Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.7% → 81.9%

Time: 34.2s

Alternatives: 33

Speedup: 0.5×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
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) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
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) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* (* i j) (- (* a (/ 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 t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (i * j) * ((a * (c / i)) - y);
	}
	return tmp;
}

Java

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (i * j) * ((a * (c / i)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(i * j) * Float64(Float64(a * Float64(c / i)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (i * j) * ((a * (c / i)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(c / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 95.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 8.5%

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

      1. fma-define 8.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + i \cdot \color{blue}{\mathsf{fma}\left(-1, j \cdot y, \frac{a \cdot \left(c \cdot j\right)}{i}\right)} \]

      2. associate-/l* 8.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + i \cdot \mathsf{fma}\left(-1, j \cdot y, \color{blue}{a \cdot \frac{c \cdot j}{i}}\right) \]

      3. *-commutative 8.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + i \cdot \mathsf{fma}\left(-1, j \cdot y, a \cdot \frac{\color{blue}{j \cdot c}}{i}\right) \]

   5. Simplified 8.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{i \cdot \mathsf{fma}\left(-1, j \cdot y, a \cdot \frac{j \cdot c}{i}\right)} \]

   6. Taylor expanded in j around inf 52.9%

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

      1. associate-*r* 49.6%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-1 \cdot y + \frac{a \cdot c}{i}\right)} \]

      2. +-commutative 49.6%

         \[\leadsto \left(i \cdot j\right) \cdot \color{blue}{\left(\frac{a \cdot c}{i} + -1 \cdot y\right)} \]

      3. neg-mul-1 49.6%

         \[\leadsto \left(i \cdot j\right) \cdot \left(\frac{a \cdot c}{i} + \color{blue}{\left(-y\right)}\right) \]

      4. sub-neg 49.6%

         \[\leadsto \left(i \cdot j\right) \cdot \color{blue}{\left(\frac{a \cdot c}{i} - y\right)} \]

      5. associate-/l* 47.8%

         \[\leadsto \left(i \cdot j\right) \cdot \left(\color{blue}{a \cdot \frac{c}{i}} - y\right) \]

   8. Simplified 47.8%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(a \cdot \frac{c}{i} - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

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

Alternative 2: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \frac{j}{x} - t\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+193}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(a \cdot t\_1\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-275}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-248}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-189}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+213}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+215}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot a\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* c (/ j x)) t))
        (t_2 (- (* i (* y (- j))) (* b (* z c))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -5.2e+193)
     t_4
     (if (<= x -3.1e+51)
       (* x (* y (- z (* i (/ j x)))))
       (if (<= x -2.6e-20)
         (* x (* a t_1))
         (if (<= x -3.7e-55)
           t_2
           (if (<= x -1.5e-89)
             (- (* t (* b i)) (* x (* t a)))
             (if (<= x -2.4e-145)
               t_3
               (if (<= x -2.9e-255)
                 (* b (- (* t i) (* z c)))
                 (if (<= x -1.15e-275)
                   t_3
                   (if (<= x 9e-248)
                     (* i (- (* t b) (* y j)))
                     (if (<= x 1.45e-189)
                       t_3
                       (if (<= x 5e+36)
                         t_2
                         (if (<= x 2.1e+120)
                           (* y (- (* x z) (* i j)))
                           (if (<= x 6.5e+213)
                             t_4
                             (if (<= x 1.28e+215)
                               (* b (* z (- c)))
                               (* (* x a) t_1)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * (j / x)) - t;
	double t_2 = (i * (y * -j)) - (b * (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.2e+193) {
		tmp = t_4;
	} else if (x <= -3.1e+51) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -2.6e-20) {
		tmp = x * (a * t_1);
	} else if (x <= -3.7e-55) {
		tmp = t_2;
	} else if (x <= -1.5e-89) {
		tmp = (t * (b * i)) - (x * (t * a));
	} else if (x <= -2.4e-145) {
		tmp = t_3;
	} else if (x <= -2.9e-255) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= -1.15e-275) {
		tmp = t_3;
	} else if (x <= 9e-248) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 1.45e-189) {
		tmp = t_3;
	} else if (x <= 5e+36) {
		tmp = t_2;
	} else if (x <= 2.1e+120) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6.5e+213) {
		tmp = t_4;
	} else if (x <= 1.28e+215) {
		tmp = b * (z * -c);
	} else {
		tmp = (x * a) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (c * (j / x)) - t
    t_2 = (i * (y * -j)) - (b * (z * c))
    t_3 = j * ((a * c) - (y * i))
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-5.2d+193)) then
        tmp = t_4
    else if (x <= (-3.1d+51)) then
        tmp = x * (y * (z - (i * (j / x))))
    else if (x <= (-2.6d-20)) then
        tmp = x * (a * t_1)
    else if (x <= (-3.7d-55)) then
        tmp = t_2
    else if (x <= (-1.5d-89)) then
        tmp = (t * (b * i)) - (x * (t * a))
    else if (x <= (-2.4d-145)) then
        tmp = t_3
    else if (x <= (-2.9d-255)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= (-1.15d-275)) then
        tmp = t_3
    else if (x <= 9d-248) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= 1.45d-189) then
        tmp = t_3
    else if (x <= 5d+36) then
        tmp = t_2
    else if (x <= 2.1d+120) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 6.5d+213) then
        tmp = t_4
    else if (x <= 1.28d+215) then
        tmp = b * (z * -c)
    else
        tmp = (x * a) * 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 t_1 = (c * (j / x)) - t;
	double t_2 = (i * (y * -j)) - (b * (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.2e+193) {
		tmp = t_4;
	} else if (x <= -3.1e+51) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -2.6e-20) {
		tmp = x * (a * t_1);
	} else if (x <= -3.7e-55) {
		tmp = t_2;
	} else if (x <= -1.5e-89) {
		tmp = (t * (b * i)) - (x * (t * a));
	} else if (x <= -2.4e-145) {
		tmp = t_3;
	} else if (x <= -2.9e-255) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= -1.15e-275) {
		tmp = t_3;
	} else if (x <= 9e-248) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 1.45e-189) {
		tmp = t_3;
	} else if (x <= 5e+36) {
		tmp = t_2;
	} else if (x <= 2.1e+120) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6.5e+213) {
		tmp = t_4;
	} else if (x <= 1.28e+215) {
		tmp = b * (z * -c);
	} else {
		tmp = (x * a) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * (j / x)) - t
	t_2 = (i * (y * -j)) - (b * (z * c))
	t_3 = j * ((a * c) - (y * i))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.2e+193:
		tmp = t_4
	elif x <= -3.1e+51:
		tmp = x * (y * (z - (i * (j / x))))
	elif x <= -2.6e-20:
		tmp = x * (a * t_1)
	elif x <= -3.7e-55:
		tmp = t_2
	elif x <= -1.5e-89:
		tmp = (t * (b * i)) - (x * (t * a))
	elif x <= -2.4e-145:
		tmp = t_3
	elif x <= -2.9e-255:
		tmp = b * ((t * i) - (z * c))
	elif x <= -1.15e-275:
		tmp = t_3
	elif x <= 9e-248:
		tmp = i * ((t * b) - (y * j))
	elif x <= 1.45e-189:
		tmp = t_3
	elif x <= 5e+36:
		tmp = t_2
	elif x <= 2.1e+120:
		tmp = y * ((x * z) - (i * j))
	elif x <= 6.5e+213:
		tmp = t_4
	elif x <= 1.28e+215:
		tmp = b * (z * -c)
	else:
		tmp = (x * a) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * Float64(j / x)) - t)
	t_2 = Float64(Float64(i * Float64(y * Float64(-j))) - Float64(b * Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.2e+193)
		tmp = t_4;
	elseif (x <= -3.1e+51)
		tmp = Float64(x * Float64(y * Float64(z - Float64(i * Float64(j / x)))));
	elseif (x <= -2.6e-20)
		tmp = Float64(x * Float64(a * t_1));
	elseif (x <= -3.7e-55)
		tmp = t_2;
	elseif (x <= -1.5e-89)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(x * Float64(t * a)));
	elseif (x <= -2.4e-145)
		tmp = t_3;
	elseif (x <= -2.9e-255)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= -1.15e-275)
		tmp = t_3;
	elseif (x <= 9e-248)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= 1.45e-189)
		tmp = t_3;
	elseif (x <= 5e+36)
		tmp = t_2;
	elseif (x <= 2.1e+120)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 6.5e+213)
		tmp = t_4;
	elseif (x <= 1.28e+215)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(Float64(x * a) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * (j / x)) - t;
	t_2 = (i * (y * -j)) - (b * (z * c));
	t_3 = j * ((a * c) - (y * i));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5.2e+193)
		tmp = t_4;
	elseif (x <= -3.1e+51)
		tmp = x * (y * (z - (i * (j / x))));
	elseif (x <= -2.6e-20)
		tmp = x * (a * t_1);
	elseif (x <= -3.7e-55)
		tmp = t_2;
	elseif (x <= -1.5e-89)
		tmp = (t * (b * i)) - (x * (t * a));
	elseif (x <= -2.4e-145)
		tmp = t_3;
	elseif (x <= -2.9e-255)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= -1.15e-275)
		tmp = t_3;
	elseif (x <= 9e-248)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= 1.45e-189)
		tmp = t_3;
	elseif (x <= 5e+36)
		tmp = t_2;
	elseif (x <= 2.1e+120)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 6.5e+213)
		tmp = t_4;
	elseif (x <= 1.28e+215)
		tmp = b * (z * -c);
	else
		tmp = (x * a) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+193], t$95$4, If[LessEqual[x, -3.1e+51], N[(x * N[(y * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-20], N[(x * N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.7e-55], t$95$2, If[LessEqual[x, -1.5e-89], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-145], t$95$3, If[LessEqual[x, -2.9e-255], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-275], t$95$3, If[LessEqual[x, 9e-248], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e-189], t$95$3, If[LessEqual[x, 5e+36], t$95$2, If[LessEqual[x, 2.1e+120], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+213], t$95$4, If[LessEqual[x, 1.28e+215], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(N[(x * a), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if x < -5.20000000000000026e193 or 2.1e120 < x < 6.49999999999999982e213

   1. Initial program 80.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.8%

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

   if -5.20000000000000026e193 < x < -3.10000000000000011e51

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.7%

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

   4. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\left(-\frac{i \cdot j}{x}\right)}\right)\right) \]

      2. unsub-neg 63.1%

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

      3. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   if -3.10000000000000011e51 < x < -2.59999999999999995e-20

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.1%

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

   4. Taylor expanded in a around inf 71.1%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 71.2%

         \[\leadsto x \cdot \left(a \cdot \left(\color{blue}{c \cdot \frac{j}{x}} - t\right)\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)} \]

   if -2.59999999999999995e-20 < x < -3.69999999999999985e-55 or 1.45e-189 < x < 4.99999999999999977e36

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 63.9%

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

      1. associate-*r* 63.9%

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

      2. neg-mul-1 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in c around 0 62.1%

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

      1. associate-*r* 62.1%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 62.1%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 62.1%

      \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if -3.69999999999999985e-55 < x < -1.5e-89

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 87.2%

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

      1. distribute-lft-out-- 87.2%

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

      2. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in i around inf 63.9%

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

      1. +-commutative 63.9%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{i}\right)} \]

      2. mul-1-neg 63.9%

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

      3. unsub-neg 63.9%

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

      4. *-commutative 63.9%

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

      5. associate-*r* 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in i around 0 63.0%

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

       1. +-commutative 63.0%

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

       2. mul-1-neg 63.0%

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

       3. sub-neg 63.0%

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

       4. associate-*r* 87.2%

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

       5. *-commutative 87.2%

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

       6. associate-*r* 87.4%

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

       7. *-commutative 87.4%

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

   11. Simplified 87.4%

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

   if -1.5e-89 < x < -2.40000000000000015e-145 or -2.90000000000000007e-255 < x < -1.14999999999999995e-275 or 8.9999999999999992e-248 < x < 1.45e-189

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 82.0%

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

   if -2.40000000000000015e-145 < x < -2.90000000000000007e-255

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 62.6%

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

   if -1.14999999999999995e-275 < x < 8.9999999999999992e-248

   1. Initial program 91.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 78.1%

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

   4. Taylor expanded in c around 0 65.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 65.9%

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

      1. associate-*r* 65.9%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 65.9%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 65.9%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 65.9%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 65.9%

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

      6. *-commutative 65.9%

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

      7. unsub-neg 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in y around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-rgt-neg-in 65.6%

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

      3. distribute-rgt-neg-in 65.6%

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

   10. Simplified 65.6%

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

   11. Taylor expanded in i around inf 65.6%

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

       1. *-commutative 65.6%

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

   13. Simplified 65.6%

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

   if 4.99999999999999977e36 < x < 2.1e120

   1. Initial program 58.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. *-commutative 83.6%

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

      5. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   if 6.49999999999999982e213 < x < 1.27999999999999998e215

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

   8. Simplified 100.0%

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

   if 1.27999999999999998e215 < x

   1. Initial program 60.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.0%

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

   4. Taylor expanded in a around inf 65.2%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.3%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(\frac{c \cdot j}{x} - t\right)} \]

      2. associate-/l* 65.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{c \cdot \frac{j}{x}} - t\right) \]

