	} else if (y2 <= -6.5e+126) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} else if (y2 <= -2.6e+95) {
		tmp = (c * ((y * y3) * y4)) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (y2 <= -4.8e-52) {
		tmp = (-b * fma(c, (fma(-y, y3, (t * y2)) / b), -fma(-k, y, (j * t)))) * y4;
	} else if (y2 <= 7.5e+65) {
		tmp = fma(((y4 * -b) + (y5 * i)), k, fma(((b * a) - (i * c)), x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (y2 <= 8e+122) {
		tmp = fma(t_1, a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(-y2) * x) + Float64(y3 * z))
	tmp = 0.0
	if (y2 <= -9e+215)
		tmp = Float64(Float64(-Float64(fma(c, Float64(Float64(y2 * t) / b), Float64(Float64(-j) * t)) * b)) * y4);
	elseif (y2 <= -6.5e+126)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	elseif (y2 <= -2.6e+95)
		tmp = Float64(Float64(c * Float64(Float64(y * y3) * y4)) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (y2 <= -4.8e-52)
		tmp = Float64(Float64(Float64(-b) * fma(c, Float64(fma(Float64(-y), y3, Float64(t * y2)) / b), Float64(-fma(Float64(-k), y, Float64(j * t))))) * y4);
	elseif (y2 <= 7.5e+65)
		tmp = Float64(fma(Float64(Float64(y4 * Float64(-b)) + Float64(y5 * i)), k, fma(Float64(Float64(b * a) - Float64(i * c)), x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (y2 <= 8e+122)
		tmp = Float64(fma(t_1, a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	else
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	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[((-y2) * x), $MachinePrecision] + N[(y3 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -9e+215], N[((-N[(N[(c * N[(N[(y2 * t), $MachinePrecision] / b), $MachinePrecision] + N[((-j) * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]) * y4), $MachinePrecision], If[LessEqual[y2, -6.5e+126], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.6e+95], N[(N[(c * N[(N[(y * y3), $MachinePrecision] * y4), $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], If[LessEqual[y2, -4.8e-52], N[(N[((-b) * N[(c * N[(N[((-y) * y3 + N[(t * y2), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + (-N[((-k) * y + N[(j * t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y2, 7.5e+65], N[(N[(N[(N[(y4 * (-b)), $MachinePrecision] + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * k + N[(N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y2, 8e+122], N[(N[(t$95$1 * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -9.0000000000000005e215

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 41.2%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.0%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 58.8%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.1%

       \[\leadsto \left(-\mathsf{fma}\left(c, \frac{y2 \cdot t}{b}, \left(-j\right) \cdot t\right) \cdot b\right) \cdot y4 \]

   if -9.0000000000000005e215 < y2 < -6.5000000000000005e126

   1. Initial program 39.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 32.7%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 48.2%

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

   9. Taylor expanded in y2 around inf

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

   11. Applied rewrites 61.1%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]

   if -6.5000000000000005e126 < y2 < -2.5999999999999999e95

   1. Initial program 25.0%

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

   3. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. neg-mul-1 N/A

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

      13. lower-neg.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in y3 around inf

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

   8. Applied rewrites 87.5%

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

   if -2.5999999999999999e95 < y2 < -4.8000000000000003e-52

   1. Initial program 36.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.9%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 56.3%

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

   if -4.8000000000000003e-52 < y2 < 7.50000000000000006e65

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 49.8%

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

   if 7.50000000000000006e65 < y2 < 8.00000000000000012e122

   1. Initial program 15.4%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 85.4%

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

   if 8.00000000000000012e122 < y2

   1. Initial program 17.1%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{+215}:\\ \;\;\;\;\left(-\mathsf{fma}\left(c, \frac{y2 \cdot t}{b}, \left(-j\right) \cdot t\right) \cdot b\right) \cdot y4\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(\left(y \cdot y3\right) \cdot y4\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;y2 \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y2\right) \cdot x + y3 \cdot z\\ t_2 := b \cdot a - i \cdot c\\ \mathbf{if}\;y2 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(y4, y1, \left(-y0\right) \cdot y5\right), k, \mathsf{fma}\left(\mathsf{fma}\left(y0, c, \left(-a\right) \cdot y1\right), x, \left(-t\right) \cdot \mathsf{fma}\left(y4, c, \left(-a\right) \cdot y5\right)\right)\right) \cdot y2\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, k, \mathsf{fma}\left(t\_2, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (+ (* (- y2) x) (* y3 z))) (t_2 (- (* b a) (* i c))))
   (if (<= y2 -2e+17)
     (*
      (fma
       (fma y4 y1 (* (- y0) y5))
       k
       (fma (fma y0 c (* (- a) y1)) x (* (- t) (fma y4 c (* (- a) y5)))))
      y2)
     (if (<= y2 -4.1e-63)
       (*
        (fma
         t_2
         y
         (fma (- (* y0 c) (* y1 a)) y2 (* (- j) (- (* y0 b) (* y1 i)))))
        x)
       (if (<= y2 7.5e+65)
         (*
          (fma
           (+ (* y4 (- b)) (* y5 i))
           k
           (fma t_2 x (* (- (* y4 c) (* y5 a)) y3)))
          y)
         (if (<= y2 8e+122)
           (*
            (fma
             t_1
             a
             (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
            y1)
           (*
            (fma
             t_1
             y1
             (fma (- (* y x) (* t z)) b (* (- (* y2 t) (* y3 y)) y5)))
            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 t_1 = (-y2 * x) + (y3 * z);
	double t_2 = (b * a) - (i * c);
	double tmp;
	if (y2 <= -2e+17) {
		tmp = fma(fma(y4, y1, (-y0 * y5)), k, fma(fma(y0, c, (-a * y1)), x, (-t * fma(y4, c, (-a * y5))))) * y2;
	} else if (y2 <= -4.1e-63) {
		tmp = fma(t_2, y, fma(((y0 * c) - (y1 * a)), y2, (-j * ((y0 * b) - (y1 * i))))) * x;
	} else if (y2 <= 7.5e+65) {
		tmp = fma(((y4 * -b) + (y5 * i)), k, fma(t_2, x, (((y4 * c) - (y5 * a)) * y3))) * y;
	} else if (y2 <= 8e+122) {
		tmp = fma(t_1, a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else {
		tmp = fma(t_1, y1, fma(((y * x) - (t * z)), b, (((y2 * t) - (y3 * y)) * y5))) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(-y2) * x) + Float64(y3 * z))
	t_2 = Float64(Float64(b * a) - Float64(i * c))
	tmp = 0.0
	if (y2 <= -2e+17)
		tmp = Float64(fma(fma(y4, y1, Float64(Float64(-y0) * y5)), k, fma(fma(y0, c, Float64(Float64(-a) * y1)), x, Float64(Float64(-t) * fma(y4, c, Float64(Float64(-a) * y5))))) * y2);
	elseif (y2 <= -4.1e-63)
		tmp = Float64(fma(t_2, y, fma(Float64(Float64(y0 * c) - Float64(y1 * a)), y2, Float64(Float64(-j) * Float64(Float64(y0 * b) - Float64(y1 * i))))) * x);
	elseif (y2 <= 7.5e+65)
		tmp = Float64(fma(Float64(Float64(y4 * Float64(-b)) + Float64(y5 * i)), k, fma(t_2, x, Float64(Float64(Float64(y4 * c) - Float64(y5 * a)) * y3))) * y);
	elseif (y2 <= 8e+122)
		tmp = Float64(fma(t_1, a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	else
		tmp = Float64(fma(t_1, y1, fma(Float64(Float64(y * x) - Float64(t * z)), b, Float64(Float64(Float64(y2 * t) - Float64(y3 * y)) * y5))) * a);
	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[((-y2) * x), $MachinePrecision] + N[(y3 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2e+17], N[(N[(N[(y4 * y1 + N[((-y0) * y5), $MachinePrecision]), $MachinePrecision] * k + N[(N[(y0 * c + N[((-a) * y1), $MachinePrecision]), $MachinePrecision] * x + N[((-t) * N[(y4 * c + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y2), $MachinePrecision], If[LessEqual[y2, -4.1e-63], N[(N[(t$95$2 * y + N[(N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision] * y2 + N[((-j) * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y2, 7.5e+65], N[(N[(N[(N[(y4 * (-b)), $MachinePrecision] + N[(y5 * i), $MachinePrecision]), $MachinePrecision] * k + N[(t$95$2 * x + N[(N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision] * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y2, 8e+122], N[(N[(t$95$1 * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], N[(N[(t$95$1 * y1 + N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] * b + N[(N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision] * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -2e17

   1. Initial program 33.8%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 46.3%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 46.7%

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

   12. Taylor expanded in y2 around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

   14. Applied rewrites 63.3%

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

   if -2e17 < y2 < -4.0999999999999998e-63

   1. Initial program 28.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 57.2%

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

   if -4.0999999999999998e-63 < y2 < 7.50000000000000006e65

   1. Initial program 27.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 49.8%

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

   if 7.50000000000000006e65 < y2 < 8.00000000000000012e122

   1. Initial program 15.4%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 85.4%

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

   if 8.00000000000000012e122 < y2

   1. Initial program 17.1%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(y4, y1, \left(-y0\right) \cdot y5\right), k, \mathsf{fma}\left(\mathsf{fma}\left(y0, c, \left(-a\right) \cdot y1\right), x, \left(-t\right) \cdot \mathsf{fma}\left(y4, c, \left(-a\right) \cdot y5\right)\right)\right) \cdot y2\\ \mathbf{elif}\;y2 \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a - i \cdot c, y, \mathsf{fma}\left(y0 \cdot c - y1 \cdot a, y2, \left(-j\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)\right) \cdot x\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot \left(-b\right) + y5 \cdot i, k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, y1, \mathsf{fma}\left(y \cdot x - t \cdot z, b, \left(y2 \cdot t - y3 \cdot y\right) \cdot y5\right)\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -2.7 \cdot 10^{+157}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -1.35 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 4.6 \cdot 10^{-263}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -2.7e+157)
   (* (* y y3) (fma c y4 (* (- a) y5)))
   (if (<= y3 -1.35e-219)
     (*
      (fma
       (+ (* (- y2) x) (* y3 z))
       a
       (fma (- (* y2 k) (* y3 j)) y4 (* (- (* j x) (* k z)) i)))
      y1)
     (if (<= y3 4.6e-263)
       (* (- i) (* z (fma (- c) t (* k y1))))
       (if (<= y3 2.05e+239)
         (*
          (*
           (- b)
           (fma c (/ (fma (- y) y3 (* t y2)) b) (- (fma (- k) y (* j t)))))
          y4)
         (* (* y5 (fma (- a) y3 (* i k))) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -2.7e+157) {
		tmp = (y * y3) * fma(c, y4, (-a * y5));
	} else if (y3 <= -1.35e-219) {
		tmp = fma(((-y2 * x) + (y3 * z)), a, fma(((y2 * k) - (y3 * j)), y4, (((j * x) - (k * z)) * i))) * y1;
	} else if (y3 <= 4.6e-263) {
		tmp = -i * (z * fma(-c, t, (k * y1)));
	} else if (y3 <= 2.05e+239) {
		tmp = (-b * fma(c, (fma(-y, y3, (t * y2)) / b), -fma(-k, y, (j * t)))) * y4;
	} else {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -2.7e+157)
		tmp = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)));
	elseif (y3 <= -1.35e-219)
		tmp = Float64(fma(Float64(Float64(Float64(-y2) * x) + Float64(y3 * z)), a, fma(Float64(Float64(y2 * k) - Float64(y3 * j)), y4, Float64(Float64(Float64(j * x) - Float64(k * z)) * i))) * y1);
	elseif (y3 <= 4.6e-263)
		tmp = Float64(Float64(-i) * Float64(z * fma(Float64(-c), t, Float64(k * y1))));
	elseif (y3 <= 2.05e+239)
		tmp = Float64(Float64(Float64(-b) * fma(c, Float64(fma(Float64(-y), y3, Float64(t * y2)) / b), Float64(-fma(Float64(-k), y, Float64(j * t))))) * y4);
	else
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -2.7e+157], N[(N[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.35e-219], N[(N[(N[(N[((-y2) * x), $MachinePrecision] + N[(y3 * z), $MachinePrecision]), $MachinePrecision] * a + N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * y4 + N[(N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y3, 4.6e-263], N[((-i) * N[(z * N[((-c) * t + N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.05e+239], N[(N[((-b) * N[(c * N[(N[((-y) * y3 + N[(t * y2), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + (-N[((-k) * y + N[(j * t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -2.7e157

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.6%

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

   if -2.7e157 < y3 < -1.35e-219

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 59.0%

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

   if -1.35e-219 < y3 < 4.60000000000000006e-263

   1. Initial program 35.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 46.1%

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

   6. Taylor expanded in i around -inf

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

   8. Applied rewrites 53.3%

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

   if 4.60000000000000006e-263 < y3 < 2.0500000000000001e239

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 39.4%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 38.4%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 43.5%