   6. Simplified 65.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(c \cdot \frac{j}{x} - t\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-145}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-248}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-189}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+215}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(c \cdot \frac{j}{x} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ t_3 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_4 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+193}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+135}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -7.1 \cdot 10^{+19}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -1.22 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.38 \cdot 10^{+42}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+232}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* a (* c j)))
        (t_3 (* b (* z (- c))))
        (t_4 (* x (* t (- a)))))
   (if (<= c -1e+193)
     (* j (* a c))
     (if (<= c -3.8e+135)
       t_3
       (if (<= c -3.7e+130)
         t_2
         (if (<= c -3.8e+88)
           t_3
           (if (<= c -7.1e+19)
             t_4
             (if (<= c -1.22e-123)
               (* x (* y z))
               (if (<= c -1.65e-142)
                 t_3
                 (if (<= c -2.25e-234)
                   t_4
                   (if (<= c 2.45e-195)
                     t_1
                     (if (<= c 1.25e-132)
                       (* t (* x (- a)))
                       (if (<= c 3.7e-62)
                         t_1
                         (if (<= c 1.38e+42)
                           t_4
                           (if (<= c 6.2e+232) t_3 t_2)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = a * (c * j);
	double t_3 = b * (z * -c);
	double t_4 = x * (t * -a);
	double tmp;
	if (c <= -1e+193) {
		tmp = j * (a * c);
	} else if (c <= -3.8e+135) {
		tmp = t_3;
	} else if (c <= -3.7e+130) {
		tmp = t_2;
	} else if (c <= -3.8e+88) {
		tmp = t_3;
	} else if (c <= -7.1e+19) {
		tmp = t_4;
	} else if (c <= -1.22e-123) {
		tmp = x * (y * z);
	} else if (c <= -1.65e-142) {
		tmp = t_3;
	} else if (c <= -2.25e-234) {
		tmp = t_4;
	} else if (c <= 2.45e-195) {
		tmp = t_1;
	} else if (c <= 1.25e-132) {
		tmp = t * (x * -a);
	} else if (c <= 3.7e-62) {
		tmp = t_1;
	} else if (c <= 1.38e+42) {
		tmp = t_4;
	} else if (c <= 6.2e+232) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = a * (c * j)
    t_3 = b * (z * -c)
    t_4 = x * (t * -a)
    if (c <= (-1d+193)) then
        tmp = j * (a * c)
    else if (c <= (-3.8d+135)) then
        tmp = t_3
    else if (c <= (-3.7d+130)) then
        tmp = t_2
    else if (c <= (-3.8d+88)) then
        tmp = t_3
    else if (c <= (-7.1d+19)) then
        tmp = t_4
    else if (c <= (-1.22d-123)) then
        tmp = x * (y * z)
    else if (c <= (-1.65d-142)) then
        tmp = t_3
    else if (c <= (-2.25d-234)) then
        tmp = t_4
    else if (c <= 2.45d-195) then
        tmp = t_1
    else if (c <= 1.25d-132) then
        tmp = t * (x * -a)
    else if (c <= 3.7d-62) then
        tmp = t_1
    else if (c <= 1.38d+42) then
        tmp = t_4
    else if (c <= 6.2d+232) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = a * (c * j);
	double t_3 = b * (z * -c);
	double t_4 = x * (t * -a);
	double tmp;
	if (c <= -1e+193) {
		tmp = j * (a * c);
	} else if (c <= -3.8e+135) {
		tmp = t_3;
	} else if (c <= -3.7e+130) {
		tmp = t_2;
	} else if (c <= -3.8e+88) {
		tmp = t_3;
	} else if (c <= -7.1e+19) {
		tmp = t_4;
	} else if (c <= -1.22e-123) {
		tmp = x * (y * z);
	} else if (c <= -1.65e-142) {
		tmp = t_3;
	} else if (c <= -2.25e-234) {
		tmp = t_4;
	} else if (c <= 2.45e-195) {
		tmp = t_1;
	} else if (c <= 1.25e-132) {
		tmp = t * (x * -a);
	} else if (c <= 3.7e-62) {
		tmp = t_1;
	} else if (c <= 1.38e+42) {
		tmp = t_4;
	} else if (c <= 6.2e+232) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * (c * j)
	t_3 = b * (z * -c)
	t_4 = x * (t * -a)
	tmp = 0
	if c <= -1e+193:
		tmp = j * (a * c)
	elif c <= -3.8e+135:
		tmp = t_3
	elif c <= -3.7e+130:
		tmp = t_2
	elif c <= -3.8e+88:
		tmp = t_3
	elif c <= -7.1e+19:
		tmp = t_4
	elif c <= -1.22e-123:
		tmp = x * (y * z)
	elif c <= -1.65e-142:
		tmp = t_3
	elif c <= -2.25e-234:
		tmp = t_4
	elif c <= 2.45e-195:
		tmp = t_1
	elif c <= 1.25e-132:
		tmp = t * (x * -a)
	elif c <= 3.7e-62:
		tmp = t_1
	elif c <= 1.38e+42:
		tmp = t_4
	elif c <= 6.2e+232:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(c * j))
	t_3 = Float64(b * Float64(z * Float64(-c)))
	t_4 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (c <= -1e+193)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= -3.8e+135)
		tmp = t_3;
	elseif (c <= -3.7e+130)
		tmp = t_2;
	elseif (c <= -3.8e+88)
		tmp = t_3;
	elseif (c <= -7.1e+19)
		tmp = t_4;
	elseif (c <= -1.22e-123)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -1.65e-142)
		tmp = t_3;
	elseif (c <= -2.25e-234)
		tmp = t_4;
	elseif (c <= 2.45e-195)
		tmp = t_1;
	elseif (c <= 1.25e-132)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 3.7e-62)
		tmp = t_1;
	elseif (c <= 1.38e+42)
		tmp = t_4;
	elseif (c <= 6.2e+232)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = a * (c * j);
	t_3 = b * (z * -c);
	t_4 = x * (t * -a);
	tmp = 0.0;
	if (c <= -1e+193)
		tmp = j * (a * c);
	elseif (c <= -3.8e+135)
		tmp = t_3;
	elseif (c <= -3.7e+130)
		tmp = t_2;
	elseif (c <= -3.8e+88)
		tmp = t_3;
	elseif (c <= -7.1e+19)
		tmp = t_4;
	elseif (c <= -1.22e-123)
		tmp = x * (y * z);
	elseif (c <= -1.65e-142)
		tmp = t_3;
	elseif (c <= -2.25e-234)
		tmp = t_4;
	elseif (c <= 2.45e-195)
		tmp = t_1;
	elseif (c <= 1.25e-132)
		tmp = t * (x * -a);
	elseif (c <= 3.7e-62)
		tmp = t_1;
	elseif (c <= 1.38e+42)
		tmp = t_4;
	elseif (c <= 6.2e+232)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+193], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.8e+135], t$95$3, If[LessEqual[c, -3.7e+130], t$95$2, If[LessEqual[c, -3.8e+88], t$95$3, If[LessEqual[c, -7.1e+19], t$95$4, If[LessEqual[c, -1.22e-123], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.65e-142], t$95$3, If[LessEqual[c, -2.25e-234], t$95$4, If[LessEqual[c, 2.45e-195], t$95$1, If[LessEqual[c, 1.25e-132], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e-62], t$95$1, If[LessEqual[c, 1.38e+42], t$95$4, If[LessEqual[c, 6.2e+232], t$95$3, t$95$2]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.00000000000000007e193

   1. Initial program 26.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 64.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 64.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 71.1%

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

      1. associate-*r* 75.1%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 75.1%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -1.00000000000000007e193 < c < -3.8000000000000001e135 or -3.7000000000000001e130 < c < -3.7999999999999997e88 or -1.22e-123 < c < -1.6499999999999998e-142 or 1.3800000000000001e42 < c < 6.19999999999999966e232

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.6%

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

      2. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. distribute-rgt-neg-in 45.2%

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

      3. distribute-lft-neg-in 45.2%

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

   8. Simplified 45.2%

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

   if -3.8000000000000001e135 < c < -3.7000000000000001e130 or 6.19999999999999966e232 < c

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 72.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 72.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 72.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 72.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 72.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 61.7%

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

      1. *-commutative 61.7%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 61.7%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -3.7999999999999997e88 < c < -7.1e19 or -1.6499999999999998e-142 < c < -2.25000000000000005e-234 or 3.6999999999999998e-62 < c < 1.3800000000000001e42

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 86.7%

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

   4. Taylor expanded in c around 0 77.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around inf 74.3%

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

      1. +-commutative 74.3%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} + -1 \cdot j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in a around inf 36.7%

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

      1. mul-1-neg 36.7%

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

      2. *-commutative 36.7%

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

      3. *-commutative 36.7%

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

      4. associate-*r* 43.1%

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

      5. distribute-rgt-neg-in 43.1%

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

   10. Simplified 43.1%

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

   if -7.1e19 < c < -1.22e-123

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.9%

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

      2. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in y around inf 37.3%

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

   if -2.25000000000000005e-234 < c < 2.4500000000000002e-195 or 1.25e-132 < c < 3.6999999999999998e-62

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 36.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.6%

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

      2. *-commutative 36.6%

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

   5. Simplified 36.6%

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

   6. Taylor expanded in y around inf 32.9%

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

      1. *-commutative 32.9%

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

   8. Simplified 32.9%

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

   if 2.4500000000000002e-195 < c < 1.25e-132

   1. Initial program 90.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.4%

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

      1. distribute-lft-out-- 82.4%

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

      2. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in a around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. *-commutative 47.0%

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

      3. associate-*r* 55.7%

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

      4. *-commutative 55.7%

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

      5. distribute-rgt-neg-out 55.7%

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

      6. *-commutative 55.7%

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

      7. distribute-rgt-neg-in 55.7%

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

   8. Simplified 55.7%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+193}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+135}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{+130}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -7.1 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.22 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-142}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-132}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.38 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := i \cdot \left(t \cdot b\right) + t\_1\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+113}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + t\_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+161}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* i (* t b)) t_1))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -5e+113)
     t_3
     (if (<= y -1.7e-70)
       (* x (- (* y z) (* t a)))
       (if (<= y -8.4e-86)
         t_2
         (if (<= y -5e-123)
           (* t (- (* b i) (* x a)))
           (if (<= y -1e-132)
             (+ (* x (* y z)) t_1)
             (if (<= y 2.15e+71)
               (- (* c (- (* a j) (* z b))) (* a (* x t)))
               (if (<= y 4.3e+126)
                 t_2
                 (if (<= y 1.05e+161)
                   t_3
                   (if (<= y 8e+187)
                     t_1
                     (if (<= y 4.4e+191)
                       (- (* i (* y (- j))) (* b (* z c)))
                       (if (<= y 3.4e+258)
                         (* c (* z (- (/ (* x y) c) b)))
                         t_3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (i * (t * b)) + t_1;
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5e+113) {
		tmp = t_3;
	} else if (y <= -1.7e-70) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= -8.4e-86) {
		tmp = t_2;
	} else if (y <= -5e-123) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= -1e-132) {
		tmp = (x * (y * z)) + t_1;
	} else if (y <= 2.15e+71) {
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	} else if (y <= 4.3e+126) {
		tmp = t_2;
	} else if (y <= 1.05e+161) {
		tmp = t_3;
	} else if (y <= 8e+187) {
		tmp = t_1;
	} else if (y <= 4.4e+191) {
		tmp = (i * (y * -j)) - (b * (z * c));
	} else if (y <= 3.4e+258) {
		tmp = c * (z * (((x * y) / c) - b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (i * (t * b)) + t_1
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-5d+113)) then
        tmp = t_3
    else if (y <= (-1.7d-70)) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= (-8.4d-86)) then
        tmp = t_2
    else if (y <= (-5d-123)) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= (-1d-132)) then
        tmp = (x * (y * z)) + t_1
    else if (y <= 2.15d+71) then
        tmp = (c * ((a * j) - (z * b))) - (a * (x * t))
    else if (y <= 4.3d+126) then
        tmp = t_2
    else if (y <= 1.05d+161) then
        tmp = t_3
    else if (y <= 8d+187) then
        tmp = t_1
    else if (y <= 4.4d+191) then
        tmp = (i * (y * -j)) - (b * (z * c))
    else if (y <= 3.4d+258) then
        tmp = c * (z * (((x * y) / c) - b))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (i * (t * b)) + t_1;
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5e+113) {
		tmp = t_3;
	} else if (y <= -1.7e-70) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= -8.4e-86) {
		tmp = t_2;
	} else if (y <= -5e-123) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= -1e-132) {
		tmp = (x * (y * z)) + t_1;
	} else if (y <= 2.15e+71) {
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	} else if (y <= 4.3e+126) {
		tmp = t_2;
	} else if (y <= 1.05e+161) {
		tmp = t_3;
	} else if (y <= 8e+187) {
		tmp = t_1;
	} else if (y <= 4.4e+191) {
		tmp = (i * (y * -j)) - (b * (z * c));
	} else if (y <= 3.4e+258) {
		tmp = c * (z * (((x * y) / c) - b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (i * (t * b)) + t_1
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5e+113:
		tmp = t_3
	elif y <= -1.7e-70:
		tmp = x * ((y * z) - (t * a))
	elif y <= -8.4e-86:
		tmp = t_2
	elif y <= -5e-123:
		tmp = t * ((b * i) - (x * a))
	elif y <= -1e-132:
		tmp = (x * (y * z)) + t_1
	elif y <= 2.15e+71:
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t))
	elif y <= 4.3e+126:
		tmp = t_2
	elif y <= 1.05e+161:
		tmp = t_3
	elif y <= 8e+187:
		tmp = t_1
	elif y <= 4.4e+191:
		tmp = (i * (y * -j)) - (b * (z * c))
	elif y <= 3.4e+258:
		tmp = c * (z * (((x * y) / c) - b))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(i * Float64(t * b)) + t_1)
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5e+113)
		tmp = t_3;
	elseif (y <= -1.7e-70)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= -8.4e-86)
		tmp = t_2;
	elseif (y <= -5e-123)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= -1e-132)
		tmp = Float64(Float64(x * Float64(y * z)) + t_1);
	elseif (y <= 2.15e+71)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(a * Float64(x * t)));
	elseif (y <= 4.3e+126)
		tmp = t_2;
	elseif (y <= 1.05e+161)
		tmp = t_3;
	elseif (y <= 8e+187)
		tmp = t_1;
	elseif (y <= 4.4e+191)
		tmp = Float64(Float64(i * Float64(y * Float64(-j))) - Float64(b * Float64(z * c)));
	elseif (y <= 3.4e+258)
		tmp = Float64(c * Float64(z * Float64(Float64(Float64(x * y) / c) - b)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (i * (t * b)) + t_1;
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5e+113)
		tmp = t_3;
	elseif (y <= -1.7e-70)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= -8.4e-86)
		tmp = t_2;
	elseif (y <= -5e-123)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= -1e-132)
		tmp = (x * (y * z)) + t_1;
	elseif (y <= 2.15e+71)
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	elseif (y <= 4.3e+126)
		tmp = t_2;
	elseif (y <= 1.05e+161)
		tmp = t_3;
	elseif (y <= 8e+187)
		tmp = t_1;
	elseif (y <= 4.4e+191)
		tmp = (i * (y * -j)) - (b * (z * c));
	elseif (y <= 3.4e+258)
		tmp = c * (z * (((x * y) / c) - b));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+113], t$95$3, If[LessEqual[y, -1.7e-70], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.4e-86], t$95$2, If[LessEqual[y, -5e-123], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-132], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 2.15e+71], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+126], t$95$2, If[LessEqual[y, 1.05e+161], t$95$3, If[LessEqual[y, 8e+187], t$95$1, If[LessEqual[y, 4.4e+191], N[(N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+258], N[(c * N[(z * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -5e113 or 4.3000000000000002e126 < y < 1.05e161 or 3.39999999999999981e258 < y

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

      5. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   if -5e113 < y < -1.69999999999999998e-70

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 48.3%

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

   if -1.69999999999999998e-70 < y < -8.4e-86 or 2.14999999999999992e71 < y < 4.3000000000000002e126

   1. Initial program 92.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.9%

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

      1. associate-*r* 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 73.0%

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

   5. Simplified 73.0%

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

   if -8.4e-86 < y < -5.0000000000000003e-123

   1. Initial program 83.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 75.3%

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

   4. Taylor expanded in t around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. *-commutative 67.3%

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

      5. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   if -5.0000000000000003e-123 < y < -9.9999999999999999e-133

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.0%

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

   if -9.9999999999999999e-133 < y < 2.14999999999999992e71

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 76.3%

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

   4. Taylor expanded in c around 0 87.6%

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

   5. Taylor expanded in a around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. *-commutative 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

   7. Simplified 70.9%

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

   if 1.05e161 < y < 7.99999999999999926e187

   1. Initial program 41.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 100.0%

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

   if 7.99999999999999926e187 < y < 4.4e191

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in c around 0 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 100.0%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 100.0%

      \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 4.4e191 < y < 3.39999999999999981e258

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 44.5%

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

      1. +-commutative 44.5%

         \[\leadsto c \cdot \color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{c} + -1 \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

      4. associate-/l* 51.4%

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

      5. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 72.1%

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

   11. Simplified 72.1%

       \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(\frac{y \cdot x}{c} - b\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+187}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{-19}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+228} \lor \neg \left(x \leq 6.2 \cdot 10^{+228}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -1.85e-19)
     t_3
     (if (<= x -2.3e-48)
       (* b (* z (- c)))
       (if (<= x -3e-79)
         t_1
         (if (<= x -3.4e-147)
           t_2
           (if (<= x -1.15e-220)
             (* b (- (* t i) (* z c)))
             (if (<= x 1.55e-152)
               t_2
               (if (<= x 2.95e+65)
                 t_1
                 (if (<= x 3.9e+153)
                   t_3
                   (if (<= x 2.25e+154)
                     (* a (- (* c j) (* x t)))
                     (if (or (<= x 6e+228) (not (<= x 6.2e+228)))
                       t_3
                       (* a (* c j))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.85e-19) {
		tmp = t_3;
	} else if (x <= -2.3e-48) {
		tmp = b * (z * -c);
	} else if (x <= -3e-79) {
		tmp = t_1;
	} else if (x <= -3.4e-147) {
		tmp = t_2;
	} else if (x <= -1.15e-220) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.55e-152) {
		tmp = t_2;
	} else if (x <= 2.95e+65) {
		tmp = t_1;
	} else if (x <= 3.9e+153) {
		tmp = t_3;
	} else if (x <= 2.25e+154) {
		tmp = a * ((c * j) - (x * t));
	} else if ((x <= 6e+228) || !(x <= 6.2e+228)) {
		tmp = t_3;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-1.85d-19)) then
        tmp = t_3
    else if (x <= (-2.3d-48)) then
        tmp = b * (z * -c)
    else if (x <= (-3d-79)) then
        tmp = t_1
    else if (x <= (-3.4d-147)) then
        tmp = t_2
    else if (x <= (-1.15d-220)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 1.55d-152) then
        tmp = t_2
    else if (x <= 2.95d+65) then
        tmp = t_1
    else if (x <= 3.9d+153) then
        tmp = t_3
    else if (x <= 2.25d+154) then
        tmp = a * ((c * j) - (x * t))
    else if ((x <= 6d+228) .or. (.not. (x <= 6.2d+228))) then
        tmp = t_3
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.85e-19) {
		tmp = t_3;
	} else if (x <= -2.3e-48) {
		tmp = b * (z * -c);
	} else if (x <= -3e-79) {
		tmp = t_1;
	} else if (x <= -3.4e-147) {
		tmp = t_2;
	} else if (x <= -1.15e-220) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.55e-152) {
		tmp = t_2;
	} else if (x <= 2.95e+65) {
		tmp = t_1;
	} else if (x <= 3.9e+153) {
		tmp = t_3;
	} else if (x <= 2.25e+154) {
		tmp = a * ((c * j) - (x * t));
	} else if ((x <= 6e+228) || !(x <= 6.2e+228)) {
		tmp = t_3;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = j * ((a * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.85e-19:
		tmp = t_3
	elif x <= -2.3e-48:
		tmp = b * (z * -c)
	elif x <= -3e-79:
		tmp = t_1
	elif x <= -3.4e-147:
		tmp = t_2
	elif x <= -1.15e-220:
		tmp = b * ((t * i) - (z * c))
	elif x <= 1.55e-152:
		tmp = t_2
	elif x <= 2.95e+65:
		tmp = t_1
	elif x <= 3.9e+153:
		tmp = t_3
	elif x <= 2.25e+154:
		tmp = a * ((c * j) - (x * t))
	elif (x <= 6e+228) or not (x <= 6.2e+228):
		tmp = t_3
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.85e-19)
		tmp = t_3;
	elseif (x <= -2.3e-48)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -3e-79)
		tmp = t_1;
	elseif (x <= -3.4e-147)
		tmp = t_2;
	elseif (x <= -1.15e-220)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 1.55e-152)
		tmp = t_2;
	elseif (x <= 2.95e+65)
		tmp = t_1;
	elseif (x <= 3.9e+153)
		tmp = t_3;
	elseif (x <= 2.25e+154)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif ((x <= 6e+228) || !(x <= 6.2e+228))
		tmp = t_3;
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = j * ((a * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.85e-19)
		tmp = t_3;
	elseif (x <= -2.3e-48)
		tmp = b * (z * -c);
	elseif (x <= -3e-79)
		tmp = t_1;
	elseif (x <= -3.4e-147)
		tmp = t_2;
	elseif (x <= -1.15e-220)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 1.55e-152)
		tmp = t_2;
	elseif (x <= 2.95e+65)
		tmp = t_1;
	elseif (x <= 3.9e+153)
		tmp = t_3;
	elseif (x <= 2.25e+154)
		tmp = a * ((c * j) - (x * t));
	elseif ((x <= 6e+228) || ~((x <= 6.2e+228)))
		tmp = t_3;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e-19], t$95$3, If[LessEqual[x, -2.3e-48], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e-79], t$95$1, If[LessEqual[x, -3.4e-147], t$95$2, If[LessEqual[x, -1.15e-220], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-152], t$95$2, If[LessEqual[x, 2.95e+65], t$95$1, If[LessEqual[x, 3.9e+153], t$95$3, If[LessEqual[x, 2.25e+154], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 6e+228], N[Not[LessEqual[x, 6.2e+228]], $MachinePrecision]], t$95$3, N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.85000000000000003e-19 or 2.9500000000000001e65 < x < 3.89999999999999983e153 or 2.25000000000000005e154 < x < 6.0000000000000002e228 or 6.1999999999999997e228 < x

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.4%

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

   if -1.85000000000000003e-19 < x < -2.3000000000000001e-48

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. distribute-rgt-neg-in 83.6%

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

      3. distribute-lft-neg-in 83.6%

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

   8. Simplified 83.6%

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

   if -2.3000000000000001e-48 < x < -3e-79 or 1.5499999999999999e-152 < x < 2.9500000000000001e65

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 78.4%

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

   4. Taylor expanded in c around 0 76.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 76.6%

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

      1. associate-*r* 76.6%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 76.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 76.6%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 76.6%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 76.6%

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

      6. *-commutative 76.6%

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

      7. unsub-neg 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in y around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-rgt-neg-in 70.8%

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

      3. distribute-rgt-neg-in 70.8%

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

   10. Simplified 70.8%

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

   11. Taylor expanded in i around inf 53.3%

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

       1. *-commutative 53.3%

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

   13. Simplified 53.3%

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

   if -3e-79 < x < -3.39999999999999996e-147 or -1.1499999999999999e-220 < x < 1.5499999999999999e-152

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 66.7%

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

   if -3.39999999999999996e-147 < x < -1.1499999999999999e-220

   1. Initial program 59.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 71.0%

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

   if 3.89999999999999983e153 < x < 2.25000000000000005e154

   1. Initial program 50.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 100.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 6.0000000000000002e228 < x < 6.1999999999999997e228

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 0.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 0.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 0.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 0.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 0.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 0.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 100.0%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-79}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+228} \lor \neg \left(x \leq 6.2 \cdot 10^{+228}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+192}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + t\_4\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + t\_4\\ \mathbf{elif}\;x \leq 0.009:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (* b i)) (* x (* t a))))
        (t_2 (- (* i (* y (- j))) (* b (* z c))))
        (t_3 (* x (- (* y z) (* t a))))
        (t_4 (* j (- (* a c) (* y i)))))
   (if (<= x -5.4e+192)
     t_3
     (if (<= x -2.9e+54)
       (* x (* y (- z (* i (/ j x)))))
       (if (<= x -2.05e-19)
         (* x (* a (- (* c (/ j x)) t)))
         (if (<= x -2.1e-55)
           t_2
           (if (<= x -7.4e-88)
             t_1
             (if (<= x -1.45e-140)
               (+ (* x (* y z)) t_4)
               (if (<= x -1.15e-210)
                 (* b (- (* t i) (* z c)))
                 (if (<= x 1.55e-146)
                   (+ (* i (* t b)) t_4)
                   (if (<= x 0.009)
                     t_2
                     (if (<= x 2.65e+20)
                       t_1
                       (if (<= x 4.8e+64)
                         (* y (- (* x z) (* i j)))
                         t_3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (b * i)) - (x * (t * a));
	double t_2 = (i * (y * -j)) - (b * (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -5.4e+192) {
		tmp = t_3;
	} else if (x <= -2.9e+54) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -2.05e-19) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -2.1e-55) {
		tmp = t_2;
	} else if (x <= -7.4e-88) {
		tmp = t_1;
	} else if (x <= -1.45e-140) {
		tmp = (x * (y * z)) + t_4;
	} else if (x <= -1.15e-210) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.55e-146) {
		tmp = (i * (t * b)) + t_4;
	} else if (x <= 0.009) {
		tmp = t_2;
	} else if (x <= 2.65e+20) {
		tmp = t_1;
	} else if (x <= 4.8e+64) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t * (b * i)) - (x * (t * a))
    t_2 = (i * (y * -j)) - (b * (z * c))
    t_3 = x * ((y * z) - (t * a))
    t_4 = j * ((a * c) - (y * i))
    if (x <= (-5.4d+192)) then
        tmp = t_3
    else if (x <= (-2.9d+54)) then
        tmp = x * (y * (z - (i * (j / x))))
    else if (x <= (-2.05d-19)) then
        tmp = x * (a * ((c * (j / x)) - t))
    else if (x <= (-2.1d-55)) then
        tmp = t_2
    else if (x <= (-7.4d-88)) then
        tmp = t_1
    else if (x <= (-1.45d-140)) then
        tmp = (x * (y * z)) + t_4
    else if (x <= (-1.15d-210)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 1.55d-146) then
        tmp = (i * (t * b)) + t_4
    else if (x <= 0.009d0) then
        tmp = t_2
    else if (x <= 2.65d+20) then
        tmp = t_1
    else if (x <= 4.8d+64) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (b * i)) - (x * (t * a));
	double t_2 = (i * (y * -j)) - (b * (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -5.4e+192) {
		tmp = t_3;
	} else if (x <= -2.9e+54) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -2.05e-19) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -2.1e-55) {
		tmp = t_2;
	} else if (x <= -7.4e-88) {
		tmp = t_1;
	} else if (x <= -1.45e-140) {
		tmp = (x * (y * z)) + t_4;
	} else if (x <= -1.15e-210) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.55e-146) {
		tmp = (i * (t * b)) + t_4;
	} else if (x <= 0.009) {
		tmp = t_2;
	} else if (x <= 2.65e+20) {
		tmp = t_1;
	} else if (x <= 4.8e+64) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (b * i)) - (x * (t * a))
	t_2 = (i * (y * -j)) - (b * (z * c))
	t_3 = x * ((y * z) - (t * a))
	t_4 = j * ((a * c) - (y * i))
	tmp = 0
	if x <= -5.4e+192:
		tmp = t_3
	elif x <= -2.9e+54:
		tmp = x * (y * (z - (i * (j / x))))
	elif x <= -2.05e-19:
		tmp = x * (a * ((c * (j / x)) - t))
	elif x <= -2.1e-55:
		tmp = t_2
	elif x <= -7.4e-88:
		tmp = t_1
	elif x <= -1.45e-140:
		tmp = (x * (y * z)) + t_4
	elif x <= -1.15e-210:
		tmp = b * ((t * i) - (z * c))
	elif x <= 1.55e-146:
		tmp = (i * (t * b)) + t_4
	elif x <= 0.009:
		tmp = t_2
	elif x <= 2.65e+20:
		tmp = t_1
	elif x <= 4.8e+64:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(b * i)) - Float64(x * Float64(t * a)))
	t_2 = Float64(Float64(i * Float64(y * Float64(-j))) - Float64(b * Float64(z * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_4 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -5.4e+192)
		tmp = t_3;
	elseif (x <= -2.9e+54)
		tmp = Float64(x * Float64(y * Float64(z - Float64(i * Float64(j / x)))));
	elseif (x <= -2.05e-19)
		tmp = Float64(x * Float64(a * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (x <= -2.1e-55)
		tmp = t_2;
	elseif (x <= -7.4e-88)
		tmp = t_1;
	elseif (x <= -1.45e-140)
		tmp = Float64(Float64(x * Float64(y * z)) + t_4);
	elseif (x <= -1.15e-210)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 1.55e-146)
		tmp = Float64(Float64(i * Float64(t * b)) + t_4);
	elseif (x <= 0.009)
		tmp = t_2;
	elseif (x <= 2.65e+20)
		tmp = t_1;
	elseif (x <= 4.8e+64)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (b * i)) - (x * (t * a));
	t_2 = (i * (y * -j)) - (b * (z * c));
	t_3 = x * ((y * z) - (t * a));
	t_4 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -5.4e+192)
		tmp = t_3;
	elseif (x <= -2.9e+54)
		tmp = x * (y * (z - (i * (j / x))));
	elseif (x <= -2.05e-19)
		tmp = x * (a * ((c * (j / x)) - t));
	elseif (x <= -2.1e-55)
		tmp = t_2;
	elseif (x <= -7.4e-88)
		tmp = t_1;
	elseif (x <= -1.45e-140)
		tmp = (x * (y * z)) + t_4;
	elseif (x <= -1.15e-210)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 1.55e-146)
		tmp = (i * (t * b)) + t_4;
	elseif (x <= 0.009)
		tmp = t_2;
	elseif (x <= 2.65e+20)
		tmp = t_1;
	elseif (x <= 4.8e+64)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+192], t$95$3, If[LessEqual[x, -2.9e+54], N[(x * N[(y * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.05e-19], N[(x * N[(a * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-55], t$95$2, If[LessEqual[x, -7.4e-88], t$95$1, If[LessEqual[x, -1.45e-140], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[x, -1.15e-210], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-146], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[x, 0.009], t$95$2, If[LessEqual[x, 2.65e+20], t$95$1, If[LessEqual[x, 4.8e+64], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -5.39999999999999979e192 or 4.79999999999999999e64 < x

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.1%

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

   if -5.39999999999999979e192 < x < -2.8999999999999999e54

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.7%

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

   4. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\left(-\frac{i \cdot j}{x}\right)}\right)\right) \]

      2. unsub-neg 63.1%

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

      3. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   if -2.8999999999999999e54 < x < -2.04999999999999993e-19

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.1%

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

   4. Taylor expanded in a around inf 71.1%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 71.2%

         \[\leadsto x \cdot \left(a \cdot \left(\color{blue}{c \cdot \frac{j}{x}} - t\right)\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)} \]

   if -2.04999999999999993e-19 < x < -2.1000000000000002e-55 or 1.5499999999999999e-146 < x < 0.00899999999999999932

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 65.6%

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

      1. associate-*r* 65.6%

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

      2. neg-mul-1 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around 0 68.1%

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

      1. associate-*r* 68.1%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 68.1%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 68.1%

      \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if -2.1000000000000002e-55 < x < -7.3999999999999995e-88 or 0.00899999999999999932 < x < 2.65e20

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.3%

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

      1. distribute-lft-out-- 85.3%

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

      2. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in i around inf 68.3%

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

      1. +-commutative 68.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{i}\right)} \]

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

      5. associate-*r* 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in i around 0 67.7%

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

       1. +-commutative 67.7%

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

       2. mul-1-neg 67.7%

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

       3. sub-neg 67.7%

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

       4. associate-*r* 85.3%

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

       5. *-commutative 85.3%

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

       6. associate-*r* 85.4%

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

       7. *-commutative 85.4%

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

   11. Simplified 85.4%

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

   if -7.3999999999999995e-88 < x < -1.44999999999999999e-140

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.9%

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

   if -1.44999999999999999e-140 < x < -1.15e-210

   1. Initial program 50.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.3%

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

   if -1.15e-210 < x < 1.5499999999999999e-146

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.0%

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

      1. associate-*r* 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*r* 73.7%

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

   5. Simplified 73.7%

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

   if 2.65e20 < x < 4.79999999999999999e64

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. unsub-neg 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