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

   if 2.0500000000000001e239 < y3

   1. Initial program 10.5%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.7 \cdot 10^{+157}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -1.35 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y2\right) \cdot x + y3 \cdot z, a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 4.6 \cdot 10^{-263}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -2.05 \cdot 10^{-258}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot j, t, \left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-293}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y3 -1.45e+152)
     t_1
     (if (<= y3 -3.7e+83)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y3 -4.4e-47)
         t_1
         (if (<= y3 -2.05e-258)
           (* (fma (* b j) t (* (- c) (* t y2))) y4)
           (if (<= y3 4.2e-293)
             (* y0 (* y2 (fma (- k) y5 (* c x))))
             (if (<= y3 2.5e-179)
               (* (* x (fma a b (* (- c) i))) y)
               (if (<= y3 1e-14)
                 (* (* t z) (fma c i (* (- a) b)))
                 (if (<= y3 5e+86)
                   (* (* x y0) (fma c y2 (* (- b) j)))
                   (if (<= y3 2.05e+239)
                     (* (* j (fma b t (* y1 (- y3)))) y4)
                     (* (* y5 (fma (- a) y3 (* i k))) y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y3 <= -1.45e+152) {
		tmp = t_1;
	} else if (y3 <= -3.7e+83) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y3 <= -4.4e-47) {
		tmp = t_1;
	} else if (y3 <= -2.05e-258) {
		tmp = fma((b * j), t, (-c * (t * y2))) * y4;
	} else if (y3 <= 4.2e-293) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} else if (y3 <= 2.5e-179) {
		tmp = (x * fma(a, b, (-c * i))) * y;
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 5e+86) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else if (y3 <= 2.05e+239) {
		tmp = (j * fma(b, t, (y1 * -y3))) * y4;
	} else {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y3 <= -1.45e+152)
		tmp = t_1;
	elseif (y3 <= -3.7e+83)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y3 <= -4.4e-47)
		tmp = t_1;
	elseif (y3 <= -2.05e-258)
		tmp = Float64(fma(Float64(b * j), t, Float64(Float64(-c) * Float64(t * y2))) * y4);
	elseif (y3 <= 4.2e-293)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	elseif (y3 <= 2.5e-179)
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 5e+86)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	elseif (y3 <= 2.05e+239)
		tmp = Float64(Float64(j * fma(b, t, Float64(y1 * Float64(-y3)))) * y4);
	else
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	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[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.45e+152], t$95$1, If[LessEqual[y3, -3.7e+83], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.4e-47], t$95$1, If[LessEqual[y3, -2.05e-258], N[(N[(N[(b * j), $MachinePrecision] * t + N[((-c) * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y3, 4.2e-293], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.5e-179], N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5e+86], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.05e+239], N[(N[(j * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -1.4499999999999999e152 or -3.7000000000000002e83 < y3 < -4.40000000000000037e-47

   1. Initial program 15.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 53.7%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

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

   if -1.4499999999999999e152 < y3 < -3.7000000000000002e83

   1. Initial program 39.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 67.5%

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

   9. Taylor expanded in j around inf

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

   11. Applied rewrites 73.0%

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

   if -4.40000000000000037e-47 < y3 < -2.05e-258

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 45.2%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 43.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right) + b \cdot \left(j \cdot t\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 47.9%

       \[\leadsto \mathsf{fma}\left(b \cdot j, t, -c \cdot \left(t \cdot y2\right)\right) \cdot y4 \]

   if -2.05e-258 < y3 < 4.2000000000000001e-293

   1. Initial program 43.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 25.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 62.7%

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

   9. Taylor expanded in y2 around inf

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

   11. Applied rewrites 62.9%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]

   if 4.2000000000000001e-293 < y3 < 2.4999999999999999e-179

   1. Initial program 33.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y \]

   if 2.4999999999999999e-179 < y3 < 9.99999999999999999e-15

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.4%

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

   if 9.99999999999999999e-15 < y3 < 4.9999999999999998e86

   1. Initial program 18.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 37.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 50.8%

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

   if 4.9999999999999998e86 < y3 < 2.0500000000000001e239

   1. Initial program 35.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 39.7%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

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

   9. Taylor expanded in j around inf

      \[\leadsto \left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 50.8%

       \[\leadsto \left(j \cdot \mathsf{fma}\left(b, t, -y1 \cdot y3\right)\right) \cdot y4 \]

   if 2.0500000000000001e239 < y3

   1. Initial program 10.5%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]
3. Recombined 9 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-47}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -2.05 \cdot 10^{-258}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot j, t, \left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-293}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 31.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -2.05 \cdot 10^{-258}:\\ \;\;\;\;\left(t \cdot \mathsf{fma}\left(-c, y2, b \cdot j\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-293}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y3 -1.45e+152)
     t_1
     (if (<= y3 -3.7e+83)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y3 -4.4e-47)
         t_1
         (if (<= y3 -2.05e-258)
           (* (* t (fma (- c) y2 (* b j))) y4)
           (if (<= y3 4.2e-293)
             (* y0 (* y2 (fma (- k) y5 (* c x))))
             (if (<= y3 2.5e-179)
               (* (* x (fma a b (* (- c) i))) y)
               (if (<= y3 1e-14)
                 (* (* t z) (fma c i (* (- a) b)))
                 (if (<= y3 5e+86)
                   (* (* x y0) (fma c y2 (* (- b) j)))
                   (if (<= y3 2.05e+239)
                     (* (* j (fma b t (* y1 (- y3)))) y4)
                     (* (* y5 (fma (- a) y3 (* i k))) y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y3 <= -1.45e+152) {
		tmp = t_1;
	} else if (y3 <= -3.7e+83) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y3 <= -4.4e-47) {
		tmp = t_1;
	} else if (y3 <= -2.05e-258) {
		tmp = (t * fma(-c, y2, (b * j))) * y4;
	} else if (y3 <= 4.2e-293) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} else if (y3 <= 2.5e-179) {
		tmp = (x * fma(a, b, (-c * i))) * y;
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 5e+86) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else if (y3 <= 2.05e+239) {
		tmp = (j * fma(b, t, (y1 * -y3))) * y4;
	} else {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y3 <= -1.45e+152)
		tmp = t_1;
	elseif (y3 <= -3.7e+83)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y3 <= -4.4e-47)
		tmp = t_1;
	elseif (y3 <= -2.05e-258)
		tmp = Float64(Float64(t * fma(Float64(-c), y2, Float64(b * j))) * y4);
	elseif (y3 <= 4.2e-293)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	elseif (y3 <= 2.5e-179)
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 5e+86)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	elseif (y3 <= 2.05e+239)
		tmp = Float64(Float64(j * fma(b, t, Float64(y1 * Float64(-y3)))) * y4);
	else
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	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[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.45e+152], t$95$1, If[LessEqual[y3, -3.7e+83], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.4e-47], t$95$1, If[LessEqual[y3, -2.05e-258], N[(N[(t * N[((-c) * y2 + N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y3, 4.2e-293], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.5e-179], N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5e+86], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.05e+239], N[(N[(j * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -1.4499999999999999e152 or -3.7000000000000002e83 < y3 < -4.40000000000000037e-47

   1. Initial program 15.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 53.7%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

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

   if -1.4499999999999999e152 < y3 < -3.7000000000000002e83

   1. Initial program 39.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 67.5%

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

   9. Taylor expanded in j around inf

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

   11. Applied rewrites 73.0%

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

   if -4.40000000000000037e-47 < y3 < -2.05e-258

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 45.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot \left(c \cdot y2\right) + b \cdot j\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 47.7%

      \[\leadsto \left(t \cdot \mathsf{fma}\left(-c, y2, b \cdot j\right)\right) \cdot y4 \]

   if -2.05e-258 < y3 < 4.2000000000000001e-293

   1. Initial program 43.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 25.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 62.7%

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

   9. Taylor expanded in y2 around inf

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

   11. Applied rewrites 62.9%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]

   if 4.2000000000000001e-293 < y3 < 2.4999999999999999e-179

   1. Initial program 33.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y \]

   if 2.4999999999999999e-179 < y3 < 9.99999999999999999e-15

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.4%

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

   if 9.99999999999999999e-15 < y3 < 4.9999999999999998e86

   1. Initial program 18.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 37.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 50.8%

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

   if 4.9999999999999998e86 < y3 < 2.0500000000000001e239

   1. Initial program 35.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 39.7%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

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

   9. Taylor expanded in j around inf

      \[\leadsto \left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 50.8%

       \[\leadsto \left(j \cdot \mathsf{fma}\left(b, t, -y1 \cdot y3\right)\right) \cdot y4 \]

   if 2.0500000000000001e239 < y3

   1. Initial program 10.5%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]
3. Recombined 9 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-47}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -2.05 \cdot 10^{-258}:\\ \;\;\;\;\left(t \cdot \mathsf{fma}\left(-c, y2, b \cdot j\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-293}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -0.0003:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y5 \leq 5.1 \cdot 10^{+56}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.8e+49)
   (* (* y5 (fma (- a) y3 (* i k))) y)
   (if (<= y5 -0.0003)
     (* (* x (fma (- a) y2 (* i j))) y1)
     (if (<= y5 5.1e+56)
       (*
        (*
         (- b)
         (fma c (/ (fma (- y) y3 (* t y2)) b) (- (fma (- k) y (* j t)))))
        y4)
       (* y0 (* y2 (fma (- k) y5 (* c x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.8e+49) {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	} else if (y5 <= -0.0003) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (y5 <= 5.1e+56) {
		tmp = (-b * fma(c, (fma(-y, y3, (t * y2)) / b), -fma(-k, y, (j * t)))) * y4;
	} else {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.8e+49)
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	elseif (y5 <= -0.0003)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (y5 <= 5.1e+56)
		tmp = Float64(Float64(Float64(-b) * fma(c, Float64(fma(Float64(-y), y3, Float64(t * y2)) / b), Float64(-fma(Float64(-k), y, Float64(j * t))))) * y4);
	else
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.8e+49], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y5, -0.0003], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y5, 5.1e+56], N[(N[((-b) * N[(c * N[(N[((-y) * y3 + N[(t * y2), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + (-N[((-k) * y + N[(j * t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.79999999999999998e49

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.7%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 57.9%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   if -1.79999999999999998e49 < y5 < -2.99999999999999974e-4

   1. Initial program 30.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 70.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 80.2%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if -2.99999999999999974e-4 < y5 < 5.1000000000000002e56

   1. Initial program 27.8%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 38.3%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 40.1%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 43.0%

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

   if 5.1000000000000002e56 < y5

   1. Initial program 23.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in y2 around inf

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

   11. Applied rewrites 56.1%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -0.0003:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y5 \leq 5.1 \cdot 10^{+56}:\\ \;\;\;\;\left(\left(-b\right) \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y3 -1.45e+152)
     t_1
     (if (<= y3 -3.7e+83)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y3 -7e-96)
         t_1
         (if (<= y3 7.8e-292)
           (* (* x (fma (- a) y2 (* i j))) y1)
           (if (<= y3 2.5e-179)
             (* (* x (fma a b (* (- c) i))) y)
             (if (<= y3 1e-14)
               (* (* t z) (fma c i (* (- a) b)))
               (if (<= y3 5e+86)
                 (* (* x y0) (fma c y2 (* (- b) j)))
                 (if (<= y3 2.05e+239)
                   (* (* j (fma b t (* y1 (- y3)))) y4)
                   (* (* y5 (fma (- a) y3 (* i k))) y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y3 <= -1.45e+152) {
		tmp = t_1;
	} else if (y3 <= -3.7e+83) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y3 <= -7e-96) {
		tmp = t_1;
	} else if (y3 <= 7.8e-292) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (y3 <= 2.5e-179) {
		tmp = (x * fma(a, b, (-c * i))) * y;
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 5e+86) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else if (y3 <= 2.05e+239) {
		tmp = (j * fma(b, t, (y1 * -y3))) * y4;
	} else {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y3 <= -1.45e+152)
		tmp = t_1;
	elseif (y3 <= -3.7e+83)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y3 <= -7e-96)
		tmp = t_1;
	elseif (y3 <= 7.8e-292)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (y3 <= 2.5e-179)
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 5e+86)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	elseif (y3 <= 2.05e+239)
		tmp = Float64(Float64(j * fma(b, t, Float64(y1 * Float64(-y3)))) * y4);
	else
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	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[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.45e+152], t$95$1, If[LessEqual[y3, -3.7e+83], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7e-96], t$95$1, If[LessEqual[y3, 7.8e-292], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y3, 2.5e-179], N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5e+86], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.05e+239], N[(N[(j * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -1.4499999999999999e152 or -3.7000000000000002e83 < y3 < -6.9999999999999998e-96

   1. Initial program 18.0%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 52.8%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.2%

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

   if -1.4499999999999999e152 < y3 < -3.7000000000000002e83

   1. Initial program 39.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 67.5%

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

   9. Taylor expanded in j around inf

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

   11. Applied rewrites 73.0%

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

   if -6.9999999999999998e-96 < y3 < 7.8e-292

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 46.1%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if 7.8e-292 < y3 < 2.4999999999999999e-179

   1. Initial program 33.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y \]

   if 2.4999999999999999e-179 < y3 < 9.99999999999999999e-15

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.4%

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

   if 9.99999999999999999e-15 < y3 < 4.9999999999999998e86

   1. Initial program 18.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 37.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 50.8%

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

   if 4.9999999999999998e86 < y3 < 2.0500000000000001e239

   1. Initial program 35.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 39.7%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