   5. Simplified 85.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 0.009:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+193}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.3 \cdot 10^{-137}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + t\_3\\ \mathbf{elif}\;x \leq 0.009:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (* b i)) (* x (* t a))))
        (t_2 (- (* i (* y (- j))) (* b (* z c))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -4.5e+193)
     t_4
     (if (<= x -2.55e+54)
       (* x (* y (- z (* i (/ j x)))))
       (if (<= x -8e-21)
         (* x (* a (- (* c (/ j x)) t)))
         (if (<= x -2.5e-55)
           t_2
           (if (<= x -7.8e-88)
             t_1
             (if (<= x -7.3e-137)
               t_3
               (if (<= x -1.28e-210)
                 (* b (- (* t i) (* z c)))
                 (if (<= x 2.05e-146)
                   (+ (* i (* t b)) t_3)
                   (if (<= x 0.009)
                     t_2
                     (if (<= x 7.2e+17)
                       t_1
                       (if (<= x 2.9e+63)
                         (* y (- (* x z) (* i j)))
                         t_4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (b * i)) - (x * (t * a));
	double t_2 = (i * (y * -j)) - (b * (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.5e+193) {
		tmp = t_4;
	} else if (x <= -2.55e+54) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -8e-21) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -2.5e-55) {
		tmp = t_2;
	} else if (x <= -7.8e-88) {
		tmp = t_1;
	} else if (x <= -7.3e-137) {
		tmp = t_3;
	} else if (x <= -1.28e-210) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 2.05e-146) {
		tmp = (i * (t * b)) + t_3;
	} else if (x <= 0.009) {
		tmp = t_2;
	} else if (x <= 7.2e+17) {
		tmp = t_1;
	} else if (x <= 2.9e+63) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t * (b * i)) - (x * (t * a))
    t_2 = (i * (y * -j)) - (b * (z * c))
    t_3 = j * ((a * c) - (y * i))
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-4.5d+193)) then
        tmp = t_4
    else if (x <= (-2.55d+54)) then
        tmp = x * (y * (z - (i * (j / x))))
    else if (x <= (-8d-21)) then
        tmp = x * (a * ((c * (j / x)) - t))
    else if (x <= (-2.5d-55)) then
        tmp = t_2
    else if (x <= (-7.8d-88)) then
        tmp = t_1
    else if (x <= (-7.3d-137)) then
        tmp = t_3
    else if (x <= (-1.28d-210)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 2.05d-146) then
        tmp = (i * (t * b)) + t_3
    else if (x <= 0.009d0) then
        tmp = t_2
    else if (x <= 7.2d+17) then
        tmp = t_1
    else if (x <= 2.9d+63) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (b * i)) - (x * (t * a));
	double t_2 = (i * (y * -j)) - (b * (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.5e+193) {
		tmp = t_4;
	} else if (x <= -2.55e+54) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -8e-21) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -2.5e-55) {
		tmp = t_2;
	} else if (x <= -7.8e-88) {
		tmp = t_1;
	} else if (x <= -7.3e-137) {
		tmp = t_3;
	} else if (x <= -1.28e-210) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 2.05e-146) {
		tmp = (i * (t * b)) + t_3;
	} else if (x <= 0.009) {
		tmp = t_2;
	} else if (x <= 7.2e+17) {
		tmp = t_1;
	} else if (x <= 2.9e+63) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (b * i)) - (x * (t * a))
	t_2 = (i * (y * -j)) - (b * (z * c))
	t_3 = j * ((a * c) - (y * i))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.5e+193:
		tmp = t_4
	elif x <= -2.55e+54:
		tmp = x * (y * (z - (i * (j / x))))
	elif x <= -8e-21:
		tmp = x * (a * ((c * (j / x)) - t))
	elif x <= -2.5e-55:
		tmp = t_2
	elif x <= -7.8e-88:
		tmp = t_1
	elif x <= -7.3e-137:
		tmp = t_3
	elif x <= -1.28e-210:
		tmp = b * ((t * i) - (z * c))
	elif x <= 2.05e-146:
		tmp = (i * (t * b)) + t_3
	elif x <= 0.009:
		tmp = t_2
	elif x <= 7.2e+17:
		tmp = t_1
	elif x <= 2.9e+63:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(b * i)) - Float64(x * Float64(t * a)))
	t_2 = Float64(Float64(i * Float64(y * Float64(-j))) - Float64(b * Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.5e+193)
		tmp = t_4;
	elseif (x <= -2.55e+54)
		tmp = Float64(x * Float64(y * Float64(z - Float64(i * Float64(j / x)))));
	elseif (x <= -8e-21)
		tmp = Float64(x * Float64(a * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (x <= -2.5e-55)
		tmp = t_2;
	elseif (x <= -7.8e-88)
		tmp = t_1;
	elseif (x <= -7.3e-137)
		tmp = t_3;
	elseif (x <= -1.28e-210)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 2.05e-146)
		tmp = Float64(Float64(i * Float64(t * b)) + t_3);
	elseif (x <= 0.009)
		tmp = t_2;
	elseif (x <= 7.2e+17)
		tmp = t_1;
	elseif (x <= 2.9e+63)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (b * i)) - (x * (t * a));
	t_2 = (i * (y * -j)) - (b * (z * c));
	t_3 = j * ((a * c) - (y * i));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.5e+193)
		tmp = t_4;
	elseif (x <= -2.55e+54)
		tmp = x * (y * (z - (i * (j / x))));
	elseif (x <= -8e-21)
		tmp = x * (a * ((c * (j / x)) - t));
	elseif (x <= -2.5e-55)
		tmp = t_2;
	elseif (x <= -7.8e-88)
		tmp = t_1;
	elseif (x <= -7.3e-137)
		tmp = t_3;
	elseif (x <= -1.28e-210)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 2.05e-146)
		tmp = (i * (t * b)) + t_3;
	elseif (x <= 0.009)
		tmp = t_2;
	elseif (x <= 7.2e+17)
		tmp = t_1;
	elseif (x <= 2.9e+63)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+193], t$95$4, If[LessEqual[x, -2.55e+54], N[(x * N[(y * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-21], N[(x * N[(a * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-55], t$95$2, If[LessEqual[x, -7.8e-88], t$95$1, If[LessEqual[x, -7.3e-137], t$95$3, If[LessEqual[x, -1.28e-210], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-146], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[x, 0.009], t$95$2, If[LessEqual[x, 7.2e+17], t$95$1, If[LessEqual[x, 2.9e+63], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -4.49999999999999999e193 or 2.8999999999999999e63 < x

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.1%

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

   if -4.49999999999999999e193 < x < -2.55000000000000005e54

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.7%

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

   4. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\left(-\frac{i \cdot j}{x}\right)}\right)\right) \]

      2. unsub-neg 63.1%

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

      3. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   if -2.55000000000000005e54 < x < -7.99999999999999926e-21

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.1%

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

   4. Taylor expanded in a around inf 71.1%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 71.2%

         \[\leadsto x \cdot \left(a \cdot \left(\color{blue}{c \cdot \frac{j}{x}} - t\right)\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)} \]

   if -7.99999999999999926e-21 < x < -2.5000000000000001e-55 or 2.0499999999999999e-146 < x < 0.00899999999999999932

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 65.6%

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

      1. associate-*r* 65.6%

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

      2. neg-mul-1 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around 0 68.1%

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

      1. associate-*r* 68.1%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 68.1%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 68.1%

      \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if -2.5000000000000001e-55 < x < -7.79999999999999985e-88 or 0.00899999999999999932 < x < 7.2e17

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.3%

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

      1. distribute-lft-out-- 85.3%

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

      2. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in i around inf 68.3%

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

      1. +-commutative 68.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{i}\right)} \]

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

      5. associate-*r* 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in i around 0 67.7%

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

       1. +-commutative 67.7%

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

       2. mul-1-neg 67.7%

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

       3. sub-neg 67.7%

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

       4. associate-*r* 85.3%

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

       5. *-commutative 85.3%

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

       6. associate-*r* 85.4%

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

       7. *-commutative 85.4%

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

   11. Simplified 85.4%

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

   if -7.79999999999999985e-88 < x < -7.29999999999999961e-137

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 80.2%

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

   if -7.29999999999999961e-137 < x < -1.27999999999999994e-210

   1. Initial program 50.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.3%

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

   if -1.27999999999999994e-210 < x < 2.0499999999999999e-146

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.0%

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

      1. associate-*r* 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*r* 73.7%

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

   5. Simplified 73.7%

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

   if 7.2e17 < x < 2.8999999999999999e63

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. unsub-neg 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

   5. Simplified 85.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -7.3 \cdot 10^{-137}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 0.009:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+152} \lor \neg \left(x \leq 6.5 \cdot 10^{+192}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))) (t_2 (* b (* z (- c)))) (t_3 (* z (* x y))))
   (if (<= x -1.7e+64)
     t_3
     (if (<= x -3.2e-19)
       t_1
       (if (<= x -4.6e-56)
         t_2
         (if (<= x -1.3e-220)
           (* t (* b i))
           (if (<= x 1.3e-204)
             (* j (* a c))
             (if (<= x 1.4e-88)
               t_2
               (if (<= x 1.75e+16)
                 t_1
                 (if (<= x 2.55e+65)
                   (* y (* x z))
                   (if (<= x 3.3e+65)
                     (* b (* t i))
                     (if (or (<= x 5.8e+152) (not (<= x 6.5e+192)))
                       t_3
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double t_2 = b * (z * -c);
	double t_3 = z * (x * y);
	double tmp;
	if (x <= -1.7e+64) {
		tmp = t_3;
	} else if (x <= -3.2e-19) {
		tmp = t_1;
	} else if (x <= -4.6e-56) {
		tmp = t_2;
	} else if (x <= -1.3e-220) {
		tmp = t * (b * i);
	} else if (x <= 1.3e-204) {
		tmp = j * (a * c);
	} else if (x <= 1.4e-88) {
		tmp = t_2;
	} else if (x <= 1.75e+16) {
		tmp = t_1;
	} else if (x <= 2.55e+65) {
		tmp = y * (x * z);
	} else if (x <= 3.3e+65) {
		tmp = b * (t * i);
	} else if ((x <= 5.8e+152) || !(x <= 6.5e+192)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (x * -a)
    t_2 = b * (z * -c)
    t_3 = z * (x * y)
    if (x <= (-1.7d+64)) then
        tmp = t_3
    else if (x <= (-3.2d-19)) then
        tmp = t_1
    else if (x <= (-4.6d-56)) then
        tmp = t_2
    else if (x <= (-1.3d-220)) then
        tmp = t * (b * i)
    else if (x <= 1.3d-204) then
        tmp = j * (a * c)
    else if (x <= 1.4d-88) then
        tmp = t_2
    else if (x <= 1.75d+16) then
        tmp = t_1
    else if (x <= 2.55d+65) then
        tmp = y * (x * z)
    else if (x <= 3.3d+65) then
        tmp = b * (t * i)
    else if ((x <= 5.8d+152) .or. (.not. (x <= 6.5d+192))) then
        tmp = t_3
    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 t_1 = t * (x * -a);
	double t_2 = b * (z * -c);
	double t_3 = z * (x * y);
	double tmp;
	if (x <= -1.7e+64) {
		tmp = t_3;
	} else if (x <= -3.2e-19) {
		tmp = t_1;
	} else if (x <= -4.6e-56) {
		tmp = t_2;
	} else if (x <= -1.3e-220) {
		tmp = t * (b * i);
	} else if (x <= 1.3e-204) {
		tmp = j * (a * c);
	} else if (x <= 1.4e-88) {
		tmp = t_2;
	} else if (x <= 1.75e+16) {
		tmp = t_1;
	} else if (x <= 2.55e+65) {
		tmp = y * (x * z);
	} else if (x <= 3.3e+65) {
		tmp = b * (t * i);
	} else if ((x <= 5.8e+152) || !(x <= 6.5e+192)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	t_2 = b * (z * -c)
	t_3 = z * (x * y)
	tmp = 0
	if x <= -1.7e+64:
		tmp = t_3
	elif x <= -3.2e-19:
		tmp = t_1
	elif x <= -4.6e-56:
		tmp = t_2
	elif x <= -1.3e-220:
		tmp = t * (b * i)
	elif x <= 1.3e-204:
		tmp = j * (a * c)
	elif x <= 1.4e-88:
		tmp = t_2
	elif x <= 1.75e+16:
		tmp = t_1
	elif x <= 2.55e+65:
		tmp = y * (x * z)
	elif x <= 3.3e+65:
		tmp = b * (t * i)
	elif (x <= 5.8e+152) or not (x <= 6.5e+192):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	t_3 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.7e+64)
		tmp = t_3;
	elseif (x <= -3.2e-19)
		tmp = t_1;
	elseif (x <= -4.6e-56)
		tmp = t_2;
	elseif (x <= -1.3e-220)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 1.3e-204)
		tmp = Float64(j * Float64(a * c));
	elseif (x <= 1.4e-88)
		tmp = t_2;
	elseif (x <= 1.75e+16)
		tmp = t_1;
	elseif (x <= 2.55e+65)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= 3.3e+65)
		tmp = Float64(b * Float64(t * i));
	elseif ((x <= 5.8e+152) || !(x <= 6.5e+192))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * -a);
	t_2 = b * (z * -c);
	t_3 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.7e+64)
		tmp = t_3;
	elseif (x <= -3.2e-19)
		tmp = t_1;
	elseif (x <= -4.6e-56)
		tmp = t_2;
	elseif (x <= -1.3e-220)
		tmp = t * (b * i);
	elseif (x <= 1.3e-204)
		tmp = j * (a * c);
	elseif (x <= 1.4e-88)
		tmp = t_2;
	elseif (x <= 1.75e+16)
		tmp = t_1;
	elseif (x <= 2.55e+65)
		tmp = y * (x * z);
	elseif (x <= 3.3e+65)
		tmp = b * (t * i);
	elseif ((x <= 5.8e+152) || ~((x <= 6.5e+192)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+64], t$95$3, If[LessEqual[x, -3.2e-19], t$95$1, If[LessEqual[x, -4.6e-56], t$95$2, If[LessEqual[x, -1.3e-220], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-204], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-88], t$95$2, If[LessEqual[x, 1.75e+16], t$95$1, If[LessEqual[x, 2.55e+65], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+65], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.8e+152], N[Not[LessEqual[x, 6.5e+192]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.7000000000000001e64 or 3.30000000000000023e65 < x < 5.7999999999999997e152 or 6.50000000000000033e192 < x

   1. Initial program 65.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 52.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around inf 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if -1.7000000000000001e64 < x < -3.19999999999999982e-19 or 1.39999999999999988e-88 < x < 1.75e16 or 5.7999999999999997e152 < x < 6.50000000000000033e192

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.8%

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

      1. distribute-lft-out-- 51.8%

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

      2. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in a around inf 35.7%

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

      1. mul-1-neg 35.7%

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

      2. *-commutative 35.7%

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

      3. associate-*r* 39.1%

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

      4. *-commutative 39.1%

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

      5. distribute-rgt-neg-out 39.1%

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

      6. *-commutative 39.1%

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

      7. distribute-rgt-neg-in 39.1%

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

   8. Simplified 39.1%

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

   if -3.19999999999999982e-19 < x < -4.60000000000000005e-56 or 1.29999999999999991e-204 < x < 1.39999999999999988e-88

   1. Initial program 70.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 44.6%

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

      2. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in y around 0 48.0%

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

      1. mul-1-neg 48.0%

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

      2. distribute-rgt-neg-in 48.0%

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

      3. distribute-lft-neg-in 48.0%

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

   8. Simplified 48.0%

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

   if -4.60000000000000005e-56 < x < -1.3e-220

   1. Initial program 67.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 75.4%

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

   4. Taylor expanded in c around 0 60.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around inf 37.7%

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

      1. *-commutative 37.7%

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

      2. *-commutative 37.7%

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

      3. associate-*r* 40.4%

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

   7. Simplified 40.4%

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

   if -1.3e-220 < x < 1.29999999999999991e-204

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 28.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 28.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 28.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 28.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 28.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 28.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 28.8%

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

      1. associate-*r* 33.5%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if 1.75e16 < x < 2.54999999999999994e65

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 66.5%

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

   4. Taylor expanded in c around 0 55.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in z around inf 36.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