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

   9. Taylor expanded in j around inf

      \[\leadsto \left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 50.8%

       \[\leadsto \left(j \cdot \mathsf{fma}\left(b, t, -y1 \cdot y3\right)\right) \cdot y4 \]

   if 2.0500000000000001e239 < y3

   1. Initial program 10.5%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.1%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-96}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 5 \cdot 10^{+86}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{elif}\;y3 \leq 2.05 \cdot 10^{+239}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(-b, y4, \frac{\left(x \cdot b\right) \cdot a}{k}\right) \cdot k\right) \cdot y\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-194}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \mathbf{elif}\;b \leq 135000000:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (fma (- b) y4 (/ (* (* x b) a) k)) k) y)))
   (if (<= b -3.1e+109)
     t_1
     (if (<= b 3.9e-194)
       (* y0 (fma (- y5) (fma k y2 (* (- j) y3)) (* c (* x y2))))
       (if (<= b 3.6e-94)
         (* (* y5 (fma (- a) y3 (* i k))) y)
         (if (<= b 135000000.0)
           (* (* x (fma (- a) y2 (* i j))) y1)
           (if (<= b 2.1e+183) t_1 (* (* j (fma b t (* y1 (- y3)))) y4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (fma(-b, y4, (((x * b) * a) / k)) * k) * y;
	double tmp;
	if (b <= -3.1e+109) {
		tmp = t_1;
	} else if (b <= 3.9e-194) {
		tmp = y0 * fma(-y5, fma(k, y2, (-j * y3)), (c * (x * y2)));
	} else if (b <= 3.6e-94) {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	} else if (b <= 135000000.0) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (b <= 2.1e+183) {
		tmp = t_1;
	} else {
		tmp = (j * fma(b, t, (y1 * -y3))) * y4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(fma(Float64(-b), y4, Float64(Float64(Float64(x * b) * a) / k)) * k) * y)
	tmp = 0.0
	if (b <= -3.1e+109)
		tmp = t_1;
	elseif (b <= 3.9e-194)
		tmp = Float64(y0 * fma(Float64(-y5), fma(k, y2, Float64(Float64(-j) * y3)), Float64(c * Float64(x * y2))));
	elseif (b <= 3.6e-94)
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	elseif (b <= 135000000.0)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (b <= 2.1e+183)
		tmp = t_1;
	else
		tmp = Float64(Float64(j * fma(b, t, Float64(y1 * Float64(-y3)))) * y4);
	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[(N[((-b) * y4 + N[(N[(N[(x * b), $MachinePrecision] * a), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision] * k), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[b, -3.1e+109], t$95$1, If[LessEqual[b, 3.9e-194], N[(y0 * N[((-y5) * N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-94], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[b, 135000000.0], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[b, 2.1e+183], t$95$1, N[(N[(j * N[(b * t + N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.09999999999999992e109 or 1.35e8 < b < 2.1e183

   1. Initial program 16.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 33.6%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 48.3%

       \[\leadsto \left(b \cdot \mathsf{fma}\left(-k, y4, a \cdot x\right)\right) \cdot y \]

   12. Taylor expanded in k around inf

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

   14. Applied rewrites 53.1%

       \[\leadsto \left(\mathsf{fma}\left(-b, y4, \frac{\left(x \cdot b\right) \cdot a}{k}\right) \cdot k\right) \cdot y \]

   if -3.09999999999999992e109 < b < 3.8999999999999999e-194

   1. Initial program 32.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 35.5%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 47.1%

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

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 47.4%

       \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]

   if 3.8999999999999999e-194 < b < 3.6e-94

   1. Initial program 43.8%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 57.6%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   if 3.6e-94 < b < 1.35e8

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 55.1%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if 2.1e183 < b

   1. Initial program 23.0%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 50.5%

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

   9. Taylor expanded in j around inf

      \[\leadsto \left(j \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 59.7%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, y4, \frac{\left(x \cdot b\right) \cdot a}{k}\right) \cdot k\right) \cdot y\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-194}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \mathbf{elif}\;b \leq 135000000:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+183}:\\ \;\;\;\;\left(\mathsf{fma}\left(-b, y4, \frac{\left(x \cdot b\right) \cdot a}{k}\right) \cdot k\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \mathsf{fma}\left(b, t, y1 \cdot \left(-y3\right)\right)\right) \cdot y4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{+215}:\\ \;\;\;\;\left(-\mathsf{fma}\left(c, \frac{y2 \cdot t}{b}, \left(-j\right) \cdot t\right) \cdot b\right) \cdot y4\\ \mathbf{elif}\;y2 \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(\left(y \cdot y3\right) \cdot y4\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;y2 \leq -1.25 \cdot 10^{-202}:\\ \;\;\;\;\mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-36}:\\ \;\;\;\;\left(-c\right) \cdot \left(z \cdot \mathsf{fma}\left(-i, t, y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -9e+215)
   (* (- (* (fma c (/ (* y2 t) b) (* (- j) t)) b)) y4)
   (if (<= y2 -6.5e+126)
     (* y0 (* y2 (fma (- k) y5 (* c x))))
     (if (<= y2 -4.6e+94)
       (+
        (* c (* (* y y3) y4))
        (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
       (if (<= y2 -1.25e-202)
         (* (fma (- c) (fma t y2 (* (- y) y3)) (* b (fma j t (* (- k) y)))) y4)
         (if (<= y2 7.6e-36)
           (* (- c) (* z (fma (- i) t (* y0 y3))))
           (* (* x (fma (- a) y2 (* i j))) y1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -9e+215) {
		tmp = -(fma(c, ((y2 * t) / b), (-j * t)) * b) * y4;
	} else if (y2 <= -6.5e+126) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} else if (y2 <= -4.6e+94) {
		tmp = (c * ((y * y3) * y4)) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (y2 <= -1.25e-202) {
		tmp = fma(-c, fma(t, y2, (-y * y3)), (b * fma(j, t, (-k * y)))) * y4;
	} else if (y2 <= 7.6e-36) {
		tmp = -c * (z * fma(-i, t, (y0 * y3)));
	} else {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -9e+215)
		tmp = Float64(Float64(-Float64(fma(c, Float64(Float64(y2 * t) / b), Float64(Float64(-j) * t)) * b)) * y4);
	elseif (y2 <= -6.5e+126)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	elseif (y2 <= -4.6e+94)
		tmp = Float64(Float64(c * Float64(Float64(y * y3) * y4)) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (y2 <= -1.25e-202)
		tmp = Float64(fma(Float64(-c), fma(t, y2, Float64(Float64(-y) * y3)), Float64(b * fma(j, t, Float64(Float64(-k) * y)))) * y4);
	elseif (y2 <= 7.6e-36)
		tmp = Float64(Float64(-c) * Float64(z * fma(Float64(-i), t, Float64(y0 * y3))));
	else
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -9e+215], N[((-N[(N[(c * N[(N[(y2 * t), $MachinePrecision] / b), $MachinePrecision] + N[((-j) * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]) * y4), $MachinePrecision], If[LessEqual[y2, -6.5e+126], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.6e+94], N[(N[(c * N[(N[(y * y3), $MachinePrecision] * y4), $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], If[LessEqual[y2, -1.25e-202], N[(N[((-c) * N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(j * t + N[((-k) * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y2, 7.6e-36], N[((-c) * N[(z * N[((-i) * t + N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -9.0000000000000005e215

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 41.2%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 53.0%

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

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 58.8%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.1%

       \[\leadsto \left(-\mathsf{fma}\left(c, \frac{y2 \cdot t}{b}, \left(-j\right) \cdot t\right) \cdot b\right) \cdot y4 \]

   if -9.0000000000000005e215 < y2 < -6.5000000000000005e126

   1. Initial program 39.9%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 32.7%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 48.2%

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

   9. Taylor expanded in y2 around inf

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

   11. Applied rewrites 61.1%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]

   if -6.5000000000000005e126 < y2 < -4.5999999999999999e94

   1. Initial program 25.0%

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

   3. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-*.f64 N/A

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

      12. neg-mul-1 N/A

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

      13. lower-neg.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in y3 around inf

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

   8. Applied rewrites 87.5%

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

   if -4.5999999999999999e94 < y2 < -1.24999999999999993e-202

   1. Initial program 35.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.5%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 50.1%

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

   if -1.24999999999999993e-202 < y2 < 7.59999999999999942e-36

   1. Initial program 29.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 50.7%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 46.9%

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

   if 7.59999999999999942e-36 < y2

   1. Initial program 14.4%

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

   3. Taylor expanded in y1 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 51.4%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 46.8%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 14: 30.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y3 -1.45e+152)
     t_1
     (if (<= y3 -3.7e+83)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y3 -7e-96)
         t_1
         (if (<= y3 7.8e-292)
           (* (* x (fma (- a) y2 (* i j))) y1)
           (if (<= y3 2.5e-179)
             (* (* x (fma a b (* (- c) i))) y)
             (if (<= y3 1e-14)
               (* (* t z) (fma c i (* (- a) b)))
               (if (<= y3 1.05e+70)
                 (* (* x y0) (fma c y2 (* (- b) j)))
                 (* (* y5 (fma (- a) y3 (* i k))) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y3 <= -1.45e+152) {
		tmp = t_1;
	} else if (y3 <= -3.7e+83) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y3 <= -7e-96) {
		tmp = t_1;
	} else if (y3 <= 7.8e-292) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (y3 <= 2.5e-179) {
		tmp = (x * fma(a, b, (-c * i))) * y;
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 1.05e+70) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y3 <= -1.45e+152)
		tmp = t_1;
	elseif (y3 <= -3.7e+83)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y3 <= -7e-96)
		tmp = t_1;
	elseif (y3 <= 7.8e-292)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (y3 <= 2.5e-179)
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 1.05e+70)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	else
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	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[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.45e+152], t$95$1, If[LessEqual[y3, -3.7e+83], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7e-96], t$95$1, If[LessEqual[y3, 7.8e-292], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y3, 2.5e-179], N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.05e+70], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -1.4499999999999999e152 or -3.7000000000000002e83 < y3 < -6.9999999999999998e-96

   1. Initial program 18.0%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 52.8%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.2%

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

   if -1.4499999999999999e152 < y3 < -3.7000000000000002e83

   1. Initial program 39.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 67.5%

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

   9. Taylor expanded in j around inf

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

   11. Applied rewrites 73.0%

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

   if -6.9999999999999998e-96 < y3 < 7.8e-292

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 46.1%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if 7.8e-292 < y3 < 2.4999999999999999e-179

   1. Initial program 33.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y \]

   if 2.4999999999999999e-179 < y3 < 9.99999999999999999e-15

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.4%

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

   if 9.99999999999999999e-15 < y3 < 1.05000000000000004e70

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 34.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 56.5%

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

   if 1.05000000000000004e70 < y3

   1. Initial program 23.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 35.6%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 46.1%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-96}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y3 -1.45e+152)
     t_1
     (if (<= y3 -3.7e+83)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y3 -7e-96)
         t_1
         (if (<= y3 7.8e-292)
           (* (* x (fma (- a) y2 (* i j))) y1)
           (if (<= y3 2.5e-179)
             (* (* x (fma a b (* (- c) i))) y)
             (if (<= y3 1e-14)
               (* (* t z) (fma c i (* (- a) b)))
               (if (<= y3 1.25e+70)
                 (* (* x y0) (fma c y2 (* (- b) j)))
                 (* (* y0 y3) (fma j y5 (* (- c) z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y3 <= -1.45e+152) {
		tmp = t_1;
	} else if (y3 <= -3.7e+83) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y3 <= -7e-96) {
		tmp = t_1;
	} else if (y3 <= 7.8e-292) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (y3 <= 2.5e-179) {
		tmp = (x * fma(a, b, (-c * i))) * y;
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 1.25e+70) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else {
		tmp = (y0 * y3) * fma(j, y5, (-c * z));
	}
	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(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y3 <= -1.45e+152)
		tmp = t_1;
	elseif (y3 <= -3.7e+83)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y3 <= -7e-96)
		tmp = t_1;
	elseif (y3 <= 7.8e-292)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (y3 <= 2.5e-179)
		tmp = Float64(Float64(x * fma(a, b, Float64(Float64(-c) * i))) * y);
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 1.25e+70)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	else
		tmp = Float64(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)));
	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[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.45e+152], t$95$1, If[LessEqual[y3, -3.7e+83], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7e-96], t$95$1, If[LessEqual[y3, 7.8e-292], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y3, 2.5e-179], N[(N[(x * N[(a * b + N[((-c) * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.25e+70], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -1.4499999999999999e152 or -3.7000000000000002e83 < y3 < -6.9999999999999998e-96

   1. Initial program 18.0%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 52.8%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.2%

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

   if -1.4499999999999999e152 < y3 < -3.7000000000000002e83

   1. Initial program 39.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 67.5%

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

   9. Taylor expanded in j around inf

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

   11. Applied rewrites 73.0%

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

   if -6.9999999999999998e-96 < y3 < 7.8e-292

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 46.1%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if 7.8e-292 < y3 < 2.4999999999999999e-179

   1. Initial program 33.2%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.3%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y \]

   if 2.4999999999999999e-179 < y3 < 9.99999999999999999e-15

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.4%

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

   if 9.99999999999999999e-15 < y3 < 1.2500000000000001e70

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 34.1%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 56.5%

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

   if 1.2500000000000001e70 < y3

   1. Initial program 23.7%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 35.6%

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

   6. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. sub-neg N/A

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

      12. mul-1-neg N/A

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

      13. lower-fma.f64 N/A

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

   8. Applied rewrites 41.3%

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

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 46.1%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-96}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-179}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(a, b, \left(-c\right) \cdot i\right)\right) \cdot y\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;\left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-28}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;y5 \leq 1.1 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{+244}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.8e+49)
   (* (* y5 (fma (- a) y3 (* i k))) y)
   (if (<= y5 -5.4e-28)
     (* (* x (fma (- a) y2 (* i j))) y1)
     (if (<= y5 1.1e+32)
       (* (fma (- c) (fma t y2 (* (- y) y3)) (* b (fma j t (* (- k) y)))) y4)
       (if (<= y5 6e+244)
         (* (* y y3) (fma c y4 (* (- a) y5)))
         (* y0 (fma (- y5) (fma k y2 (* (- j) y3)) (* c (* x y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.8e+49) {
		tmp = (y5 * fma(-a, y3, (i * k))) * y;
	} else if (y5 <= -5.4e-28) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (y5 <= 1.1e+32) {
		tmp = fma(-c, fma(t, y2, (-y * y3)), (b * fma(j, t, (-k * y)))) * y4;
	} else if (y5 <= 6e+244) {
		tmp = (y * y3) * fma(c, y4, (-a * y5));
	} else {
		tmp = y0 * fma(-y5, fma(k, y2, (-j * y3)), (c * (x * y2)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.8e+49)
		tmp = Float64(Float64(y5 * fma(Float64(-a), y3, Float64(i * k))) * y);
	elseif (y5 <= -5.4e-28)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (y5 <= 1.1e+32)
		tmp = Float64(fma(Float64(-c), fma(t, y2, Float64(Float64(-y) * y3)), Float64(b * fma(j, t, Float64(Float64(-k) * y)))) * y4);
	elseif (y5 <= 6e+244)
		tmp = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)));
	else
		tmp = Float64(y0 * fma(Float64(-y5), fma(k, y2, Float64(Float64(-j) * y3)), Float64(c * Float64(x * 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[y5, -1.8e+49], N[(N[(y5 * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y5, -5.4e-28], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[y5, 1.1e+32], N[(N[((-c) * N[(t * y2 + N[((-y) * y3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(j * t + N[((-k) * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y5, 6e+244], N[(N[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[((-y5) * N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.79999999999999998e49

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 48.7%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 57.9%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   if -1.79999999999999998e49 < y5 < -5.3999999999999998e-28

   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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 62.1%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if -5.3999999999999998e-28 < y5 < 1.1e32

   1. Initial program 27.7%

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

   3. Taylor expanded in y4 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 39.5%

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

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 41.4%

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

   if 1.1e32 < y5 < 5.9999999999999995e244

   1. Initial program 20.9%

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

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 58.5%

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

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 58.7%

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

   if 5.9999999999999995e244 < y5

   1. Initial program 38.5%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 38.7%

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

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 69.3%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 69.6%

       \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 17: 34.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+109}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-90}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-\left(\left(\frac{y2 \cdot c}{b} - j\right) \cdot t\right) \cdot b\right) \cdot y4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -6.8e+109)
   (* (- i) (* z (fma (- c) t (* k y1))))
   (if (<= t 3.9e-90)
     (* y0 (fma (- y5) (fma k y2 (* (- j) y3)) (* c (* x y2))))
     (if (<= t 4.6e+65)
       (* j (* y1 (fma (- y3) y4 (* i x))))
       (if (<= t 6.5e+160)
         (* (* t z) (fma c i (* (- a) b)))
         (* (- (* (* (- (/ (* y2 c) b) j) t) b)) y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -6.8e+109) {
		tmp = -i * (z * fma(-c, t, (k * y1)));
	} else if (t <= 3.9e-90) {
		tmp = y0 * fma(-y5, fma(k, y2, (-j * y3)), (c * (x * y2)));
	} else if (t <= 4.6e+65) {
		tmp = j * (y1 * fma(-y3, y4, (i * x)));
	} else if (t <= 6.5e+160) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else {
		tmp = -(((((y2 * c) / b) - j) * t) * b) * y4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -6.8e+109)
		tmp = Float64(Float64(-i) * Float64(z * fma(Float64(-c), t, Float64(k * y1))));
	elseif (t <= 3.9e-90)
		tmp = Float64(y0 * fma(Float64(-y5), fma(k, y2, Float64(Float64(-j) * y3)), Float64(c * Float64(x * y2))));
	elseif (t <= 4.6e+65)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(i * x))));
	elseif (t <= 6.5e+160)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(Float64(Float64(y2 * c) / b) - j) * t) * b)) * y4);
	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, -6.8e+109], N[((-i) * N[(z * N[((-c) * t + N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-90], N[(y0 * N[((-y5) * N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+65], N[(j * N[(y1 * N[((-y3) * y4 + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+160], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[(N[(N[(N[(N[(y2 * c), $MachinePrecision] / b), $MachinePrecision] - j), $MachinePrecision] * t), $MachinePrecision] * b), $MachinePrecision]) * y4), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.80000000000000013e109

   1. Initial program 11.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in i around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(z \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.0%

      \[\leadsto \left(-i\right) \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)} \]

   if -6.80000000000000013e109 < t < 3.90000000000000005e-90

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 48.1%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 40.3%

       \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]

   if 3.90000000000000005e-90 < t < 4.6e65

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.3%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if 4.6e65 < t < 6.4999999999999995e160

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 53.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.3%

      \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)} \]

   if 6.4999999999999995e160 < t

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 58.4%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in b around -inf

      \[\leadsto \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \left(k \cdot y\right) + j \cdot t\right) + \frac{c \cdot \left(-1 \cdot \left(y \cdot y3\right) + t \cdot y2\right)}{b}\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 62.7%

       \[\leadsto \left(-b \cdot \mathsf{fma}\left(c, \frac{\mathsf{fma}\left(-y, y3, t \cdot y2\right)}{b}, -\mathsf{fma}\left(-k, y, j \cdot t\right)\right)\right) \cdot y4 \]

   12. Taylor expanded in t around inf

       \[\leadsto \left(-b \cdot \left(t \cdot \left(\frac{c \cdot y2}{b} - j\right)\right)\right) \cdot y4 \]
   13. Step-by-step derivation

   14. Applied rewrites 75.2%

       \[\leadsto \left(-\left(\left(\frac{y2 \cdot c}{b} - j\right) \cdot t\right) \cdot b\right) \cdot y4 \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 18: 29.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+284}:\\ \;\;\;\;\left(c \cdot z\right) \cdot \mathsf{fma}\left(-y0, y3, i \cdot t\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{+225}:\\ \;\;\;\;\left(\left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-163}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-274}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= c -5.8e+284)
   (* (* c z) (fma (- y0) y3 (* i t)))
   (if (<= c -9.2e+225)
     (* (* (- c) (* t y2)) y4)
     (if (<= c -1.7e-163)
       (* y0 (* y2 (fma (- k) y5 (* c x))))
       (if (<= c 7.5e-274)
         (* (* x (fma (- a) y2 (* i j))) y1)
         (if (<= c 3.8e-103)
           (* j (* y1 (fma (- y3) y4 (* i x))))
           (if (<= c 1.3e+134)
             (* (* y0 y3) (fma j y5 (* (- c) z)))
             (* (* c y0) (fma x y2 (* (- y3) z))))))))))

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 (c <= -5.8e+284) {
		tmp = (c * z) * fma(-y0, y3, (i * t));
	} else if (c <= -9.2e+225) {
		tmp = (-c * (t * y2)) * y4;
	} else if (c <= -1.7e-163) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} else if (c <= 7.5e-274) {
		tmp = (x * fma(-a, y2, (i * j))) * y1;
	} else if (c <= 3.8e-103) {
		tmp = j * (y1 * fma(-y3, y4, (i * x)));
	} else if (c <= 1.3e+134) {
		tmp = (y0 * y3) * fma(j, y5, (-c * z));
	} else {
		tmp = (c * y0) * fma(x, y2, (-y3 * z));
	}
	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 (c <= -5.8e+284)
		tmp = Float64(Float64(c * z) * fma(Float64(-y0), y3, Float64(i * t)));
	elseif (c <= -9.2e+225)
		tmp = Float64(Float64(Float64(-c) * Float64(t * y2)) * y4);
	elseif (c <= -1.7e-163)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	elseif (c <= 7.5e-274)
		tmp = Float64(Float64(x * fma(Float64(-a), y2, Float64(i * j))) * y1);
	elseif (c <= 3.8e-103)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(i * x))));
	elseif (c <= 1.3e+134)
		tmp = Float64(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)));
	else
		tmp = Float64(Float64(c * y0) * fma(x, y2, Float64(Float64(-y3) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[c, -5.8e+284], N[(N[(c * z), $MachinePrecision] * N[((-y0) * y3 + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.2e+225], N[(N[((-c) * N[(t * y2), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[c, -1.7e-163], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e-274], N[(N[(x * N[((-a) * y2 + N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y1), $MachinePrecision], If[LessEqual[c, 3.8e-103], N[(j * N[(y1 * N[((-y3) * y4 + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e+134], N[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * y0), $MachinePrecision] * N[(x * y2 + N[((-y3) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -5.7999999999999997e284

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 62.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 26.9%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 87.6%

       \[\leadsto \left(c \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-y0, y3, i \cdot t\right)} \]

   if -5.7999999999999997e284 < c < -9.1999999999999998e225

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 10.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 37.8%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in y2 around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 65.4%

       \[\leadsto \left(-c \cdot \left(t \cdot y2\right)\right) \cdot y4 \]

   if -9.1999999999999998e225 < c < -1.70000000000000007e-163

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 43.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 41.0%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 42.3%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]

   if -1.70000000000000007e-163 < c < 7.49999999999999968e-274

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 53.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) + i \cdot j\right)\right) \cdot y1 \]
   7. Step-by-step derivation

   8. Applied rewrites 54.3%

      \[\leadsto \left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1 \]

   if 7.49999999999999968e-274 < c < 3.8000000000000001e-103

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 45.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.4%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if 3.8000000000000001e-103 < c < 1.3000000000000001e134

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 45.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 57.0%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 51.3%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]

   if 1.3000000000000001e134 < c

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 43.1%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(y3 \cdot z\right) + x \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 55.4%

       \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+284}:\\ \;\;\;\;\left(c \cdot z\right) \cdot \mathsf{fma}\left(-y0, y3, i \cdot t\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{+225}:\\ \;\;\;\;\left(\left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-163}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-274}:\\ \;\;\;\;\left(x \cdot \mathsf{fma}\left(-a, y2, i \cdot j\right)\right) \cdot y1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -3.15 \cdot 10^{-217}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y3 -1.45e+152)
     t_1
     (if (<= y3 -3.7e+83)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y3 -4.8e-95)
         t_1
         (if (<= y3 -3.15e-217)
           (* j (* y1 (fma (- y3) y4 (* i x))))
           (if (<= y3 1e-14)
             (* (* t z) (fma c i (* (- a) b)))
             (if (<= y3 1.25e+70)
               (* (* x y0) (fma c y2 (* (- b) j)))
               (* (* y0 y3) (fma j y5 (* (- c) z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y3 <= -1.45e+152) {
		tmp = t_1;
	} else if (y3 <= -3.7e+83) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y3 <= -4.8e-95) {
		tmp = t_1;
	} else if (y3 <= -3.15e-217) {
		tmp = j * (y1 * fma(-y3, y4, (i * x)));
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 1.25e+70) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else {
		tmp = (y0 * y3) * fma(j, y5, (-c * z));
	}
	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(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y3 <= -1.45e+152)
		tmp = t_1;
	elseif (y3 <= -3.7e+83)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y3 <= -4.8e-95)
		tmp = t_1;
	elseif (y3 <= -3.15e-217)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(i * x))));
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 1.25e+70)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	else
		tmp = Float64(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)));
	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[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.45e+152], t$95$1, If[LessEqual[y3, -3.7e+83], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.8e-95], t$95$1, If[LessEqual[y3, -3.15e-217], N[(j * N[(y1 * N[((-y3) * y4 + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.25e+70], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -1.4499999999999999e152 or -3.7000000000000002e83 < y3 < -4.8e-95

   1. Initial program 18.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 52.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.2%

      \[\leadsto \left(y \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)} \]

   if -1.4499999999999999e152 < y3 < -3.7000000000000002e83

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 62.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 67.5%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 73.0%

       \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -b \cdot x\right)}\right) \]

   if -4.8e-95 < y3 < -3.14999999999999999e-217

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 59.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 38.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -3.14999999999999999e-217 < y3 < 9.99999999999999999e-15

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 42.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.6%

      \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)} \]

   if 9.99999999999999999e-15 < y3 < 1.2500000000000001e70

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 34.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 50.1%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 56.5%

       \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, -b \cdot j\right)} \]

   if 1.2500000000000001e70 < y3

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 41.3%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 46.1%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.7 \cdot 10^{+83}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.15 \cdot 10^{-217}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+109}:\\ \;\;\;\;\left(-i\right) \cdot \left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-90}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \mathsf{fma}\left(-c, y2, b \cdot j\right)\right) \cdot y4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -6.8e+109)
   (* (- i) (* z (fma (- c) t (* k y1))))
   (if (<= t 3.9e-90)
     (* y0 (fma (- y5) (fma k y2 (* (- j) y3)) (* c (* x y2))))
     (if (<= t 4.6e+65)
       (* j (* y1 (fma (- y3) y4 (* i x))))
       (if (<= t 6.5e+160)
         (* (* t z) (fma c i (* (- a) b)))
         (* (* t (fma (- c) y2 (* b j))) y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -6.8e+109) {
		tmp = -i * (z * fma(-c, t, (k * y1)));
	} else if (t <= 3.9e-90) {
		tmp = y0 * fma(-y5, fma(k, y2, (-j * y3)), (c * (x * y2)));
	} else if (t <= 4.6e+65) {
		tmp = j * (y1 * fma(-y3, y4, (i * x)));
	} else if (t <= 6.5e+160) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else {
		tmp = (t * fma(-c, y2, (b * j))) * y4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -6.8e+109)
		tmp = Float64(Float64(-i) * Float64(z * fma(Float64(-c), t, Float64(k * y1))));
	elseif (t <= 3.9e-90)
		tmp = Float64(y0 * fma(Float64(-y5), fma(k, y2, Float64(Float64(-j) * y3)), Float64(c * Float64(x * y2))));
	elseif (t <= 4.6e+65)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(i * x))));
	elseif (t <= 6.5e+160)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	else
		tmp = Float64(Float64(t * fma(Float64(-c), y2, Float64(b * j))) * y4);
	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, -6.8e+109], N[((-i) * N[(z * N[((-c) * t + N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-90], N[(y0 * N[((-y5) * N[(k * y2 + N[((-j) * y3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+65], N[(j * N[(y1 * N[((-y3) * y4 + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+160], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[((-c) * y2 + N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.80000000000000013e109