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

      2. *-commutative 36.6%

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

      3. associate-*r* 47.2%

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

   7. Simplified 47.2%

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

   if 2.54999999999999994e65 < x < 3.30000000000000023e65

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in j around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in i around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+152} \lor \neg \left(x \leq 6.5 \cdot 10^{+192}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(x \cdot t\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right) - t\_3\\ \mathbf{if}\;y \leq -7 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-59}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - t\_3\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (* x t)))
        (t_4 (- (* i (- (* t b) (* y j))) t_3)))
   (if (<= y -7e+116)
     t_2
     (if (<= y -7.2e+78)
       t_4
       (if (<= y -7.5e-27)
         (* z (- (* x y) (* b c)))
         (if (<= y -9e-59)
           t_4
           (if (<= y 6e+69)
             (- (* c (- (* a j) (* z b))) t_3)
             (if (<= y 1.22e+126)
               (+ (* i (* t b)) t_1)
               (if (<= y 2.8e+164)
                 t_2
                 (if (<= y 4.2e+187)
                   t_1
                   (if (<= y 3.3e+191)
                     (- (* i (* y (- j))) (* b (* z c)))
                     (if (<= y 3.4e+258)
                       (* c (* z (- (/ (* x y) c) b)))
                       t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * (x * t);
	double t_4 = (i * ((t * b) - (y * j))) - t_3;
	double tmp;
	if (y <= -7e+116) {
		tmp = t_2;
	} else if (y <= -7.2e+78) {
		tmp = t_4;
	} else if (y <= -7.5e-27) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -9e-59) {
		tmp = t_4;
	} else if (y <= 6e+69) {
		tmp = (c * ((a * j) - (z * b))) - t_3;
	} else if (y <= 1.22e+126) {
		tmp = (i * (t * b)) + t_1;
	} else if (y <= 2.8e+164) {
		tmp = t_2;
	} else if (y <= 4.2e+187) {
		tmp = t_1;
	} else if (y <= 3.3e+191) {
		tmp = (i * (y * -j)) - (b * (z * c));
	} else if (y <= 3.4e+258) {
		tmp = c * (z * (((x * y) / c) - b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * (x * t)
    t_4 = (i * ((t * b) - (y * j))) - t_3
    if (y <= (-7d+116)) then
        tmp = t_2
    else if (y <= (-7.2d+78)) then
        tmp = t_4
    else if (y <= (-7.5d-27)) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= (-9d-59)) then
        tmp = t_4
    else if (y <= 6d+69) then
        tmp = (c * ((a * j) - (z * b))) - t_3
    else if (y <= 1.22d+126) then
        tmp = (i * (t * b)) + t_1
    else if (y <= 2.8d+164) then
        tmp = t_2
    else if (y <= 4.2d+187) then
        tmp = t_1
    else if (y <= 3.3d+191) then
        tmp = (i * (y * -j)) - (b * (z * c))
    else if (y <= 3.4d+258) then
        tmp = c * (z * (((x * y) / c) - b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * (x * t);
	double t_4 = (i * ((t * b) - (y * j))) - t_3;
	double tmp;
	if (y <= -7e+116) {
		tmp = t_2;
	} else if (y <= -7.2e+78) {
		tmp = t_4;
	} else if (y <= -7.5e-27) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -9e-59) {
		tmp = t_4;
	} else if (y <= 6e+69) {
		tmp = (c * ((a * j) - (z * b))) - t_3;
	} else if (y <= 1.22e+126) {
		tmp = (i * (t * b)) + t_1;
	} else if (y <= 2.8e+164) {
		tmp = t_2;
	} else if (y <= 4.2e+187) {
		tmp = t_1;
	} else if (y <= 3.3e+191) {
		tmp = (i * (y * -j)) - (b * (z * c));
	} else if (y <= 3.4e+258) {
		tmp = c * (z * (((x * y) / c) - b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * (x * t)
	t_4 = (i * ((t * b) - (y * j))) - t_3
	tmp = 0
	if y <= -7e+116:
		tmp = t_2
	elif y <= -7.2e+78:
		tmp = t_4
	elif y <= -7.5e-27:
		tmp = z * ((x * y) - (b * c))
	elif y <= -9e-59:
		tmp = t_4
	elif y <= 6e+69:
		tmp = (c * ((a * j) - (z * b))) - t_3
	elif y <= 1.22e+126:
		tmp = (i * (t * b)) + t_1
	elif y <= 2.8e+164:
		tmp = t_2
	elif y <= 4.2e+187:
		tmp = t_1
	elif y <= 3.3e+191:
		tmp = (i * (y * -j)) - (b * (z * c))
	elif y <= 3.4e+258:
		tmp = c * (z * (((x * y) / c) - b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(x * t))
	t_4 = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - t_3)
	tmp = 0.0
	if (y <= -7e+116)
		tmp = t_2;
	elseif (y <= -7.2e+78)
		tmp = t_4;
	elseif (y <= -7.5e-27)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= -9e-59)
		tmp = t_4;
	elseif (y <= 6e+69)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - t_3);
	elseif (y <= 1.22e+126)
		tmp = Float64(Float64(i * Float64(t * b)) + t_1);
	elseif (y <= 2.8e+164)
		tmp = t_2;
	elseif (y <= 4.2e+187)
		tmp = t_1;
	elseif (y <= 3.3e+191)
		tmp = Float64(Float64(i * Float64(y * Float64(-j))) - Float64(b * Float64(z * c)));
	elseif (y <= 3.4e+258)
		tmp = Float64(c * Float64(z * Float64(Float64(Float64(x * y) / c) - b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * (x * t);
	t_4 = (i * ((t * b) - (y * j))) - t_3;
	tmp = 0.0;
	if (y <= -7e+116)
		tmp = t_2;
	elseif (y <= -7.2e+78)
		tmp = t_4;
	elseif (y <= -7.5e-27)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= -9e-59)
		tmp = t_4;
	elseif (y <= 6e+69)
		tmp = (c * ((a * j) - (z * b))) - t_3;
	elseif (y <= 1.22e+126)
		tmp = (i * (t * b)) + t_1;
	elseif (y <= 2.8e+164)
		tmp = t_2;
	elseif (y <= 4.2e+187)
		tmp = t_1;
	elseif (y <= 3.3e+191)
		tmp = (i * (y * -j)) - (b * (z * c));
	elseif (y <= 3.4e+258)
		tmp = c * (z * (((x * y) / c) - b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]}, If[LessEqual[y, -7e+116], t$95$2, If[LessEqual[y, -7.2e+78], t$95$4, If[LessEqual[y, -7.5e-27], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-59], t$95$4, If[LessEqual[y, 6e+69], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[y, 1.22e+126], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 2.8e+164], t$95$2, If[LessEqual[y, 4.2e+187], t$95$1, If[LessEqual[y, 3.3e+191], N[(N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+258], N[(c * N[(z * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -6.99999999999999993e116 or 1.21999999999999995e126 < y < 2.8000000000000002e164 or 3.39999999999999981e258 < y

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

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

      1. +-commutative 84.6%

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

      2. mul-1-neg 84.6%

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

      3. unsub-neg 84.6%

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

      4. *-commutative 84.6%

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

      5. *-commutative 84.6%

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

   5. Simplified 84.6%

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

   if -6.99999999999999993e116 < y < -7.20000000000000039e78 or -7.50000000000000029e-27 < y < -9.00000000000000023e-59

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 66.6%

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

   4. Taylor expanded in c around 0 61.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 61.4%

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

      1. associate-*r* 61.4%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 61.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 61.4%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 61.4%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 61.4%

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

      6. *-commutative 61.4%

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

      7. unsub-neg 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in y around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. distribute-rgt-neg-in 71.7%

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

      3. distribute-rgt-neg-in 71.7%

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

   10. Simplified 71.7%

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

   if -7.20000000000000039e78 < y < -7.50000000000000029e-27

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -9.00000000000000023e-59 < y < 5.99999999999999967e69

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 75.5%

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

   4. Taylor expanded in c around 0 85.4%

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

   5. Taylor expanded in a around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

   7. Simplified 67.4%

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

   if 5.99999999999999967e69 < y < 1.21999999999999995e126

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 68.1%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*r* 68.2%

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

   5. Simplified 68.2%

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

   if 2.8000000000000002e164 < y < 4.2e187

   1. Initial program 41.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 100.0%

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

   if 4.2e187 < y < 3.2999999999999998e191

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in c around 0 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 100.0%

         \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 100.0%

      \[\leadsto \left(-b\right) \cdot \left(c \cdot z\right) + \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if 3.2999999999999998e191 < y < 3.39999999999999981e258

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 44.5%

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

      1. +-commutative 44.5%

         \[\leadsto c \cdot \color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{c} + -1 \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

      4. associate-/l* 51.4%

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

      5. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 72.1%

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

   11. Simplified 72.1%

       \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(\frac{y \cdot x}{c} - b\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+193}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-21}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (* a (- (* c j) (* x t)))))
   (if (<= x -1.3e+193)
     t_4
     (if (<= x -1.45e+169)
       t_2
       (if (<= x -6.4e-21)
         t_4
         (if (<= x -1.6e-55)
           (* b (* z (- c)))
           (if (<= x -1.55e-60)
             (* i (* y (- j)))
             (if (<= x -2.5e-89)
               t_1
               (if (<= x -4e-142)
                 t_3
                 (if (<= x -2e-211)
                   (* b (- (* t i) (* z c)))
                   (if (<= x 1.32e-164)
                     t_3
                     (if (<= x 1.26e+154) t_2 t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = a * ((c * j) - (x * t));
	double tmp;
	if (x <= -1.3e+193) {
		tmp = t_4;
	} else if (x <= -1.45e+169) {
		tmp = t_2;
	} else if (x <= -6.4e-21) {
		tmp = t_4;
	} else if (x <= -1.6e-55) {
		tmp = b * (z * -c);
	} else if (x <= -1.55e-60) {
		tmp = i * (y * -j);
	} else if (x <= -2.5e-89) {
		tmp = t_1;
	} else if (x <= -4e-142) {
		tmp = t_3;
	} else if (x <= -2e-211) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.32e-164) {
		tmp = t_3;
	} else if (x <= 1.26e+154) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = i * ((t * b) - (y * j))
    t_3 = j * ((a * c) - (y * i))
    t_4 = a * ((c * j) - (x * t))
    if (x <= (-1.3d+193)) then
        tmp = t_4
    else if (x <= (-1.45d+169)) then
        tmp = t_2
    else if (x <= (-6.4d-21)) then
        tmp = t_4
    else if (x <= (-1.6d-55)) then
        tmp = b * (z * -c)
    else if (x <= (-1.55d-60)) then
        tmp = i * (y * -j)
    else if (x <= (-2.5d-89)) then
        tmp = t_1
    else if (x <= (-4d-142)) then
        tmp = t_3
    else if (x <= (-2d-211)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 1.32d-164) then
        tmp = t_3
    else if (x <= 1.26d+154) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = a * ((c * j) - (x * t));
	double tmp;
	if (x <= -1.3e+193) {
		tmp = t_4;
	} else if (x <= -1.45e+169) {
		tmp = t_2;
	} else if (x <= -6.4e-21) {
		tmp = t_4;
	} else if (x <= -1.6e-55) {
		tmp = b * (z * -c);
	} else if (x <= -1.55e-60) {
		tmp = i * (y * -j);
	} else if (x <= -2.5e-89) {
		tmp = t_1;
	} else if (x <= -4e-142) {
		tmp = t_3;
	} else if (x <= -2e-211) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.32e-164) {
		tmp = t_3;
	} else if (x <= 1.26e+154) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = i * ((t * b) - (y * j))
	t_3 = j * ((a * c) - (y * i))
	t_4 = a * ((c * j) - (x * t))
	tmp = 0
	if x <= -1.3e+193:
		tmp = t_4
	elif x <= -1.45e+169:
		tmp = t_2
	elif x <= -6.4e-21:
		tmp = t_4
	elif x <= -1.6e-55:
		tmp = b * (z * -c)
	elif x <= -1.55e-60:
		tmp = i * (y * -j)
	elif x <= -2.5e-89:
		tmp = t_1
	elif x <= -4e-142:
		tmp = t_3
	elif x <= -2e-211:
		tmp = b * ((t * i) - (z * c))
	elif x <= 1.32e-164:
		tmp = t_3
	elif x <= 1.26e+154:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (x <= -1.3e+193)
		tmp = t_4;
	elseif (x <= -1.45e+169)
		tmp = t_2;
	elseif (x <= -6.4e-21)
		tmp = t_4;
	elseif (x <= -1.6e-55)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -1.55e-60)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (x <= -2.5e-89)
		tmp = t_1;
	elseif (x <= -4e-142)
		tmp = t_3;
	elseif (x <= -2e-211)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 1.32e-164)
		tmp = t_3;
	elseif (x <= 1.26e+154)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = i * ((t * b) - (y * j));
	t_3 = j * ((a * c) - (y * i));
	t_4 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (x <= -1.3e+193)
		tmp = t_4;
	elseif (x <= -1.45e+169)
		tmp = t_2;
	elseif (x <= -6.4e-21)
		tmp = t_4;
	elseif (x <= -1.6e-55)
		tmp = b * (z * -c);
	elseif (x <= -1.55e-60)
		tmp = i * (y * -j);
	elseif (x <= -2.5e-89)
		tmp = t_1;
	elseif (x <= -4e-142)
		tmp = t_3;
	elseif (x <= -2e-211)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 1.32e-164)
		tmp = t_3;
	elseif (x <= 1.26e+154)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+193], t$95$4, If[LessEqual[x, -1.45e+169], t$95$2, If[LessEqual[x, -6.4e-21], t$95$4, If[LessEqual[x, -1.6e-55], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e-60], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-89], t$95$1, If[LessEqual[x, -4e-142], t$95$3, If[LessEqual[x, -2e-211], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e-164], t$95$3, If[LessEqual[x, 1.26e+154], t$95$2, t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.30000000000000007e193 or -1.45e169 < x < -6.4000000000000003e-21

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 52.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 52.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -1.30000000000000007e193 < x < -1.45e169 or 1.3199999999999999e-164 < x < 1.26e154

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 67.7%

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

   4. Taylor expanded in c around 0 71.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 71.0%

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

      1. associate-*r* 71.0%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 71.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 71.0%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 71.0%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 71.0%

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

      6. *-commutative 71.0%

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

      7. unsub-neg 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in y around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-rgt-neg-in 61.8%

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

      3. distribute-rgt-neg-in 61.8%

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

   10. Simplified 61.8%

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

   11. Taylor expanded in i around inf 51.3%

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

       1. *-commutative 51.3%

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

   13. Simplified 51.3%

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

   if -6.4000000000000003e-21 < x < -1.6000000000000001e-55

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-rgt-neg-in 85.9%

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

      3. distribute-lft-neg-in 85.9%

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

   8. Simplified 85.9%

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

   if -1.6000000000000001e-55 < x < -1.54999999999999994e-60

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in c around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if -1.54999999999999994e-60 < x < -2.49999999999999983e-89 or 1.26e154 < x

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 69.5%

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

   4. Taylor expanded in t around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

      5. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if -2.49999999999999983e-89 < x < -4.0000000000000002e-142 or -2.00000000000000017e-211 < x < 1.3199999999999999e-164

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 64.7%

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

   if -4.0000000000000002e-142 < x < -2.00000000000000017e-211

   1. Initial program 50.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+193}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+169}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-142}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+154}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.00011:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-280}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 10^{+68}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+156}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= z -1.6e+157)
     t_1
     (if (<= z -0.00011)
       t_2
       (if (<= z -6.5e-37)
         t_1
         (if (<= z -2.7e-70)
           t_2
           (if (<= z 2.5e-280)
             t_3
             (if (<= z 2.15e-215)
               t_2
               (if (<= z 1e+68)
                 t_3
                 (if (<= z 1.35e+140)
                   (* z (* x y))
                   (if (<= z 5.5e+156)
                     t_3
                     (if (<= z 1.02e+273) t_1 (* z (* c (- b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (z <= -1.6e+157) {
		tmp = t_1;
	} else if (z <= -0.00011) {
		tmp = t_2;
	} else if (z <= -6.5e-37) {
		tmp = t_1;
	} else if (z <= -2.7e-70) {
		tmp = t_2;
	} else if (z <= 2.5e-280) {
		tmp = t_3;
	} else if (z <= 2.15e-215) {
		tmp = t_2;
	} else if (z <= 1e+68) {
		tmp = t_3;
	} else if (z <= 1.35e+140) {
		tmp = z * (x * y);
	} else if (z <= 5.5e+156) {
		tmp = t_3;
	} else if (z <= 1.02e+273) {
		tmp = t_1;
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    t_3 = i * ((t * b) - (y * j))
    if (z <= (-1.6d+157)) then
        tmp = t_1
    else if (z <= (-0.00011d0)) then
        tmp = t_2
    else if (z <= (-6.5d-37)) then
        tmp = t_1
    else if (z <= (-2.7d-70)) then
        tmp = t_2
    else if (z <= 2.5d-280) then
        tmp = t_3
    else if (z <= 2.15d-215) then
        tmp = t_2
    else if (z <= 1d+68) then
        tmp = t_3
    else if (z <= 1.35d+140) then
        tmp = z * (x * y)
    else if (z <= 5.5d+156) then
        tmp = t_3
    else if (z <= 1.02d+273) then
        tmp = t_1
    else
        tmp = z * (c * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (z <= -1.6e+157) {
		tmp = t_1;
	} else if (z <= -0.00011) {
		tmp = t_2;
	} else if (z <= -6.5e-37) {
		tmp = t_1;
	} else if (z <= -2.7e-70) {
		tmp = t_2;
	} else if (z <= 2.5e-280) {
		tmp = t_3;
	} else if (z <= 2.15e-215) {
		tmp = t_2;
	} else if (z <= 1e+68) {
		tmp = t_3;
	} else if (z <= 1.35e+140) {
		tmp = z * (x * y);
	} else if (z <= 5.5e+156) {
		tmp = t_3;
	} else if (z <= 1.02e+273) {
		tmp = t_1;
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if z <= -1.6e+157:
		tmp = t_1
	elif z <= -0.00011:
		tmp = t_2
	elif z <= -6.5e-37:
		tmp = t_1
	elif z <= -2.7e-70:
		tmp = t_2
	elif z <= 2.5e-280:
		tmp = t_3
	elif z <= 2.15e-215:
		tmp = t_2
	elif z <= 1e+68:
		tmp = t_3
	elif z <= 1.35e+140:
		tmp = z * (x * y)
	elif z <= 5.5e+156:
		tmp = t_3
	elif z <= 1.02e+273:
		tmp = t_1
	else:
		tmp = z * (c * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (z <= -1.6e+157)
		tmp = t_1;
	elseif (z <= -0.00011)
		tmp = t_2;
	elseif (z <= -6.5e-37)
		tmp = t_1;
	elseif (z <= -2.7e-70)
		tmp = t_2;
	elseif (z <= 2.5e-280)
		tmp = t_3;
	elseif (z <= 2.15e-215)
		tmp = t_2;
	elseif (z <= 1e+68)
		tmp = t_3;
	elseif (z <= 1.35e+140)
		tmp = Float64(z * Float64(x * y));
	elseif (z <= 5.5e+156)
		tmp = t_3;
	elseif (z <= 1.02e+273)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(c * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (z <= -1.6e+157)
		tmp = t_1;
	elseif (z <= -0.00011)
		tmp = t_2;
	elseif (z <= -6.5e-37)
		tmp = t_1;
	elseif (z <= -2.7e-70)
		tmp = t_2;
	elseif (z <= 2.5e-280)
		tmp = t_3;
	elseif (z <= 2.15e-215)
		tmp = t_2;
	elseif (z <= 1e+68)
		tmp = t_3;
	elseif (z <= 1.35e+140)
		tmp = z * (x * y);
	elseif (z <= 5.5e+156)
		tmp = t_3;
	elseif (z <= 1.02e+273)
		tmp = t_1;
	else
		tmp = z * (c * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+157], t$95$1, If[LessEqual[z, -0.00011], t$95$2, If[LessEqual[z, -6.5e-37], t$95$1, If[LessEqual[z, -2.7e-70], t$95$2, If[LessEqual[z, 2.5e-280], t$95$3, If[LessEqual[z, 2.15e-215], t$95$2, If[LessEqual[z, 1e+68], t$95$3, If[LessEqual[z, 1.35e+140], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+156], t$95$3, If[LessEqual[z, 1.02e+273], t$95$1, N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6e157 or -1.10000000000000004e-4 < z < -6.5000000000000001e-37 or 5.5000000000000003e156 < z < 1.01999999999999997e273