   1. Initial program 11.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in i around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(z \cdot \left(-1 \cdot \left(c \cdot t\right) + k \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.0%

      \[\leadsto \left(-i\right) \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-c, t, k \cdot y1\right)\right)} \]

   if -6.80000000000000013e109 < t < 3.90000000000000005e-90

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 48.1%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 40.3%

       \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right) \cdot y3}\right), c \cdot \left(x \cdot y2\right)\right) \]

   if 3.90000000000000005e-90 < t < 4.6e65

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.3%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if 4.6e65 < t < 6.4999999999999995e160

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 53.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.3%

      \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)} \]

   if 6.4999999999999995e160 < t

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in t around inf

      \[\leadsto \left(t \cdot \left(-1 \cdot \left(c \cdot y2\right) + b \cdot j\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.1%

      \[\leadsto \left(t \cdot \mathsf{fma}\left(-c, y2, b \cdot j\right)\right) \cdot y4 \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 21: 30.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2350000:\\ \;\;\;\;\left(b \cdot \mathsf{fma}\left(-a, t, k \cdot y0\right)\right) \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-85}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y -4.6e+79)
     t_1
     (if (<= y -2350000.0)
       (* (* b (fma (- a) t (* k y0))) z)
       (if (<= y -2e-104)
         (* y0 (* j (fma y3 y5 (* (- b) x))))
         (if (<= y 1.6e-85) (* y0 (* y2 (fma (- k) y5 (* c x)))) 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 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y <= -4.6e+79) {
		tmp = t_1;
	} else if (y <= -2350000.0) {
		tmp = (b * fma(-a, t, (k * y0))) * z;
	} else if (y <= -2e-104) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y <= 1.6e-85) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} 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(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y <= -4.6e+79)
		tmp = t_1;
	elseif (y <= -2350000.0)
		tmp = Float64(Float64(b * fma(Float64(-a), t, Float64(k * y0))) * z);
	elseif (y <= -2e-104)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y <= 1.6e-85)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	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[(N[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+79], t$95$1, If[LessEqual[y, -2350000.0], N[(N[(b * N[((-a) * t + N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, -2e-104], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-85], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000001e79 or 1.60000000000000014e-85 < y

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.9%

      \[\leadsto \left(y \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)} \]

   if -4.6000000000000001e79 < y < -2.35e6

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 41.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 54.4%

      \[\leadsto \left(b \cdot \mathsf{fma}\left(-a, t, k \cdot y0\right)\right) \cdot z \]

   if -2.35e6 < y < -1.99999999999999985e-104

   1. Initial program 45.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 65.6%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 61.4%

       \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -b \cdot x\right)}\right) \]

   if -1.99999999999999985e-104 < y < 1.60000000000000014e-85

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 29.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 42.2%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.3%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+79}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y \leq -2350000:\\ \;\;\;\;\left(b \cdot \mathsf{fma}\left(-a, t, k \cdot y0\right)\right) \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-85}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.6% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-22}:\\ \;\;\;\;\left(a \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\right) \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-85}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y y3) (fma c y4 (* (- a) y5)))))
   (if (<= y -7.5e+77)
     t_1
     (if (<= y -3e-22)
       (* (* a (fma (- b) t (* y1 y3))) z)
       (if (<= y -2e-104)
         (* y0 (* j (fma y3 y5 (* (- b) x))))
         (if (<= y 1.6e-85) (* y0 (* y2 (fma (- k) y5 (* c x)))) 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 = (y * y3) * fma(c, y4, (-a * y5));
	double tmp;
	if (y <= -7.5e+77) {
		tmp = t_1;
	} else if (y <= -3e-22) {
		tmp = (a * fma(-b, t, (y1 * y3))) * z;
	} else if (y <= -2e-104) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y <= 1.6e-85) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} 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(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)))
	tmp = 0.0
	if (y <= -7.5e+77)
		tmp = t_1;
	elseif (y <= -3e-22)
		tmp = Float64(Float64(a * fma(Float64(-b), t, Float64(y1 * y3))) * z);
	elseif (y <= -2e-104)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y <= 1.6e-85)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	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[(N[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+77], t$95$1, If[LessEqual[y, -3e-22], N[(N[(a * N[((-b) * t + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, -2e-104], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-85], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.49999999999999955e77 or 1.60000000000000014e-85 < y

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 54.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.3%

      \[\leadsto \left(y \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)} \]

   if -7.49999999999999955e77 < y < -2.9999999999999999e-22

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 45.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(a \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 51.1%

      \[\leadsto \left(a \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\right) \cdot z \]

   if -2.9999999999999999e-22 < y < -1.99999999999999985e-104

   1. Initial program 45.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 39.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 67.3%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 62.4%

       \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -b \cdot x\right)}\right) \]

   if -1.99999999999999985e-104 < y < 1.60000000000000014e-85

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 29.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 42.2%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.3%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-22}:\\ \;\;\;\;\left(a \cdot \mathsf{fma}\left(-b, t, y1 \cdot y3\right)\right) \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-85}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+46}:\\ \;\;\;\;\left(y \cdot y5\right) \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-68}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-85}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.95e+46)
   (* (* y y5) (fma (- a) y3 (* i k)))
   (if (<= y -1.2e-68)
     (* (* c y0) (fma x y2 (* (- y3) z)))
     (if (<= y -2e-104)
       (* y0 (* j (fma y3 y5 (* (- b) x))))
       (if (<= y 1.6e-85)
         (* y0 (* y2 (fma (- k) y5 (* c x))))
         (* (* y y3) (fma c y4 (* (- a) y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.95e+46) {
		tmp = (y * y5) * fma(-a, y3, (i * k));
	} else if (y <= -1.2e-68) {
		tmp = (c * y0) * fma(x, y2, (-y3 * z));
	} else if (y <= -2e-104) {
		tmp = y0 * (j * fma(y3, y5, (-b * x)));
	} else if (y <= 1.6e-85) {
		tmp = y0 * (y2 * fma(-k, y5, (c * x)));
	} else {
		tmp = (y * y3) * fma(c, y4, (-a * y5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -1.95e+46)
		tmp = Float64(Float64(y * y5) * fma(Float64(-a), y3, Float64(i * k)));
	elseif (y <= -1.2e-68)
		tmp = Float64(Float64(c * y0) * fma(x, y2, Float64(Float64(-y3) * z)));
	elseif (y <= -2e-104)
		tmp = Float64(y0 * Float64(j * fma(y3, y5, Float64(Float64(-b) * x))));
	elseif (y <= 1.6e-85)
		tmp = Float64(y0 * Float64(y2 * fma(Float64(-k), y5, Float64(c * x))));
	else
		tmp = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -1.95e+46], N[(N[(y * y5), $MachinePrecision] * N[((-a) * y3 + N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-68], N[(N[(c * y0), $MachinePrecision] * N[(x * y2 + N[((-y3) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-104], N[(y0 * N[(j * N[(y3 * y5 + N[((-b) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-85], N[(y0 * N[(y2 * N[((-k) * y5 + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.94999999999999997e46

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto y \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 44.4%

      \[\leadsto \left(y \cdot y5\right) \cdot \color{blue}{\mathsf{fma}\left(-a, y3, i \cdot k\right)} \]

   if -1.94999999999999997e46 < y < -1.19999999999999996e-68

   1. Initial program 43.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 19.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 62.5%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(y3 \cdot z\right) + x \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 57.0%

       \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)} \]

   if -1.19999999999999996e-68 < y < -1.99999999999999985e-104

   1. Initial program 50.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 76.0%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 76.5%

       \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\mathsf{fma}\left(y3, y5, -b \cdot x\right)}\right) \]

   if -1.99999999999999985e-104 < y < 1.60000000000000014e-85

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 29.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 42.2%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y2 around inf

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.3%

       \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\mathsf{fma}\left(-k, y5, c \cdot x\right)}\right) \]

   if 1.60000000000000014e-85 < y

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.0%

      \[\leadsto \left(y \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+46}:\\ \;\;\;\;\left(y \cdot y5\right) \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-68}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(j \cdot \mathsf{fma}\left(y3, y5, \left(-b\right) \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-85}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-k, y5, c \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.15 \cdot 10^{-217}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -4.8e-95)
   (* (* y y3) (fma c y4 (* (- a) y5)))
   (if (<= y3 -3.15e-217)
     (* j (* y1 (fma (- y3) y4 (* i x))))
     (if (<= y3 1e-14)
       (* (* t z) (fma c i (* (- a) b)))
       (if (<= y3 1.25e+70)
         (* (* x y0) (fma c y2 (* (- b) j)))
         (* (* y0 y3) (fma j y5 (* (- c) z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -4.8e-95) {
		tmp = (y * y3) * fma(c, y4, (-a * y5));
	} else if (y3 <= -3.15e-217) {
		tmp = j * (y1 * fma(-y3, y4, (i * x)));
	} else if (y3 <= 1e-14) {
		tmp = (t * z) * fma(c, i, (-a * b));
	} else if (y3 <= 1.25e+70) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else {
		tmp = (y0 * y3) * fma(j, y5, (-c * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -4.8e-95)
		tmp = Float64(Float64(y * y3) * fma(c, y4, Float64(Float64(-a) * y5)));
	elseif (y3 <= -3.15e-217)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(i * x))));
	elseif (y3 <= 1e-14)
		tmp = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)));
	elseif (y3 <= 1.25e+70)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	else
		tmp = Float64(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -4.8e-95], N[(N[(y * y3), $MachinePrecision] * N[(c * y4 + N[((-a) * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.15e-217], N[(j * N[(y1 * N[((-y3) * y4 + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1e-14], N[(N[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.25e+70], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -4.8e-95

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 54.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto y \cdot \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.6%

      \[\leadsto \left(y \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)} \]

   if -4.8e-95 < y3 < -3.14999999999999999e-217

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 59.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 38.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if -3.14999999999999999e-217 < y3 < 9.99999999999999999e-15

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 42.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.6%

      \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)} \]

   if 9.99999999999999999e-15 < y3 < 1.2500000000000001e70

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 34.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 50.1%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 56.5%

       \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, -b \cdot j\right)} \]

   if 1.2500000000000001e70 < y3

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 41.3%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 46.1%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.8 \cdot 10^{-95}:\\ \;\;\;\;\left(y \cdot y3\right) \cdot \mathsf{fma}\left(c, y4, \left(-a\right) \cdot y5\right)\\ \mathbf{elif}\;y3 \leq -3.15 \cdot 10^{-217}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{-14}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.2% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.48 \cdot 10^{-269}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(j \cdot t\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* t z) (fma c i (* (- a) b)))))
   (if (<= t -1.26e+48)
     t_1
     (if (<= t -1.48e-269)
       (* (* y0 y3) (fma j y5 (* (- c) z)))
       (if (<= t 4.6e+65)
         (* j (* y1 (fma (- y3) y4 (* i x))))
         (if (<= t 6.5e+160) t_1 (* b (* (* j t) y4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * z) * fma(c, i, (-a * b));
	double tmp;
	if (t <= -1.26e+48) {
		tmp = t_1;
	} else if (t <= -1.48e-269) {
		tmp = (y0 * y3) * fma(j, y5, (-c * z));
	} else if (t <= 4.6e+65) {
		tmp = j * (y1 * fma(-y3, y4, (i * x)));
	} else if (t <= 6.5e+160) {
		tmp = t_1;
	} else {
		tmp = b * ((j * t) * y4);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)))
	tmp = 0.0
	if (t <= -1.26e+48)
		tmp = t_1;
	elseif (t <= -1.48e-269)
		tmp = Float64(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)));
	elseif (t <= 4.6e+65)
		tmp = Float64(j * Float64(y1 * fma(Float64(-y3), y4, Float64(i * x))));
	elseif (t <= 6.5e+160)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(j * t) * y4));
	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[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+48], t$95$1, If[LessEqual[t, -1.48e-269], N[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+65], N[(j * N[(y1 * N[((-y3) * y4 + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+160], t$95$1, N[(b * N[(N[(j * t), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.26000000000000001e48 or 4.6e65 < t < 6.4999999999999995e160

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 43.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.2%

      \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)} \]

   if -1.26000000000000001e48 < t < -1.48e-269

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 38.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 43.5%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 36.6%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]

   if -1.48e-269 < t < 4.6e65

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y1} \]

   5. Applied rewrites 39.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y2 \cdot x - y3 \cdot z\right), a, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y4, \left(j \cdot x - k \cdot z\right) \cdot i\right)\right) \cdot y1} \]

   6. Taylor expanded in j around inf

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.2%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)} \]

   if 6.4999999999999995e160 < t

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.1%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 54.7%

       \[\leadsto b \cdot \left(\left(j \cdot t\right) \cdot \color{blue}{y4}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+48}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;t \leq -1.48 \cdot 10^{-269}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(-y3, y4, i \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(j \cdot t\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 28.1% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{if}\;y3 \leq -2.45 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -600:\\ \;\;\;\;\left(c \cdot \left(y \cdot y3\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq -1.5 \cdot 10^{-256}:\\ \;\;\;\;\left(\left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y3) (fma j y5 (* (- c) z)))))
   (if (<= y3 -2.45e+76)
     t_1
     (if (<= y3 -600.0)
       (* (* c (* y y3)) y4)
       (if (<= y3 -1.5e-256)
         (* (* (- c) (* t y2)) y4)
         (if (<= y3 1.25e+70) (* (* x y0) (fma c y2 (* (- b) 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 = (y0 * y3) * fma(j, y5, (-c * z));
	double tmp;
	if (y3 <= -2.45e+76) {
		tmp = t_1;
	} else if (y3 <= -600.0) {
		tmp = (c * (y * y3)) * y4;
	} else if (y3 <= -1.5e-256) {
		tmp = (-c * (t * y2)) * y4;
	} else if (y3 <= 1.25e+70) {
		tmp = (x * y0) * fma(c, y2, (-b * 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(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)))
	tmp = 0.0
	if (y3 <= -2.45e+76)
		tmp = t_1;
	elseif (y3 <= -600.0)
		tmp = Float64(Float64(c * Float64(y * y3)) * y4);
	elseif (y3 <= -1.5e-256)
		tmp = Float64(Float64(Float64(-c) * Float64(t * y2)) * y4);
	elseif (y3 <= 1.25e+70)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * 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[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.45e+76], t$95$1, If[LessEqual[y3, -600.0], N[(N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y3, -1.5e-256], N[(N[((-c) * N[(t * y2), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y3, 1.25e+70], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -2.45000000000000013e76 or 1.2500000000000001e70 < y3

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 45.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 45.1%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 47.4%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]

   if -2.45000000000000013e76 < y3 < -600

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 27.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 34.2%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \left(c \cdot \left(y \cdot y3\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 47.4%

       \[\leadsto \left(c \cdot \left(y \cdot y3\right)\right) \cdot y4 \]

   if -600 < y3 < -1.4999999999999999e-256

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 40.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 41.1%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in y2 around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 33.4%

       \[\leadsto \left(-c \cdot \left(t \cdot y2\right)\right) \cdot y4 \]

   if -1.4999999999999999e-256 < y3 < 1.2500000000000001e70

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 40.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 43.2%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 39.0%

       \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, -b \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.45 \cdot 10^{+76}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{elif}\;y3 \leq -600:\\ \;\;\;\;\left(c \cdot \left(y \cdot y3\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq -1.5 \cdot 10^{-256}:\\ \;\;\;\;\left(\left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;y3 \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.5% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \mathbf{if}\;y5 \leq -2.25 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.36 \cdot 10^{-92}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;y5 \leq 2.75 \cdot 10^{-74}:\\ \;\;\;\;\left(\left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;\left(y0 \cdot z\right) \cdot \left(\left(-c\right) \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (- a) (* y3 y5)) y)))
   (if (<= y5 -2.25e+78)
     t_1
     (if (<= y5 -1.36e-92)
       (* (* (* z b) y0) k)
       (if (<= y5 2.75e-74)
         (* (* (- c) (* t y2)) y4)
         (if (<= y5 1.3e+33) (* (* y0 z) (* (- c) y3)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (-a * (y3 * y5)) * y;
	double tmp;
	if (y5 <= -2.25e+78) {
		tmp = t_1;
	} else if (y5 <= -1.36e-92) {
		tmp = ((z * b) * y0) * k;
	} else if (y5 <= 2.75e-74) {
		tmp = (-c * (t * y2)) * y4;
	} else if (y5 <= 1.3e+33) {
		tmp = (y0 * z) * (-c * y3);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-a * (y3 * y5)) * y
    if (y5 <= (-2.25d+78)) then
        tmp = t_1
    else if (y5 <= (-1.36d-92)) then
        tmp = ((z * b) * y0) * k
    else if (y5 <= 2.75d-74) then
        tmp = (-c * (t * y2)) * y4
    else if (y5 <= 1.3d+33) then
        tmp = (y0 * z) * (-c * y3)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (-a * (y3 * y5)) * y;
	double tmp;
	if (y5 <= -2.25e+78) {
		tmp = t_1;
	} else if (y5 <= -1.36e-92) {
		tmp = ((z * b) * y0) * k;
	} else if (y5 <= 2.75e-74) {
		tmp = (-c * (t * y2)) * y4;
	} else if (y5 <= 1.3e+33) {
		tmp = (y0 * z) * (-c * y3);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (-a * (y3 * y5)) * y
	tmp = 0
	if y5 <= -2.25e+78:
		tmp = t_1
	elif y5 <= -1.36e-92:
		tmp = ((z * b) * y0) * k
	elif y5 <= 2.75e-74:
		tmp = (-c * (t * y2)) * y4
	elif y5 <= 1.3e+33:
		tmp = (y0 * z) * (-c * 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(Float64(Float64(-a) * Float64(y3 * y5)) * y)
	tmp = 0.0
	if (y5 <= -2.25e+78)
		tmp = t_1;
	elseif (y5 <= -1.36e-92)
		tmp = Float64(Float64(Float64(z * b) * y0) * k);
	elseif (y5 <= 2.75e-74)
		tmp = Float64(Float64(Float64(-c) * Float64(t * y2)) * y4);
	elseif (y5 <= 1.3e+33)
		tmp = Float64(Float64(y0 * z) * Float64(Float64(-c) * y3));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (-a * (y3 * y5)) * y;
	tmp = 0.0;
	if (y5 <= -2.25e+78)
		tmp = t_1;
	elseif (y5 <= -1.36e-92)
		tmp = ((z * b) * y0) * k;
	elseif (y5 <= 2.75e-74)
		tmp = (-c * (t * y2)) * y4;
	elseif (y5 <= 1.3e+33)
		tmp = (y0 * z) * (-c * y3);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[((-a) * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y5, -2.25e+78], t$95$1, If[LessEqual[y5, -1.36e-92], N[(N[(N[(z * b), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y5, 2.75e-74], N[(N[((-c) * N[(t * y2), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[y5, 1.3e+33], N[(N[(y0 * z), $MachinePrecision] * N[((-c) * y3), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.25e78 or 1.2999999999999999e33 < y5

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 50.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 52.6%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 47.3%

       \[\leadsto \left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y \]

   if -2.25e78 < y5 < -1.36e-92

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 45.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.2%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 34.7%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 37.3%

       \[\leadsto \left(\left(z \cdot b\right) \cdot y0\right) \cdot k \]

   if -1.36e-92 < y5 < 2.75e-74

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 33.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in y2 around inf

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 22.4%

       \[\leadsto \left(-c \cdot \left(t \cdot y2\right)\right) \cdot y4 \]

   if 2.75e-74 < y5 < 1.2999999999999999e33

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 29.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(c \cdot y3\right) + b \cdot k\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.4%

      \[\leadsto \left(y0 \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-c, y3, b \cdot k\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \left(y0 \cdot z\right) \cdot \left(-1 \cdot \left(c \cdot \color{blue}{y3}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 36.7%

       \[\leadsto \left(y0 \cdot z\right) \cdot \left(\left(-c\right) \cdot y3\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.25 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -1.36 \cdot 10^{-92}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;y5 \leq 2.75 \cdot 10^{-74}:\\ \;\;\;\;\left(\left(-c\right) \cdot \left(t \cdot y2\right)\right) \cdot y4\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;\left(y0 \cdot z\right) \cdot \left(\left(-c\right) \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.0% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-154}:\\ \;\;\;\;\left(c \cdot \left(y \cdot y3\right)\right) \cdot y4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-83}:\\ \;\;\;\;\left(\left(x \cdot b\right) \cdot a\right) \cdot y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;\left(\left(y4 \cdot b\right) \cdot y\right) \cdot \left(-k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- a) (* b (* t z)))))
   (if (<= z -2.75e+29)
     t_1
     (if (<= z -5.5e-154)
       (* (* c (* y y3)) y4)
       (if (<= z 9.2e-83)
         (* (* (* x b) a) y)
         (if (<= z 3.3e+106) (* (* (* y4 b) y) (- k)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -a * (b * (t * z));
	double tmp;
	if (z <= -2.75e+29) {
		tmp = t_1;
	} else if (z <= -5.5e-154) {
		tmp = (c * (y * y3)) * y4;
	} else if (z <= 9.2e-83) {
		tmp = ((x * b) * a) * y;
	} else if (z <= 3.3e+106) {
		tmp = ((y4 * b) * y) * -k;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (b * (t * z))
    if (z <= (-2.75d+29)) then
        tmp = t_1
    else if (z <= (-5.5d-154)) then
        tmp = (c * (y * y3)) * y4
    else if (z <= 9.2d-83) then
        tmp = ((x * b) * a) * y
    else if (z <= 3.3d+106) then
        tmp = ((y4 * b) * y) * -k
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -a * (b * (t * z));
	double tmp;
	if (z <= -2.75e+29) {
		tmp = t_1;
	} else if (z <= -5.5e-154) {
		tmp = (c * (y * y3)) * y4;
	} else if (z <= 9.2e-83) {
		tmp = ((x * b) * a) * y;
	} else if (z <= 3.3e+106) {
		tmp = ((y4 * b) * y) * -k;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -a * (b * (t * z))
	tmp = 0
	if z <= -2.75e+29:
		tmp = t_1
	elif z <= -5.5e-154:
		tmp = (c * (y * y3)) * y4
	elif z <= 9.2e-83:
		tmp = ((x * b) * a) * y
	elif z <= 3.3e+106:
		tmp = ((y4 * b) * y) * -k
	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(Float64(-a) * Float64(b * Float64(t * z)))
	tmp = 0.0
	if (z <= -2.75e+29)
		tmp = t_1;
	elseif (z <= -5.5e-154)
		tmp = Float64(Float64(c * Float64(y * y3)) * y4);
	elseif (z <= 9.2e-83)
		tmp = Float64(Float64(Float64(x * b) * a) * y);
	elseif (z <= 3.3e+106)
		tmp = Float64(Float64(Float64(y4 * b) * y) * Float64(-k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -a * (b * (t * z));
	tmp = 0.0;
	if (z <= -2.75e+29)
		tmp = t_1;
	elseif (z <= -5.5e-154)
		tmp = (c * (y * y3)) * y4;
	elseif (z <= 9.2e-83)
		tmp = ((x * b) * a) * y;
	elseif (z <= 3.3e+106)
		tmp = ((y4 * b) * y) * -k;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-a) * N[(b * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e+29], t$95$1, If[LessEqual[z, -5.5e-154], N[(N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[z, 9.2e-83], N[(N[(N[(x * b), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 3.3e+106], N[(N[(N[(y4 * b), $MachinePrecision] * y), $MachinePrecision] * (-k)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75e29 or 3.30000000000000008e106 < z

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 53.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.7%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \left(a \cdot \color{blue}{\left(b \cdot \left(t \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 37.2%

       \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   if -2.75e29 < z < -5.50000000000000002e-154

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 38.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 35.1%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \left(c \cdot \left(y \cdot y3\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 35.3%

       \[\leadsto \left(c \cdot \left(y \cdot y3\right)\right) \cdot y4 \]

   if -5.50000000000000002e-154 < z < 9.19999999999999959e-83

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 38.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 31.0%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 26.9%

       \[\leadsto \left(b \cdot \mathsf{fma}\left(-k, y4, a \cdot x\right)\right) \cdot y \]

   12. Taylor expanded in x around inf

       \[\leadsto \left(a \cdot \left(b \cdot x\right)\right) \cdot y \]
   13. Step-by-step derivation

   14. Applied rewrites 27.0%

       \[\leadsto \left(\left(x \cdot b\right) \cdot a\right) \cdot y \]

   if 9.19999999999999959e-83 < z < 3.30000000000000008e106

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 34.5%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(y \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 21.8%

       \[\leadsto -b \cdot \left(\left(k \cdot y\right) \cdot y4\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 31.1%

       \[\leadsto \left(\left(y4 \cdot b\right) \cdot y\right) \cdot \left(-k\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 29: 29.3% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(j \cdot t\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* t z) (fma c i (* (- a) b)))))
   (if (<= t -1.26e+48)
     t_1
     (if (<= t 4.2e+63)
       (* (* y0 y3) (fma j y5 (* (- c) z)))
       (if (<= t 6.5e+160) t_1 (* b (* (* j t) y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * z) * fma(c, i, (-a * b));
	double tmp;
	if (t <= -1.26e+48) {
		tmp = t_1;
	} else if (t <= 4.2e+63) {
		tmp = (y0 * y3) * fma(j, y5, (-c * z));
	} else if (t <= 6.5e+160) {
		tmp = t_1;
	} else {
		tmp = b * ((j * t) * y4);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * z) * fma(c, i, Float64(Float64(-a) * b)))
	tmp = 0.0
	if (t <= -1.26e+48)
		tmp = t_1;
	elseif (t <= 4.2e+63)
		tmp = Float64(Float64(y0 * y3) * fma(j, y5, Float64(Float64(-c) * z)));
	elseif (t <= 6.5e+160)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(j * t) * y4));
	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[(t * z), $MachinePrecision] * N[(c * i + N[((-a) * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+48], t$95$1, If[LessEqual[t, 4.2e+63], N[(N[(y0 * y3), $MachinePrecision] * N[(j * y5 + N[((-c) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+160], t$95$1, N[(b * N[(N[(j * t), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.26000000000000001e48 or 4.2000000000000004e63 < t < 6.4999999999999995e160

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 43.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.2%