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.9%

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

   if -1.6e157 < z < -1.10000000000000004e-4 or -6.5000000000000001e-37 < z < -2.7000000000000001e-70 or 2.50000000000000014e-280 < z < 2.15000000000000012e-215

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 63.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 63.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 63.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 63.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 63.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -2.7000000000000001e-70 < z < 2.50000000000000014e-280 or 2.15000000000000012e-215 < z < 9.99999999999999953e67 or 1.35000000000000009e140 < z < 5.5000000000000003e156

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 78.9%

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

   4. Taylor expanded in c around 0 74.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 74.6%

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

      1. associate-*r* 74.6%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 74.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 74.6%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 74.6%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 74.6%

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

      6. *-commutative 74.6%

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

      7. unsub-neg 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-rgt-neg-in 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

   10. Simplified 67.4%

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

   11. Taylor expanded in i around inf 59.3%

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

       1. *-commutative 59.3%

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

   13. Simplified 59.3%

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

   if 9.99999999999999953e67 < z < 1.35000000000000009e140

   1. Initial program 92.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 65.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around inf 39.6%

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

      1. *-commutative 39.6%

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

   8. Simplified 39.6%

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

   if 1.01999999999999997e273 < z

   1. Initial program 58.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 88.7%

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

      2. *-commutative 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in y around 0 67.8%

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

      1. neg-mul-1 67.8%

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

      2. distribute-rgt-neg-in 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+157}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -0.00011:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-280}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 10^{+68}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+156}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+273}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(x \cdot t\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right) - t\_3\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-57}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - t\_3\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+189}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (* x t)))
        (t_4 (- (* i (- (* t b) (* y j))) t_3)))
   (if (<= y -5.7e+116)
     t_2
     (if (<= y -5.8e+78)
       t_4
       (if (<= y -9.5e-33)
         (* z (- (* x y) (* b c)))
         (if (<= y -9e-57)
           t_4
           (if (<= y 1.75e+65)
             (- (* c (- (* a j) (* z b))) t_3)
             (if (<= y 1.26e+126)
               (+ (* i (* t b)) t_1)
               (if (<= y 6.8e+163)
                 t_2
                 (if (<= y 3.4e+189)
                   (- t_1 (* b (* z c)))
                   (if (<= y 4.4e+258)
                     (* c (* z (- (/ (* x y) c) b)))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * (x * t);
	double t_4 = (i * ((t * b) - (y * j))) - t_3;
	double tmp;
	if (y <= -5.7e+116) {
		tmp = t_2;
	} else if (y <= -5.8e+78) {
		tmp = t_4;
	} else if (y <= -9.5e-33) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -9e-57) {
		tmp = t_4;
	} else if (y <= 1.75e+65) {
		tmp = (c * ((a * j) - (z * b))) - t_3;
	} else if (y <= 1.26e+126) {
		tmp = (i * (t * b)) + t_1;
	} else if (y <= 6.8e+163) {
		tmp = t_2;
	} else if (y <= 3.4e+189) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 4.4e+258) {
		tmp = c * (z * (((x * y) / c) - b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * (x * t)
    t_4 = (i * ((t * b) - (y * j))) - t_3
    if (y <= (-5.7d+116)) then
        tmp = t_2
    else if (y <= (-5.8d+78)) then
        tmp = t_4
    else if (y <= (-9.5d-33)) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= (-9d-57)) then
        tmp = t_4
    else if (y <= 1.75d+65) then
        tmp = (c * ((a * j) - (z * b))) - t_3
    else if (y <= 1.26d+126) then
        tmp = (i * (t * b)) + t_1
    else if (y <= 6.8d+163) then
        tmp = t_2
    else if (y <= 3.4d+189) then
        tmp = t_1 - (b * (z * c))
    else if (y <= 4.4d+258) then
        tmp = c * (z * (((x * y) / c) - b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * (x * t);
	double t_4 = (i * ((t * b) - (y * j))) - t_3;
	double tmp;
	if (y <= -5.7e+116) {
		tmp = t_2;
	} else if (y <= -5.8e+78) {
		tmp = t_4;
	} else if (y <= -9.5e-33) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -9e-57) {
		tmp = t_4;
	} else if (y <= 1.75e+65) {
		tmp = (c * ((a * j) - (z * b))) - t_3;
	} else if (y <= 1.26e+126) {
		tmp = (i * (t * b)) + t_1;
	} else if (y <= 6.8e+163) {
		tmp = t_2;
	} else if (y <= 3.4e+189) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 4.4e+258) {
		tmp = c * (z * (((x * y) / c) - b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * (x * t)
	t_4 = (i * ((t * b) - (y * j))) - t_3
	tmp = 0
	if y <= -5.7e+116:
		tmp = t_2
	elif y <= -5.8e+78:
		tmp = t_4
	elif y <= -9.5e-33:
		tmp = z * ((x * y) - (b * c))
	elif y <= -9e-57:
		tmp = t_4
	elif y <= 1.75e+65:
		tmp = (c * ((a * j) - (z * b))) - t_3
	elif y <= 1.26e+126:
		tmp = (i * (t * b)) + t_1
	elif y <= 6.8e+163:
		tmp = t_2
	elif y <= 3.4e+189:
		tmp = t_1 - (b * (z * c))
	elif y <= 4.4e+258:
		tmp = c * (z * (((x * y) / c) - b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(x * t))
	t_4 = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - t_3)
	tmp = 0.0
	if (y <= -5.7e+116)
		tmp = t_2;
	elseif (y <= -5.8e+78)
		tmp = t_4;
	elseif (y <= -9.5e-33)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= -9e-57)
		tmp = t_4;
	elseif (y <= 1.75e+65)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - t_3);
	elseif (y <= 1.26e+126)
		tmp = Float64(Float64(i * Float64(t * b)) + t_1);
	elseif (y <= 6.8e+163)
		tmp = t_2;
	elseif (y <= 3.4e+189)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (y <= 4.4e+258)
		tmp = Float64(c * Float64(z * Float64(Float64(Float64(x * y) / c) - b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * (x * t);
	t_4 = (i * ((t * b) - (y * j))) - t_3;
	tmp = 0.0;
	if (y <= -5.7e+116)
		tmp = t_2;
	elseif (y <= -5.8e+78)
		tmp = t_4;
	elseif (y <= -9.5e-33)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= -9e-57)
		tmp = t_4;
	elseif (y <= 1.75e+65)
		tmp = (c * ((a * j) - (z * b))) - t_3;
	elseif (y <= 1.26e+126)
		tmp = (i * (t * b)) + t_1;
	elseif (y <= 6.8e+163)
		tmp = t_2;
	elseif (y <= 3.4e+189)
		tmp = t_1 - (b * (z * c));
	elseif (y <= 4.4e+258)
		tmp = c * (z * (((x * y) / c) - b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]}, If[LessEqual[y, -5.7e+116], t$95$2, If[LessEqual[y, -5.8e+78], t$95$4, If[LessEqual[y, -9.5e-33], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-57], t$95$4, If[LessEqual[y, 1.75e+65], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[y, 1.26e+126], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 6.8e+163], t$95$2, If[LessEqual[y, 3.4e+189], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+258], N[(c * N[(z * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -5.69999999999999983e116 or 1.26000000000000004e126 < y < 6.8000000000000002e163 or 4.39999999999999965e258 < y

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.6%

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

      1. +-commutative 84.6%

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

      2. mul-1-neg 84.6%

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

      3. unsub-neg 84.6%

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

      4. *-commutative 84.6%

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

      5. *-commutative 84.6%

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

   5. Simplified 84.6%

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

   if -5.69999999999999983e116 < y < -5.80000000000000034e78 or -9.50000000000000019e-33 < y < -8.99999999999999945e-57

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 66.6%

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

   4. Taylor expanded in c around 0 61.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 61.4%

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

      1. associate-*r* 61.4%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 61.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 61.4%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 61.4%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 61.4%

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

      6. *-commutative 61.4%

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

      7. unsub-neg 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in y around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. distribute-rgt-neg-in 71.7%

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

      3. distribute-rgt-neg-in 71.7%

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

   10. Simplified 71.7%

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

   if -5.80000000000000034e78 < y < -9.50000000000000019e-33

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -8.99999999999999945e-57 < y < 1.75e65

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 75.5%

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

   4. Taylor expanded in c around 0 85.4%

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

   5. Taylor expanded in a around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

   7. Simplified 67.4%

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

   if 1.75e65 < y < 1.26000000000000004e126

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 68.1%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*r* 68.2%

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

   5. Simplified 68.2%

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

   if 6.8000000000000002e163 < y < 3.39999999999999983e189

   1. Initial program 58.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   if 3.39999999999999983e189 < y < 4.39999999999999965e258

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 44.5%

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

      1. +-commutative 44.5%

         \[\leadsto c \cdot \color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{c} + -1 \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

      4. associate-/l* 51.4%

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

      5. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 72.1%

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

   11. Simplified 72.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-57}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+189}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+258}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t\_2 - x \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+198}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + t\_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - t\_1\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - t\_1\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+25}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (- t_2 (* x (* t a)))))
   (if (<= z -1.4e+198)
     (* c (* z (- (/ (* x y) c) b)))
     (if (<= z -9.5e+137)
       (+ (* x (* y z)) t_2)
       (if (<= z -2.5e+69)
         (* x (- (* y z) (* t a)))
         (if (<= z -1.6e+37)
           t_2
           (if (<= z -5.8e-31)
             (- (* c (- (* a j) (* z b))) t_1)
             (if (<= z -3.85e-208)
               t_3
               (if (<= z 8e-119)
                 (- (* i (- (* t b) (* y j))) t_1)
                 (if (<= z 2.85e+25) t_3 (* z (- (* x y) (* b c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 - (x * (t * a));
	double tmp;
	if (z <= -1.4e+198) {
		tmp = c * (z * (((x * y) / c) - b));
	} else if (z <= -9.5e+137) {
		tmp = (x * (y * z)) + t_2;
	} else if (z <= -2.5e+69) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -1.6e+37) {
		tmp = t_2;
	} else if (z <= -5.8e-31) {
		tmp = (c * ((a * j) - (z * b))) - t_1;
	} else if (z <= -3.85e-208) {
		tmp = t_3;
	} else if (z <= 8e-119) {
		tmp = (i * ((t * b) - (y * j))) - t_1;
	} else if (z <= 2.85e+25) {
		tmp = t_3;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (x * t)
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 - (x * (t * a))
    if (z <= (-1.4d+198)) then
        tmp = c * (z * (((x * y) / c) - b))
    else if (z <= (-9.5d+137)) then
        tmp = (x * (y * z)) + t_2
    else if (z <= (-2.5d+69)) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= (-1.6d+37)) then
        tmp = t_2
    else if (z <= (-5.8d-31)) then
        tmp = (c * ((a * j) - (z * b))) - t_1
    else if (z <= (-3.85d-208)) then
        tmp = t_3
    else if (z <= 8d-119) then
        tmp = (i * ((t * b) - (y * j))) - t_1
    else if (z <= 2.85d+25) then
        tmp = t_3
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 - (x * (t * a));
	double tmp;
	if (z <= -1.4e+198) {
		tmp = c * (z * (((x * y) / c) - b));
	} else if (z <= -9.5e+137) {
		tmp = (x * (y * z)) + t_2;
	} else if (z <= -2.5e+69) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= -1.6e+37) {
		tmp = t_2;
	} else if (z <= -5.8e-31) {
		tmp = (c * ((a * j) - (z * b))) - t_1;
	} else if (z <= -3.85e-208) {
		tmp = t_3;
	} else if (z <= 8e-119) {
		tmp = (i * ((t * b) - (y * j))) - t_1;
	} else if (z <= 2.85e+25) {
		tmp = t_3;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 - (x * (t * a))
	tmp = 0
	if z <= -1.4e+198:
		tmp = c * (z * (((x * y) / c) - b))
	elif z <= -9.5e+137:
		tmp = (x * (y * z)) + t_2
	elif z <= -2.5e+69:
		tmp = x * ((y * z) - (t * a))
	elif z <= -1.6e+37:
		tmp = t_2
	elif z <= -5.8e-31:
		tmp = (c * ((a * j) - (z * b))) - t_1
	elif z <= -3.85e-208:
		tmp = t_3
	elif z <= 8e-119:
		tmp = (i * ((t * b) - (y * j))) - t_1
	elif z <= 2.85e+25:
		tmp = t_3
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 - Float64(x * Float64(t * a)))
	tmp = 0.0
	if (z <= -1.4e+198)
		tmp = Float64(c * Float64(z * Float64(Float64(Float64(x * y) / c) - b)));
	elseif (z <= -9.5e+137)
		tmp = Float64(Float64(x * Float64(y * z)) + t_2);
	elseif (z <= -2.5e+69)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= -1.6e+37)
		tmp = t_2;
	elseif (z <= -5.8e-31)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - t_1);
	elseif (z <= -3.85e-208)
		tmp = t_3;
	elseif (z <= 8e-119)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - t_1);
	elseif (z <= 2.85e+25)
		tmp = t_3;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 - (x * (t * a));
	tmp = 0.0;
	if (z <= -1.4e+198)
		tmp = c * (z * (((x * y) / c) - b));
	elseif (z <= -9.5e+137)
		tmp = (x * (y * z)) + t_2;
	elseif (z <= -2.5e+69)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= -1.6e+37)
		tmp = t_2;
	elseif (z <= -5.8e-31)
		tmp = (c * ((a * j) - (z * b))) - t_1;
	elseif (z <= -3.85e-208)
		tmp = t_3;
	elseif (z <= 8e-119)
		tmp = (i * ((t * b) - (y * j))) - t_1;
	elseif (z <= 2.85e+25)
		tmp = t_3;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+198], N[(c * N[(z * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e+137], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[z, -2.5e+69], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e+37], t$95$2, If[LessEqual[z, -5.8e-31], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, -3.85e-208], t$95$3, If[LessEqual[z, 8e-119], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 2.85e+25], t$95$3, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -1.4e198