      \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)} \]

   if -1.26000000000000001e48 < t < 4.2000000000000004e63

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 41.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 47.3%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.6%

       \[\leadsto \left(y0 \cdot y3\right) \cdot \color{blue}{\mathsf{fma}\left(j, y5, -c \cdot z\right)} \]

   if 6.4999999999999995e160 < t

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.1%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 54.7%

       \[\leadsto b \cdot \left(\left(j \cdot t\right) \cdot \color{blue}{y4}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+48}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \mathsf{fma}\left(j, y5, \left(-c\right) \cdot z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \mathsf{fma}\left(c, i, \left(-a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(j \cdot t\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 25.6% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -2.25 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -1.35 \cdot 10^{-76}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+147}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(k \cdot y5\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -2.25e+78)
   (* (* (- a) (* y3 y5)) y)
   (if (<= y5 -1.35e-76)
     (* (* (* z b) y0) k)
     (if (<= y5 1.2e+147)
       (* (* x y0) (fma c y2 (* (- b) j)))
       (* (* i (* k y5)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.25e+78) {
		tmp = (-a * (y3 * y5)) * y;
	} else if (y5 <= -1.35e-76) {
		tmp = ((z * b) * y0) * k;
	} else if (y5 <= 1.2e+147) {
		tmp = (x * y0) * fma(c, y2, (-b * j));
	} else {
		tmp = (i * (k * y5)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -2.25e+78)
		tmp = Float64(Float64(Float64(-a) * Float64(y3 * y5)) * y);
	elseif (y5 <= -1.35e-76)
		tmp = Float64(Float64(Float64(z * b) * y0) * k);
	elseif (y5 <= 1.2e+147)
		tmp = Float64(Float64(x * y0) * fma(c, y2, Float64(Float64(-b) * j)));
	else
		tmp = Float64(Float64(i * Float64(k * y5)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -2.25e+78], N[(N[((-a) * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y5, -1.35e-76], N[(N[(N[(z * b), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y5, 1.2e+147], N[(N[(x * y0), $MachinePrecision] * N[(c * y2 + N[((-b) * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.25e78

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 47.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 55.6%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 51.7%

       \[\leadsto \left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y \]

   if -2.25e78 < y5 < -1.35e-76

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 40.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.2%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 38.0%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 41.1%

       \[\leadsto \left(\left(z \cdot b\right) \cdot y0\right) \cdot k \]

   if -1.35e-76 < y5 < 1.20000000000000001e147

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 37.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 34.7%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot j\right) + c \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 30.1%

       \[\leadsto \left(x \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(c, y2, -b \cdot j\right)} \]

   if 1.20000000000000001e147 < y5

   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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 56.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 51.9%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 49.0%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.25 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -1.35 \cdot 10^{-76}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+147}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \mathsf{fma}\left(c, y2, \left(-b\right) \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(k \cdot y5\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 25.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -2.25 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \mathbf{elif}\;y5 \leq -1.4 \cdot 10^{-129}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;y5 \leq 1.18 \cdot 10^{+190}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(k \cdot y5\right)\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -2.25e+78)
   (* (* (- a) (* y3 y5)) y)
   (if (<= y5 -1.4e-129)
     (* (* (* z b) y0) k)
     (if (<= y5 1.18e+190)
       (* (* c y0) (fma x y2 (* (- y3) z)))
       (* (* i (* k y5)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.25e+78) {
		tmp = (-a * (y3 * y5)) * y;
	} else if (y5 <= -1.4e-129) {
		tmp = ((z * b) * y0) * k;
	} else if (y5 <= 1.18e+190) {
		tmp = (c * y0) * fma(x, y2, (-y3 * z));
	} else {
		tmp = (i * (k * y5)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -2.25e+78)
		tmp = Float64(Float64(Float64(-a) * Float64(y3 * y5)) * y);
	elseif (y5 <= -1.4e-129)
		tmp = Float64(Float64(Float64(z * b) * y0) * k);
	elseif (y5 <= 1.18e+190)
		tmp = Float64(Float64(c * y0) * fma(x, y2, Float64(Float64(-y3) * z)));
	else
		tmp = Float64(Float64(i * Float64(k * y5)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -2.25e+78], N[(N[((-a) * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y5, -1.4e-129], N[(N[(N[(z * b), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y5, 1.18e+190], N[(N[(c * y0), $MachinePrecision] * N[(x * y2 + N[((-y3) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.25e78

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 47.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 55.6%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 51.7%

       \[\leadsto \left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y \]

   if -2.25e78 < y5 < -1.4e-129

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 42.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.9%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 30.8%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 35.3%

       \[\leadsto \left(\left(z \cdot b\right) \cdot y0\right) \cdot k \]

   if -1.4e-129 < y5 < 1.1799999999999999e190

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 40.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto y0 \cdot \left(\color{blue}{\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} + \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot y5, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y5\right)}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(\color{blue}{-y5}, k \cdot y2 - j \cdot y3, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{k \cdot y2 + \left(\mathsf{neg}\left(j\right)\right) \cdot y3}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \color{blue}{\mathsf{fma}\left(k, y2, \left(\mathsf{neg}\left(j\right)\right) \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(\mathsf{neg}\left(j\right)\right) \cdot y3}\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \color{blue}{\left(-j\right)} \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      11. sub-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\mathsf{neg}\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      12. mul-1-neg N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \color{blue}{\mathsf{fma}\left(c, x \cdot y2 - y3 \cdot z, -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

   8. Applied rewrites 36.3%

      \[\leadsto \color{blue}{y0 \cdot \mathsf{fma}\left(-y5, \mathsf{fma}\left(k, y2, \left(-j\right) \cdot y3\right), \mathsf{fma}\left(c, \mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right), \left(-b\right) \cdot \mathsf{fma}\left(j, x, \left(-k\right) \cdot z\right)\right)\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(y3 \cdot z\right) + x \cdot y2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 31.6%

       \[\leadsto \left(c \cdot y0\right) \cdot \color{blue}{\mathsf{fma}\left(x, y2, \left(-y3\right) \cdot z\right)} \]

   if 1.1799999999999999e190 < y5

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 45.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 46.5%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 54.5%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 32: 22.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y\\ \mathbf{if}\;y5 \leq -2.25 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-129}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+33}:\\ \;\;\;\;\left(y0 \cdot z\right) \cdot \left(\left(-c\right) \cdot y3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* (- a) (* y3 y5)) y)))
   (if (<= y5 -2.25e+78)
     t_1
     (if (<= y5 -3e-129)
       (* (* (* z b) y0) k)
       (if (<= y5 1.3e+33) (* (* y0 z) (* (- c) y3)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (-a * (y3 * y5)) * y;
	double tmp;
	if (y5 <= -2.25e+78) {
		tmp = t_1;
	} else if (y5 <= -3e-129) {
		tmp = ((z * b) * y0) * k;
	} else if (y5 <= 1.3e+33) {
		tmp = (y0 * z) * (-c * y3);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-a * (y3 * y5)) * y
    if (y5 <= (-2.25d+78)) then
        tmp = t_1
    else if (y5 <= (-3d-129)) then
        tmp = ((z * b) * y0) * k
    else if (y5 <= 1.3d+33) then
        tmp = (y0 * z) * (-c * y3)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (-a * (y3 * y5)) * y;
	double tmp;
	if (y5 <= -2.25e+78) {
		tmp = t_1;
	} else if (y5 <= -3e-129) {
		tmp = ((z * b) * y0) * k;
	} else if (y5 <= 1.3e+33) {
		tmp = (y0 * z) * (-c * y3);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (-a * (y3 * y5)) * y
	tmp = 0
	if y5 <= -2.25e+78:
		tmp = t_1
	elif y5 <= -3e-129:
		tmp = ((z * b) * y0) * k
	elif y5 <= 1.3e+33:
		tmp = (y0 * z) * (-c * 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(Float64(Float64(-a) * Float64(y3 * y5)) * y)
	tmp = 0.0
	if (y5 <= -2.25e+78)
		tmp = t_1;
	elseif (y5 <= -3e-129)
		tmp = Float64(Float64(Float64(z * b) * y0) * k);
	elseif (y5 <= 1.3e+33)
		tmp = Float64(Float64(y0 * z) * Float64(Float64(-c) * y3));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (-a * (y3 * y5)) * y;
	tmp = 0.0;
	if (y5 <= -2.25e+78)
		tmp = t_1;
	elseif (y5 <= -3e-129)
		tmp = ((z * b) * y0) * k;
	elseif (y5 <= 1.3e+33)
		tmp = (y0 * z) * (-c * y3);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[((-a) * N[(y3 * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y5, -2.25e+78], t$95$1, If[LessEqual[y5, -3e-129], N[(N[(N[(z * b), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[y5, 1.3e+33], N[(N[(y0 * z), $MachinePrecision] * N[((-c) * y3), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -2.25e78 or 1.2999999999999999e33 < y5

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 50.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 52.6%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around inf

      \[\leadsto \left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 47.3%

       \[\leadsto \left(\left(-a\right) \cdot \left(y3 \cdot y5\right)\right) \cdot y \]

   if -2.25e78 < y5 < -2.9999999999999998e-129

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 42.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.9%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 30.8%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 35.3%

       \[\leadsto \left(\left(z \cdot b\right) \cdot y0\right) \cdot k \]

   if -2.9999999999999998e-129 < y5 < 1.2999999999999999e33

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 32.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto y0 \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(c \cdot y3\right) + b \cdot k\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.6%

      \[\leadsto \left(y0 \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-c, y3, b \cdot k\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \left(y0 \cdot z\right) \cdot \left(-1 \cdot \left(c \cdot \color{blue}{y3}\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 21.8%

       \[\leadsto \left(y0 \cdot z\right) \cdot \left(\left(-c\right) \cdot y3\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 33: 22.0% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;\left(-a\right) \cdot \left(b \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-154}:\\ \;\;\;\;\left(c \cdot \left(y \cdot y3\right)\right) \cdot y4\\ \mathbf{elif}\;z \leq 620000000000:\\ \;\;\;\;\left(\left(x \cdot b\right) \cdot a\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.75e+29)
   (* (- a) (* b (* t z)))
   (if (<= z -5.5e-154)
     (* (* c (* y y3)) y4)
     (if (<= z 620000000000.0) (* (* (* x b) a) y) (* (* (* z b) y0) k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.75e+29) {
		tmp = -a * (b * (t * z));
	} else if (z <= -5.5e-154) {
		tmp = (c * (y * y3)) * y4;
	} else if (z <= 620000000000.0) {
		tmp = ((x * b) * a) * y;
	} else {
		tmp = ((z * b) * y0) * k;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-2.75d+29)) then
        tmp = -a * (b * (t * z))
    else if (z <= (-5.5d-154)) then
        tmp = (c * (y * y3)) * y4
    else if (z <= 620000000000.0d0) then
        tmp = ((x * b) * a) * y
    else
        tmp = ((z * b) * y0) * k
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.75e+29) {
		tmp = -a * (b * (t * z));
	} else if (z <= -5.5e-154) {
		tmp = (c * (y * y3)) * y4;
	} else if (z <= 620000000000.0) {
		tmp = ((x * b) * a) * y;
	} else {
		tmp = ((z * b) * y0) * k;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -2.75e+29:
		tmp = -a * (b * (t * z))
	elif z <= -5.5e-154:
		tmp = (c * (y * y3)) * y4
	elif z <= 620000000000.0:
		tmp = ((x * b) * a) * y
	else:
		tmp = ((z * b) * y0) * k
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -2.75e+29)
		tmp = Float64(Float64(-a) * Float64(b * Float64(t * z)));
	elseif (z <= -5.5e-154)
		tmp = Float64(Float64(c * Float64(y * y3)) * y4);
	elseif (z <= 620000000000.0)
		tmp = Float64(Float64(Float64(x * b) * a) * y);
	else
		tmp = Float64(Float64(Float64(z * b) * y0) * k);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -2.75e+29)
		tmp = -a * (b * (t * z));
	elseif (z <= -5.5e-154)
		tmp = (c * (y * y3)) * y4;
	elseif (z <= 620000000000.0)
		tmp = ((x * b) * a) * y;
	else
		tmp = ((z * b) * y0) * k;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -2.75e+29], N[((-a) * N[(b * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-154], N[(N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision], If[LessEqual[z, 620000000000.0], N[(N[(N[(x * b), $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(z * b), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75e29

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 54.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.4%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto -1 \cdot \left(a \cdot \color{blue}{\left(b \cdot \left(t \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 35.8%

       \[\leadsto \left(-a\right) \cdot \left(b \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   if -2.75e29 < z < -5.50000000000000002e-154

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 38.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in y1 around 0

      \[\leadsto \left(-1 \cdot \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + b \cdot \left(j \cdot t - k \cdot y\right)\right) \cdot y4 \]
   7. Step-by-step derivation

   8. Applied rewrites 35.1%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(t, y2, \left(-y\right) \cdot y3\right), b \cdot \mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)\right) \cdot y4 \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \left(c \cdot \left(y \cdot y3\right)\right) \cdot y4 \]
   10. Step-by-step derivation

   11. Applied rewrites 35.3%

       \[\leadsto \left(c \cdot \left(y \cdot y3\right)\right) \cdot y4 \]

   if -5.50000000000000002e-154 < z < 6.2e11

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 43.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 30.2%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 29.8%

       \[\leadsto \left(b \cdot \mathsf{fma}\left(-k, y4, a \cdot x\right)\right) \cdot y \]

   12. Taylor expanded in x around inf

       \[\leadsto \left(a \cdot \left(b \cdot x\right)\right) \cdot y \]
   13. Step-by-step derivation

   14. Applied rewrites 24.9%

       \[\leadsto \left(\left(x \cdot b\right) \cdot a\right) \cdot y \]

   if 6.2e11 < z

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 48.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.6%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 27.3%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 32.3%

       \[\leadsto \left(\left(z \cdot b\right) \cdot y0\right) \cdot k \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 34: 21.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot \left(k \cdot y5\right)\right) \cdot y\\ \mathbf{if}\;y5 \leq -1.95 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+147}:\\ \;\;\;\;\left(\left(y4 \cdot t\right) \cdot j\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* i (* k y5)) y)))
   (if (<= y5 -1.95e+127)
     t_1
     (if (<= y5 -1.6e-227)
       (* b (* (* k y0) z))
       (if (<= y5 1.2e+147) (* (* (* y4 t) j) 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 = (i * (k * y5)) * y;
	double tmp;
	if (y5 <= -1.95e+127) {
		tmp = t_1;
	} else if (y5 <= -1.6e-227) {
		tmp = b * ((k * y0) * z);
	} else if (y5 <= 1.2e+147) {
		tmp = ((y4 * t) * j) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (i * (k * y5)) * y
    if (y5 <= (-1.95d+127)) then
        tmp = t_1
    else if (y5 <= (-1.6d-227)) then
        tmp = b * ((k * y0) * z)
    else if (y5 <= 1.2d+147) then
        tmp = ((y4 * t) * j) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * (k * y5)) * y;
	double tmp;
	if (y5 <= -1.95e+127) {
		tmp = t_1;
	} else if (y5 <= -1.6e-227) {
		tmp = b * ((k * y0) * z);
	} else if (y5 <= 1.2e+147) {
		tmp = ((y4 * t) * j) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * (k * y5)) * y
	tmp = 0
	if y5 <= -1.95e+127:
		tmp = t_1
	elif y5 <= -1.6e-227:
		tmp = b * ((k * y0) * z)
	elif y5 <= 1.2e+147:
		tmp = ((y4 * t) * j) * 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(Float64(i * Float64(k * y5)) * y)
	tmp = 0.0
	if (y5 <= -1.95e+127)
		tmp = t_1;
	elseif (y5 <= -1.6e-227)
		tmp = Float64(b * Float64(Float64(k * y0) * z));
	elseif (y5 <= 1.2e+147)
		tmp = Float64(Float64(Float64(y4 * t) * j) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * (k * y5)) * y;
	tmp = 0.0;
	if (y5 <= -1.95e+127)
		tmp = t_1;
	elseif (y5 <= -1.6e-227)
		tmp = b * ((k * y0) * z);
	elseif (y5 <= 1.2e+147)
		tmp = ((y4 * t) * j) * b;
	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[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y5, -1.95e+127], t$95$1, If[LessEqual[y5, -1.6e-227], N[(b * N[(N[(k * y0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.2e+147], N[(N[(N[(y4 * t), $MachinePrecision] * j), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -1.94999999999999991e127 or 1.20000000000000001e147 < y5

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot y} \]

   5. Applied rewrites 52.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(y4 \cdot b - y5 \cdot i\right), k, \mathsf{fma}\left(b \cdot a - i \cdot c, x, \left(y4 \cdot c - y5 \cdot a\right) \cdot y3\right)\right) \cdot y} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \left(y5 \cdot \left(-1 \cdot \left(a \cdot y3\right) + i \cdot k\right)\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 56.5%

      \[\leadsto \left(y5 \cdot \mathsf{fma}\left(-a, y3, i \cdot k\right)\right) \cdot y \]

   9. Taylor expanded in a around 0

      \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 40.0%

       \[\leadsto \left(i \cdot \left(k \cdot y5\right)\right) \cdot y \]

   if -1.94999999999999991e127 < y5 < -1.60000000000000005e-227

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 28.0%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 26.5%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]

   if -1.60000000000000005e-227 < y5 < 1.20000000000000001e147

   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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 36.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 27.8%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(y \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 14.8%

       \[\leadsto -b \cdot \left(\left(k \cdot y\right) \cdot y4\right) \]

   12. Taylor expanded in y around 0

       \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 22.2%

       \[\leadsto \left(\left(y4 \cdot t\right) \cdot j\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 35: 21.7% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -4.6 \cdot 10^{+62} \lor \neg \left(y4 \leq 1.2 \cdot 10^{-40}\right):\\ \;\;\;\;\left(\left(y4 \cdot t\right) \cdot j\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y4 -4.6e+62) (not (<= y4 1.2e-40)))
   (* (* (* y4 t) j) b)
   (* b (* (* k y0) z))))

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 <= -4.6e+62) || !(y4 <= 1.2e-40)) {
		tmp = ((y4 * t) * j) * b;
	} else {
		tmp = b * ((k * y0) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y4 <= (-4.6d+62)) .or. (.not. (y4 <= 1.2d-40))) then
        tmp = ((y4 * t) * j) * b
    else
        tmp = b * ((k * y0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y4 <= -4.6e+62) || !(y4 <= 1.2e-40)) {
		tmp = ((y4 * t) * j) * b;
	} else {
		tmp = b * ((k * y0) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y4 <= -4.6e+62) or not (y4 <= 1.2e-40):
		tmp = ((y4 * t) * j) * b
	else:
		tmp = b * ((k * y0) * z)
	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 <= -4.6e+62) || !(y4 <= 1.2e-40))
		tmp = Float64(Float64(Float64(y4 * t) * j) * b);
	else
		tmp = Float64(b * Float64(Float64(k * y0) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y4 <= -4.6e+62) || ~((y4 <= 1.2e-40)))
		tmp = ((y4 * t) * j) * b;
	else
		tmp = b * ((k * y0) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y4, -4.6e+62], N[Not[LessEqual[y4, 1.2e-40]], $MachinePrecision]], N[(N[(N[(y4 * t), $MachinePrecision] * j), $MachinePrecision] * b), $MachinePrecision], N[(b * N[(N[(k * y0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y4 < -4.59999999999999968e62 or 1.19999999999999996e-40 < y4

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 44.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.8%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(y \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 18.9%

       \[\leadsto -b \cdot \left(\left(k \cdot y\right) \cdot y4\right) \]

   12. Taylor expanded in y around 0

       \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 28.0%

       \[\leadsto \left(\left(y4 \cdot t\right) \cdot j\right) \cdot b \]

   if -4.59999999999999968e62 < y4 < 1.19999999999999996e-40

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 41.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 28.7%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 23.8%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.6 \cdot 10^{+62} \lor \neg \left(y4 \leq 1.2 \cdot 10^{-40}\right):\\ \;\;\;\;\left(\left(y4 \cdot t\right) \cdot j\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 21.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -30.5 \lor \neg \left(j \leq 3.9 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot \left(\left(j \cdot t\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= j -30.5) (not (<= j 3.9e+96)))
   (* b (* (* j t) y4))
   (* b (* (* k y0) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((j <= -30.5) || !(j <= 3.9e+96)) {
		tmp = b * ((j * t) * y4);
	} else {
		tmp = b * ((k * y0) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((j <= (-30.5d0)) .or. (.not. (j <= 3.9d+96))) then
        tmp = b * ((j * t) * y4)
    else
        tmp = b * ((k * y0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((j <= -30.5) || !(j <= 3.9e+96)) {
		tmp = b * ((j * t) * y4);
	} else {
		tmp = b * ((k * y0) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (j <= -30.5) or not (j <= 3.9e+96):
		tmp = b * ((j * t) * y4)
	else:
		tmp = b * ((k * y0) * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((j <= -30.5) || !(j <= 3.9e+96))
		tmp = Float64(b * Float64(Float64(j * t) * y4));
	else
		tmp = Float64(b * Float64(Float64(k * y0) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((j <= -30.5) || ~((j <= 3.9e+96)))
		tmp = b * ((j * t) * y4);
	else
		tmp = b * ((k * y0) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[j, -30.5], N[Not[LessEqual[j, 3.9e+96]], $MachinePrecision]], N[(b * N[(N[(j * t), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(k * y0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -30.5 or 3.9e96 < j

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 35.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.3%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 29.6%

       \[\leadsto b \cdot \left(\left(j \cdot t\right) \cdot \color{blue}{y4}\right) \]

   if -30.5 < j < 3.9e96

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 36.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 23.7%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 21.4%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -30.5 \lor \neg \left(j \leq 3.9 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot \left(\left(j \cdot t\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 20.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -4.6 \cdot 10^{+62}:\\ \;\;\;\;\left(\left(y4 \cdot t\right) \cdot j\right) \cdot b\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(j \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -4.6e+62)
   (* (* (* y4 t) j) b)
   (if (<= y4 1.2e-40) (* b (* (* k y0) z)) (* (* b y4) (* j t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -4.6e+62) {
		tmp = ((y4 * t) * j) * b;
	} else if (y4 <= 1.2e-40) {
		tmp = b * ((k * y0) * z);
	} else {
		tmp = (b * y4) * (j * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-4.6d+62)) then
        tmp = ((y4 * t) * j) * b
    else if (y4 <= 1.2d-40) then
        tmp = b * ((k * y0) * z)
    else
        tmp = (b * y4) * (j * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -4.6e+62) {
		tmp = ((y4 * t) * j) * b;
	} else if (y4 <= 1.2e-40) {
		tmp = b * ((k * y0) * z);
	} else {
		tmp = (b * y4) * (j * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -4.6e+62:
		tmp = ((y4 * t) * j) * b
	elif y4 <= 1.2e-40:
		tmp = b * ((k * y0) * z)
	else:
		tmp = (b * y4) * (j * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -4.6e+62)
		tmp = Float64(Float64(Float64(y4 * t) * j) * b);
	elseif (y4 <= 1.2e-40)
		tmp = Float64(b * Float64(Float64(k * y0) * z));
	else
		tmp = Float64(Float64(b * y4) * Float64(j * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -4.6e+62)
		tmp = ((y4 * t) * j) * b;
	elseif (y4 <= 1.2e-40)
		tmp = b * ((k * y0) * z);
	else
		tmp = (b * y4) * (j * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -4.6e+62], N[(N[(N[(y4 * t), $MachinePrecision] * j), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[y4, 1.2e-40], N[(b * N[(N[(k * y0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(b * y4), $MachinePrecision] * N[(j * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -4.59999999999999968e62

   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 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.1%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(k \cdot \left(y \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 19.7%

       \[\leadsto -b \cdot \left(\left(k \cdot y\right) \cdot y4\right) \]

   12. Taylor expanded in y around 0

       \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4\right)}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 31.5%

       \[\leadsto \left(\left(y4 \cdot t\right) \cdot j\right) \cdot b \]

   if -4.59999999999999968e62 < y4 < 1.19999999999999996e-40

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 41.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 28.7%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 23.8%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]

   if 1.19999999999999996e-40 < y4

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]

   5. Applied rewrites 37.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot t - k \cdot y, b, \mathsf{fma}\left(y2 \cdot k - y3 \cdot j, y1, \left(-c\right) \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)\right) \cdot y4} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 32.5%

      \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\mathsf{fma}\left(j, t, \left(-k\right) \cdot y\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \left(b \cdot y4\right) \cdot \left(j \cdot t\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 25.9%

       \[\leadsto \left(b \cdot y4\right) \cdot \left(j \cdot t\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 38: 17.3% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(k \cdot y0\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot b\right) \cdot y0\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z 1.35e+165) (* b (* (* k y0) z)) (* (* (* z b) y0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = b * ((k * y0) * z);
	} else {
		tmp = ((z * b) * y0) * k;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= 1.35d+165) then
        tmp = b * ((k * y0) * z)
    else
        tmp = ((z * b) * y0) * k
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= 1.35e+165) {
		tmp = b * ((k * y0) * z);
	} else {
		tmp = ((z * b) * y0) * k;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= 1.35e+165:
		tmp = b * ((k * y0) * z)
	else:
		tmp = ((z * b) * y0) * k
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= 1.35e+165)
		tmp = Float64(b * Float64(Float64(k * y0) * z));
	else
		tmp = Float64(Float64(Float64(z * b) * y0) * k);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= 1.35e+165)
		tmp = b * ((k * y0) * z);
	else
		tmp = ((z * b) * y0) * k;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, 1.35e+165], N[(b * N[(N[(k * y0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * b), $MachinePrecision] * y0), $MachinePrecision] * k), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e165

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 31.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 20.6%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 16.0%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]

   if 1.35e165 < z

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   5. Applied rewrites 61.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.6%

      \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 27.2%

       \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 42.4%

       \[\leadsto \left(\left(z \cdot b\right) \cdot y0\right) \cdot k \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 39: 17.1% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(\left(k \cdot y0\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* b (* (* k y0) z)))

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 b * ((k * y0) * z);
}

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 = b * ((k * y0) * z)
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 b * ((k * y0) * z);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return b * ((k * y0) * z)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(b * Float64(Float64(k * y0) * z))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = b * ((k * y0) * z);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(N[(k * y0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 27.1%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(a \cdot b - c \cdot i\right)\right) + -1 \cdot \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) - -1 \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot z} \]

5. Applied rewrites 35.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(b \cdot a - i \cdot c\right), t, \mathsf{fma}\left(-y3, y0 \cdot c - y1 \cdot a, \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

6. Taylor expanded in b around inf

   \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(a \cdot t\right) + k \cdot y0\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 22.9%

   \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(-a, t, k \cdot y0\right)} \]

9. Taylor expanded in t around 0

   \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(y0 \cdot z\right)}\right) \]
10. Step-by-step derivation

11. Applied rewrites 17.4%

    \[\leadsto b \cdot \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right) \]
12. 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 2024313 
(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)))))