   1. Initial program 59.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.5%

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

      2. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in c around inf 63.2%

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

      1. +-commutative 63.2%

         \[\leadsto c \cdot \color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{c} + -1 \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. associate-/l* 63.3%

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

      5. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in z around 0 70.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 70.7%

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

   11. Simplified 70.7%

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

   if -1.4e198 < z < -9.50000000000000031e137

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.2%

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

   if -9.50000000000000031e137 < z < -2.50000000000000018e69

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.6%

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

   if -2.50000000000000018e69 < z < -1.60000000000000007e37

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 100.0%

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

   if -1.60000000000000007e37 < z < -5.8000000000000001e-31

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 73.2%

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

   4. Taylor expanded in c around 0 73.2%

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

   5. Taylor expanded in a around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

   7. Simplified 71.8%

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

   if -5.8000000000000001e-31 < z < -3.84999999999999986e-208 or 8.0000000000000001e-119 < z < 2.8499999999999998e25

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 71.7%

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

      1. mul-1-neg 71.7%

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

      2. associate-*r* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

   5. Simplified 73.2%

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

   if -3.84999999999999986e-208 < z < 8.0000000000000001e-119

   1. Initial program 80.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 80.8%

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

   4. Taylor expanded in c around 0 76.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 76.8%

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

      1. associate-*r* 76.8%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 76.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 76.8%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 76.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 76.8%

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

      6. *-commutative 76.8%

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

      7. unsub-neg 76.8%

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

   7. Simplified 76.8%

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

   8. Taylor expanded in y around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-in 73.3%

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

      3. distribute-rgt-neg-in 73.3%

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

   10. Simplified 73.3%

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

   if 2.8499999999999998e25 < z

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+198}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq -3.85 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-157}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.4e+193)
     t_1
     (if (<= x -4.6e+56)
       (* x (* y (- z (* i (/ j x)))))
       (if (<= x -6.5e-21)
         (* x (* a (- (* c (/ j x)) t)))
         (if (<= x -1.4e-54)
           (* b (* z (- c)))
           (if (<= x -4.6e-83)
             (- (* t (* b i)) (* x (* t a)))
             (if (<= x -1.7e-157)
               (* i (- (* t b) (* y j)))
               (if (<= x -1.3e-220)
                 (* b (- (* t i) (* z c)))
                 (if (<= x 1.25e-50)
                   (* j (- (* a c) (* y i)))
                   (if (<= x 4.3e+48) (* y (- (* x z) (* i j))) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e+193) {
		tmp = t_1;
	} else if (x <= -4.6e+56) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -6.5e-21) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -1.4e-54) {
		tmp = b * (z * -c);
	} else if (x <= -4.6e-83) {
		tmp = (t * (b * i)) - (x * (t * a));
	} else if (x <= -1.7e-157) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= -1.3e-220) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.25e-50) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 4.3e+48) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.4d+193)) then
        tmp = t_1
    else if (x <= (-4.6d+56)) then
        tmp = x * (y * (z - (i * (j / x))))
    else if (x <= (-6.5d-21)) then
        tmp = x * (a * ((c * (j / x)) - t))
    else if (x <= (-1.4d-54)) then
        tmp = b * (z * -c)
    else if (x <= (-4.6d-83)) then
        tmp = (t * (b * i)) - (x * (t * a))
    else if (x <= (-1.7d-157)) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= (-1.3d-220)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 1.25d-50) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 4.3d+48) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e+193) {
		tmp = t_1;
	} else if (x <= -4.6e+56) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -6.5e-21) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -1.4e-54) {
		tmp = b * (z * -c);
	} else if (x <= -4.6e-83) {
		tmp = (t * (b * i)) - (x * (t * a));
	} else if (x <= -1.7e-157) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= -1.3e-220) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 1.25e-50) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 4.3e+48) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.4e+193:
		tmp = t_1
	elif x <= -4.6e+56:
		tmp = x * (y * (z - (i * (j / x))))
	elif x <= -6.5e-21:
		tmp = x * (a * ((c * (j / x)) - t))
	elif x <= -1.4e-54:
		tmp = b * (z * -c)
	elif x <= -4.6e-83:
		tmp = (t * (b * i)) - (x * (t * a))
	elif x <= -1.7e-157:
		tmp = i * ((t * b) - (y * j))
	elif x <= -1.3e-220:
		tmp = b * ((t * i) - (z * c))
	elif x <= 1.25e-50:
		tmp = j * ((a * c) - (y * i))
	elif x <= 4.3e+48:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.4e+193)
		tmp = t_1;
	elseif (x <= -4.6e+56)
		tmp = Float64(x * Float64(y * Float64(z - Float64(i * Float64(j / x)))));
	elseif (x <= -6.5e-21)
		tmp = Float64(x * Float64(a * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (x <= -1.4e-54)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -4.6e-83)
		tmp = Float64(Float64(t * Float64(b * i)) - Float64(x * Float64(t * a)));
	elseif (x <= -1.7e-157)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= -1.3e-220)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 1.25e-50)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 4.3e+48)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.4e+193)
		tmp = t_1;
	elseif (x <= -4.6e+56)
		tmp = x * (y * (z - (i * (j / x))));
	elseif (x <= -6.5e-21)
		tmp = x * (a * ((c * (j / x)) - t));
	elseif (x <= -1.4e-54)
		tmp = b * (z * -c);
	elseif (x <= -4.6e-83)
		tmp = (t * (b * i)) - (x * (t * a));
	elseif (x <= -1.7e-157)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= -1.3e-220)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 1.25e-50)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 4.3e+48)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+193], t$95$1, If[LessEqual[x, -4.6e+56], N[(x * N[(y * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-21], N[(x * N[(a * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e-54], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.6e-83], N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-157], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-220], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-50], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+48], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -2.4e193 or 4.29999999999999978e48 < x

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.0%

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

   if -2.4e193 < x < -4.60000000000000029e56

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.7%

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

   4. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\left(-\frac{i \cdot j}{x}\right)}\right)\right) \]

      2. unsub-neg 63.1%

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

      3. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   if -4.60000000000000029e56 < x < -6.49999999999999987e-21

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.1%

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

   4. Taylor expanded in a around inf 71.1%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 71.2%

         \[\leadsto x \cdot \left(a \cdot \left(\color{blue}{c \cdot \frac{j}{x}} - t\right)\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)} \]

   if -6.49999999999999987e-21 < x < -1.4000000000000001e-54

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-rgt-neg-in 85.9%

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

      3. distribute-lft-neg-in 85.9%

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

   8. Simplified 85.9%

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

   if -1.4000000000000001e-54 < x < -4.59999999999999979e-83

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.2%

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

      1. distribute-lft-out-- 83.2%

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

      2. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in i around inf 67.5%

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

      1. +-commutative 67.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{i}\right)} \]

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*r* 67.5%

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

   8. Simplified 67.5%

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

   9. Taylor expanded in i around 0 51.0%

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

       1. +-commutative 51.0%

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

       2. mul-1-neg 51.0%

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

       3. sub-neg 51.0%

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

       4. associate-*r* 83.2%

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

       5. *-commutative 83.2%

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

       6. associate-*r* 83.5%

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

       7. *-commutative 83.5%

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

   11. Simplified 83.5%

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

   if -4.59999999999999979e-83 < x < -1.69999999999999989e-157

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 74.0%

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

   4. Taylor expanded in c around 0 64.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 64.5%

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

      1. associate-*r* 64.5%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 64.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 64.5%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 64.5%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 64.5%

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

      6. *-commutative 64.5%

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

      7. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in y around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

   10. Simplified 64.1%

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

   11. Taylor expanded in i around inf 70.8%

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

       1. *-commutative 70.8%

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

   13. Simplified 70.8%

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

   if -1.69999999999999989e-157 < x < -1.3e-220

   1. Initial program 54.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.3%

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

   if -1.3e-220 < x < 1.24999999999999992e-50

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 62.8%

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

   if 1.24999999999999992e-50 < x < 4.29999999999999978e48

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. *-commutative 59.5%

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

      5. *-commutative 59.5%

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

   5. Simplified 59.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-157}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-159}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -4.2e+193)
     t_1
     (if (<= x -9e+54)
       (* x (* y (- z (* i (/ j x)))))
       (if (<= x -6.5e-21)
         (* x (* a (- (* c (/ j x)) t)))
         (if (<= x -5e-55)
           (* b (* z (- c)))
           (if (<= x -3.5e-83)
             (* t (- (* b i) (* x a)))
             (if (<= x -5.1e-159)
               (* i (- (* t b) (* y j)))
               (if (<= x -1.1e-220)
                 (* b (- (* t i) (* z c)))
                 (if (<= x 7.8e-53)
                   (* j (- (* a c) (* y i)))
                   (if (<= x 2e+47) (* y (- (* x z) (* i j))) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.2e+193) {
		tmp = t_1;
	} else if (x <= -9e+54) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -6.5e-21) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -5e-55) {
		tmp = b * (z * -c);
	} else if (x <= -3.5e-83) {
		tmp = t * ((b * i) - (x * a));
	} else if (x <= -5.1e-159) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= -1.1e-220) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 7.8e-53) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 2e+47) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-4.2d+193)) then
        tmp = t_1
    else if (x <= (-9d+54)) then
        tmp = x * (y * (z - (i * (j / x))))
    else if (x <= (-6.5d-21)) then
        tmp = x * (a * ((c * (j / x)) - t))
    else if (x <= (-5d-55)) then
        tmp = b * (z * -c)
    else if (x <= (-3.5d-83)) then
        tmp = t * ((b * i) - (x * a))
    else if (x <= (-5.1d-159)) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= (-1.1d-220)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 7.8d-53) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 2d+47) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.2e+193) {
		tmp = t_1;
	} else if (x <= -9e+54) {
		tmp = x * (y * (z - (i * (j / x))));
	} else if (x <= -6.5e-21) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (x <= -5e-55) {
		tmp = b * (z * -c);
	} else if (x <= -3.5e-83) {
		tmp = t * ((b * i) - (x * a));
	} else if (x <= -5.1e-159) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= -1.1e-220) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 7.8e-53) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 2e+47) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.2e+193:
		tmp = t_1
	elif x <= -9e+54:
		tmp = x * (y * (z - (i * (j / x))))
	elif x <= -6.5e-21:
		tmp = x * (a * ((c * (j / x)) - t))
	elif x <= -5e-55:
		tmp = b * (z * -c)
	elif x <= -3.5e-83:
		tmp = t * ((b * i) - (x * a))
	elif x <= -5.1e-159:
		tmp = i * ((t * b) - (y * j))
	elif x <= -1.1e-220:
		tmp = b * ((t * i) - (z * c))
	elif x <= 7.8e-53:
		tmp = j * ((a * c) - (y * i))
	elif x <= 2e+47:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.2e+193)
		tmp = t_1;
	elseif (x <= -9e+54)
		tmp = Float64(x * Float64(y * Float64(z - Float64(i * Float64(j / x)))));
	elseif (x <= -6.5e-21)
		tmp = Float64(x * Float64(a * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (x <= -5e-55)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -3.5e-83)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (x <= -5.1e-159)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= -1.1e-220)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 7.8e-53)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 2e+47)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.2e+193)
		tmp = t_1;
	elseif (x <= -9e+54)
		tmp = x * (y * (z - (i * (j / x))));
	elseif (x <= -6.5e-21)
		tmp = x * (a * ((c * (j / x)) - t));
	elseif (x <= -5e-55)
		tmp = b * (z * -c);
	elseif (x <= -3.5e-83)
		tmp = t * ((b * i) - (x * a));
	elseif (x <= -5.1e-159)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= -1.1e-220)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 7.8e-53)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 2e+47)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+193], t$95$1, If[LessEqual[x, -9e+54], N[(x * N[(y * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-21], N[(x * N[(a * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e-55], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-83], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.1e-159], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-220], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-53], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+47], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -4.2e193 or 2.0000000000000001e47 < x

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.0%

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

   if -4.2e193 < x < -8.99999999999999968e54

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.7%

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

   4. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\left(-\frac{i \cdot j}{x}\right)}\right)\right) \]

      2. unsub-neg 63.1%

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

      3. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   if -8.99999999999999968e54 < x < -6.49999999999999987e-21

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.1%

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

   4. Taylor expanded in a around inf 71.1%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(\frac{c \cdot j}{x} - t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 71.2%

         \[\leadsto x \cdot \left(a \cdot \left(\color{blue}{c \cdot \frac{j}{x}} - t\right)\right) \]

   6. Simplified 71.2%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)} \]

   if -6.49999999999999987e-21 < x < -5.0000000000000002e-55

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-rgt-neg-in 85.9%

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

      3. distribute-lft-neg-in 85.9%

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

   8. Simplified 85.9%

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

   if -5.0000000000000002e-55 < x < -3.5000000000000003e-83

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 100.0%

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

   4. Taylor expanded in t around inf 83.2%

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

      1. +-commutative 83.2%

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

      2. mul-1-neg 83.2%

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

      3. unsub-neg 83.2%

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

      4. *-commutative 83.2%

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

      5. *-commutative 83.2%

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

   6. Simplified 83.2%

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

   if -3.5000000000000003e-83 < x < -5.0999999999999995e-159

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 74.0%

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

   4. Taylor expanded in c around 0 64.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 64.5%

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

      1. associate-*r* 64.5%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 64.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 64.5%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 64.5%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 64.5%

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

      6. *-commutative 64.5%

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

      7. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in y around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

   10. Simplified 64.1%

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

   11. Taylor expanded in i around inf 70.8%

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

       1. *-commutative 70.8%

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

   13. Simplified 70.8%

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

   if -5.0999999999999995e-159 < x < -1.09999999999999993e-220

   1. Initial program 54.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.3%

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

   if -1.09999999999999993e-220 < x < 7.8000000000000004e-53

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 62.8%

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

   if 7.8000000000000004e-53 < x < 2.0000000000000001e47

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. *-commutative 59.5%

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

      5. *-commutative 59.5%

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

   5. Simplified 59.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-159}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-164}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= x -3.6e+193)
     t_2
     (if (<= x -5e+168)
       t_1
       (if (<= x -6.2e-21)
         t_2
         (if (<= x -1.4e-54)
           (* b (* z (- c)))
           (if (<= x -7.5e-128)
             t_1
             (if (<= x -8.8e-212)
               (* b (- (* t i) (* z c)))
               (if (<= x 8.5e-164)
                 (* j (- (* a c) (* y i)))
                 (if (<= x 3.5e+65)
                   t_1
                   (if (<= x 8.6e+185) (* z (* x y)) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (x <= -3.6e+193) {
		tmp = t_2;
	} else if (x <= -5e+168) {
		tmp = t_1;
	} else if (x <= -6.2e-21) {
		tmp = t_2;
	} else if (x <= -1.4e-54) {
		tmp = b * (z * -c);
	} else if (x <= -7.5e-128) {
		tmp = t_1;
	} else if (x <= -8.8e-212) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 8.5e-164) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 3.5e+65) {
		tmp = t_1;
	} else if (x <= 8.6e+185) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    if (x <= (-3.6d+193)) then
        tmp = t_2
    else if (x <= (-5d+168)) then
        tmp = t_1
    else if (x <= (-6.2d-21)) then
        tmp = t_2
    else if (x <= (-1.4d-54)) then
        tmp = b * (z * -c)
    else if (x <= (-7.5d-128)) then
        tmp = t_1
    else if (x <= (-8.8d-212)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 8.5d-164) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 3.5d+65) then
        tmp = t_1
    else if (x <= 8.6d+185) then
        tmp = z * (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (x <= -3.6e+193) {
		tmp = t_2;
	} else if (x <= -5e+168) {
		tmp = t_1;
	} else if (x <= -6.2e-21) {
		tmp = t_2;
	} else if (x <= -1.4e-54) {
		tmp = b * (z * -c);
	} else if (x <= -7.5e-128) {
		tmp = t_1;
	} else if (x <= -8.8e-212) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 8.5e-164) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 3.5e+65) {
		tmp = t_1;
	} else if (x <= 8.6e+185) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if x <= -3.6e+193:
		tmp = t_2
	elif x <= -5e+168:
		tmp = t_1
	elif x <= -6.2e-21:
		tmp = t_2
	elif x <= -1.4e-54:
		tmp = b * (z * -c)
	elif x <= -7.5e-128:
		tmp = t_1
	elif x <= -8.8e-212:
		tmp = b * ((t * i) - (z * c))
	elif x <= 8.5e-164:
		tmp = j * ((a * c) - (y * i))
	elif x <= 3.5e+65:
		tmp = t_1
	elif x <= 8.6e+185:
		tmp = z * (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (x <= -3.6e+193)
		tmp = t_2;
	elseif (x <= -5e+168)
		tmp = t_1;
	elseif (x <= -6.2e-21)
		tmp = t_2;
	elseif (x <= -1.4e-54)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -7.5e-128)
		tmp = t_1;
	elseif (x <= -8.8e-212)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 8.5e-164)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 3.5e+65)
		tmp = t_1;
	elseif (x <= 8.6e+185)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (x <= -3.6e+193)
		tmp = t_2;
	elseif (x <= -5e+168)
		tmp = t_1;
	elseif (x <= -6.2e-21)
		tmp = t_2;
	elseif (x <= -1.4e-54)
		tmp = b * (z * -c);
	elseif (x <= -7.5e-128)
		tmp = t_1;
	elseif (x <= -8.8e-212)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 8.5e-164)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 3.5e+65)
		tmp = t_1;
	elseif (x <= 8.6e+185)
		tmp = z * (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+193], t$95$2, If[LessEqual[x, -5e+168], t$95$1, If[LessEqual[x, -6.2e-21], t$95$2, If[LessEqual[x, -1.4e-54], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-128], t$95$1, If[LessEqual[x, -8.8e-212], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-164], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+65], t$95$1, If[LessEqual[x, 8.6e+185], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.6e193 or -4.99999999999999967e168 < x < -6.1999999999999997e-21 or 8.6000000000000002e185 < x

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 51.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 51.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -3.6e193 < x < -4.99999999999999967e168 or -1.4000000000000001e-54 < x < -7.50000000000000021e-128 or 8.50000000000000035e-164 < x < 3.5000000000000001e65

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 74.1%

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

   4. Taylor expanded in c around 0 75.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 75.0%

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

      1. associate-*r* 75.0%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 75.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 75.0%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 75.0%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 75.0%

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

      6. *-commutative 75.0%

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

      7. unsub-neg 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-in 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

   10. Simplified 69.2%

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

   11. Taylor expanded in i around inf 57.8%

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

       1. *-commutative 57.8%

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

   13. Simplified 57.8%

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

   if -6.1999999999999997e-21 < x < -1.4000000000000001e-54

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-rgt-neg-in 85.9%

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

      3. distribute-lft-neg-in 85.9%

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

   8. Simplified 85.9%

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

   if -7.50000000000000021e-128 < x < -8.80000000000000012e-212

   1. Initial program 54.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 60.8%

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

   if -8.80000000000000012e-212 < x < 8.50000000000000035e-164

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 63.2%

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

   if 3.5000000000000001e65 < x < 8.6000000000000002e185

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 58.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.2%

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

      2. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in y around inf 48.3%

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

      1. *-commutative 48.3%

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

   8. Simplified 48.3%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+193}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-164}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+65}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(y \cdot \left(t \cdot \frac{b}{y} - j\right)\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{+142}:\\ \;\;\;\;t\_1 + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_3 (+ (* i (* t b)) (* j (- (* a c) (* y i))))))
   (if (<= c -1.6e+191)
     (* j (* a c))
     (if (<= c -5.5e+165)
       t_2
       (if (<= c -6.8e+103)
         t_3
         (if (<= c -2.8e-8)
           t_2
           (if (<= c -1.55e-52)
             t_3
             (if (<= c -3.1e-114)
               (- (* i (* y (- (* t (/ b y)) j))) (* x (- (* t a) (* y z))))
               (if (<= c 8.8e+142)
                 (+ t_1 (* i (- (* t b) (* y j))))
                 (- (* c (- (* a j) (* z b))) (* a (* x t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	double tmp;
	if (c <= -1.6e+191) {
		tmp = j * (a * c);
	} else if (c <= -5.5e+165) {
		tmp = t_2;
	} else if (c <= -6.8e+103) {
		tmp = t_3;
	} else if (c <= -2.8e-8) {
		tmp = t_2;
	} else if (c <= -1.55e-52) {
		tmp = t_3;
	} else if (c <= -3.1e-114) {
		tmp = (i * (y * ((t * (b / y)) - j))) - (x * ((t * a) - (y * z)));
	} else if (c <= 8.8e+142) {
		tmp = t_1 + (i * ((t * b) - (y * j)));
	} else {
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)))
    if (c <= (-1.6d+191)) then
        tmp = j * (a * c)
    else if (c <= (-5.5d+165)) then
        tmp = t_2
    else if (c <= (-6.8d+103)) then
        tmp = t_3
    else if (c <= (-2.8d-8)) then
        tmp = t_2
    else if (c <= (-1.55d-52)) then
        tmp = t_3
    else if (c <= (-3.1d-114)) then
        tmp = (i * (y * ((t * (b / y)) - j))) - (x * ((t * a) - (y * z)))
    else if (c <= 8.8d+142) then
        tmp = t_1 + (i * ((t * b) - (y * j)))
    else
        tmp = (c * ((a * j) - (z * b))) - (a * (x * 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 t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	double tmp;
	if (c <= -1.6e+191) {
		tmp = j * (a * c);
	} else if (c <= -5.5e+165) {
		tmp = t_2;
	} else if (c <= -6.8e+103) {
		tmp = t_3;
	} else if (c <= -2.8e-8) {
		tmp = t_2;
	} else if (c <= -1.55e-52) {
		tmp = t_3;
	} else if (c <= -3.1e-114) {
		tmp = (i * (y * ((t * (b / y)) - j))) - (x * ((t * a) - (y * z)));
	} else if (c <= 8.8e+142) {
		tmp = t_1 + (i * ((t * b) - (y * j)));
	} else {
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)))
	tmp = 0
	if c <= -1.6e+191:
		tmp = j * (a * c)
	elif c <= -5.5e+165:
		tmp = t_2
	elif c <= -6.8e+103:
		tmp = t_3
	elif c <= -2.8e-8:
		tmp = t_2
	elif c <= -1.55e-52:
		tmp = t_3
	elif c <= -3.1e-114:
		tmp = (i * (y * ((t * (b / y)) - j))) - (x * ((t * a) - (y * z)))
	elif c <= 8.8e+142:
		tmp = t_1 + (i * ((t * b) - (y * j)))
	else:
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(Float64(i * Float64(t * b)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (c <= -1.6e+191)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= -5.5e+165)
		tmp = t_2;
	elseif (c <= -6.8e+103)
		tmp = t_3;
	elseif (c <= -2.8e-8)
		tmp = t_2;
	elseif (c <= -1.55e-52)
		tmp = t_3;
	elseif (c <= -3.1e-114)
		tmp = Float64(Float64(i * Float64(y * Float64(Float64(t * Float64(b / y)) - j))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (c <= 8.8e+142)
		tmp = Float64(t_1 + Float64(i * Float64(Float64(t * b) - Float64(y * j))));
	else
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(a * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (c <= -1.6e+191)
		tmp = j * (a * c);
	elseif (c <= -5.5e+165)
		tmp = t_2;
	elseif (c <= -6.8e+103)
		tmp = t_3;
	elseif (c <= -2.8e-8)
		tmp = t_2;
	elseif (c <= -1.55e-52)
		tmp = t_3;
	elseif (c <= -3.1e-114)
		tmp = (i * (y * ((t * (b / y)) - j))) - (x * ((t * a) - (y * z)));
	elseif (c <= 8.8e+142)
		tmp = t_1 + (i * ((t * b) - (y * j)));
	else
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.6e+191], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.5e+165], t$95$2, If[LessEqual[c, -6.8e+103], t$95$3, If[LessEqual[c, -2.8e-8], t$95$2, If[LessEqual[c, -1.55e-52], t$95$3, If[LessEqual[c, -3.1e-114], N[(N[(i * N[(y * N[(N[(t * N[(b / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e+142], N[(t$95$1 + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.6000000000000001e191

   1. Initial program 26.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 64.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 64.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 71.1%

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

      1. associate-*r* 75.1%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 75.1%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -1.6000000000000001e191 < c < -5.4999999999999998e165 or -6.7999999999999997e103 < c < -2.7999999999999999e-8

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 82.0%

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

   if -5.4999999999999998e165 < c < -6.7999999999999997e103 or -2.7999999999999999e-8 < c < -1.5499999999999999e-52

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.9%

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

      1. associate-*r* 65.1%

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

      2. *-commutative 65.1%

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

      3. associate-*r* 72.9%

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

   5. Simplified 72.9%

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

   if -1.5499999999999999e-52 < c < -3.1e-114

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 73.3%

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

   4. Taylor expanded in c around 0 65.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around inf 65.0%

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

      1. +-commutative 65.0%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} + -1 \cdot j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-commutative 65.0%

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

      5. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

   if -3.1e-114 < c < 8.79999999999999947e142

   1. Initial program 83.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 80.3%

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

   4. Taylor expanded in c around 0 74.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 74.4%

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

      1. associate-*r* 74.4%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 74.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 74.4%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 74.4%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 74.4%

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

      6. *-commutative 74.4%

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

      7. unsub-neg 74.4%

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

   7. Simplified 74.4%

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

   if 8.79999999999999947e142 < c

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 46.7%

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

   4. Taylor expanded in c around 0 66.7%

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

   5. Taylor expanded in a around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. *-commutative 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

   7. Simplified 83.6%

      \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(y \cdot \left(t \cdot \frac{b}{y} - j\right)\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := a \cdot \left(x \cdot t\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+192}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{+104}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -0.00013:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-58}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right) - t\_4\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+144}:\\ \;\;\;\;t\_1 + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_3 (+ (* i (* t b)) (* j (- (* a c) (* y i)))))
        (t_4 (* a (* x t))))
   (if (<= c -6.2e+192)
     (* j (* a c))
     (if (<= c -3.5e+165)
       t_2
       (if (<= c -5.6e+104)
         t_3
         (if (<= c -0.00013)
           t_2
           (if (<= c -2.4e-58)
             t_3
             (if (<= c -7.6e-107)
               (- (* i (* y (- (* b (/ t y)) j))) t_4)
               (if (<= c 4e+144)
                 (+ t_1 (* i (- (* t b) (* y j))))
                 (- (* c (- (* a j) (* z b))) t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	double t_4 = a * (x * t);
	double tmp;
	if (c <= -6.2e+192) {
		tmp = j * (a * c);
	} else if (c <= -3.5e+165) {
		tmp = t_2;
	} else if (c <= -5.6e+104) {
		tmp = t_3;
	} else if (c <= -0.00013) {
		tmp = t_2;
	} else if (c <= -2.4e-58) {
		tmp = t_3;
	} else if (c <= -7.6e-107) {
		tmp = (i * (y * ((b * (t / y)) - j))) - t_4;
	} else if (c <= 4e+144) {
		tmp = t_1 + (i * ((t * b) - (y * j)));
	} else {
		tmp = (c * ((a * j) - (z * b))) - t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)))
    t_4 = a * (x * t)
    if (c <= (-6.2d+192)) then
        tmp = j * (a * c)
    else if (c <= (-3.5d+165)) then
        tmp = t_2
    else if (c <= (-5.6d+104)) then
        tmp = t_3
    else if (c <= (-0.00013d0)) then
        tmp = t_2
    else if (c <= (-2.4d-58)) then
        tmp = t_3
    else if (c <= (-7.6d-107)) then
        tmp = (i * (y * ((b * (t / y)) - j))) - t_4
    else if (c <= 4d+144) then
        tmp = t_1 + (i * ((t * b) - (y * j)))
    else
        tmp = (c * ((a * j) - (z * b))) - t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	double t_4 = a * (x * t);
	double tmp;
	if (c <= -6.2e+192) {
		tmp = j * (a * c);
	} else if (c <= -3.5e+165) {
		tmp = t_2;
	} else if (c <= -5.6e+104) {
		tmp = t_3;
	} else if (c <= -0.00013) {
		tmp = t_2;
	} else if (c <= -2.4e-58) {
		tmp = t_3;
	} else if (c <= -7.6e-107) {
		tmp = (i * (y * ((b * (t / y)) - j))) - t_4;
	} else if (c <= 4e+144) {
		tmp = t_1 + (i * ((t * b) - (y * j)));
	} else {
		tmp = (c * ((a * j) - (z * b))) - t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)))
	t_4 = a * (x * t)
	tmp = 0
	if c <= -6.2e+192:
		tmp = j * (a * c)
	elif c <= -3.5e+165:
		tmp = t_2
	elif c <= -5.6e+104:
		tmp = t_3
	elif c <= -0.00013:
		tmp = t_2
	elif c <= -2.4e-58:
		tmp = t_3
	elif c <= -7.6e-107:
		tmp = (i * (y * ((b * (t / y)) - j))) - t_4
	elif c <= 4e+144:
		tmp = t_1 + (i * ((t * b) - (y * j)))
	else:
		tmp = (c * ((a * j) - (z * b))) - t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(Float64(i * Float64(t * b)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_4 = Float64(a * Float64(x * t))
	tmp = 0.0
	if (c <= -6.2e+192)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= -3.5e+165)
		tmp = t_2;
	elseif (c <= -5.6e+104)
		tmp = t_3;
	elseif (c <= -0.00013)
		tmp = t_2;
	elseif (c <= -2.4e-58)
		tmp = t_3;
	elseif (c <= -7.6e-107)
		tmp = Float64(Float64(i * Float64(y * Float64(Float64(b * Float64(t / y)) - j))) - t_4);
	elseif (c <= 4e+144)
		tmp = Float64(t_1 + Float64(i * Float64(Float64(t * b) - Float64(y * j))));
	else
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	t_3 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	t_4 = a * (x * t);
	tmp = 0.0;
	if (c <= -6.2e+192)
		tmp = j * (a * c);
	elseif (c <= -3.5e+165)
		tmp = t_2;
	elseif (c <= -5.6e+104)
		tmp = t_3;
	elseif (c <= -0.00013)
		tmp = t_2;
	elseif (c <= -2.4e-58)
		tmp = t_3;
	elseif (c <= -7.6e-107)
		tmp = (i * (y * ((b * (t / y)) - j))) - t_4;
	elseif (c <= 4e+144)
		tmp = t_1 + (i * ((t * b) - (y * j)));
	else
		tmp = (c * ((a * j) - (z * b))) - t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+192], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.5e+165], t$95$2, If[LessEqual[c, -5.6e+104], t$95$3, If[LessEqual[c, -0.00013], t$95$2, If[LessEqual[c, -2.4e-58], t$95$3, If[LessEqual[c, -7.6e-107], N[(N[(i * N[(y * N[(N[(b * N[(t / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[c, 4e+144], N[(t$95$1 + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.1999999999999997e192

   1. Initial program 26.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 64.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 64.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 71.1%

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

      1. associate-*r* 75.1%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 75.1%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -6.1999999999999997e192 < c < -3.49999999999999996e165 or -5.6e104 < c < -1.29999999999999989e-4

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 82.0%

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

   if -3.49999999999999996e165 < c < -5.6e104 or -1.29999999999999989e-4 < c < -2.4000000000000001e-58

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.9%

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

      1. associate-*r* 65.1%

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

      2. *-commutative 65.1%

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

      3. associate-*r* 72.9%

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

   5. Simplified 72.9%

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

   if -2.4000000000000001e-58 < c < -7.6000000000000004e-107

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 63.3%

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

   4. Taylor expanded in c around 0 63.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 63.3%

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

      1. associate-*r* 63.3%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 63.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 63.3%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 63.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 63.3%

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

      6. *-commutative 63.3%

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

      7. unsub-neg 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. distribute-rgt-neg-in 75.8%

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

      3. distribute-rgt-neg-in 75.8%

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

   10. Simplified 75.8%

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

   11. Taylor expanded in y around inf 75.8%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(\frac{b \cdot t}{y} - j\right)\right)} + a \cdot \left(t \cdot \left(-x\right)\right) \]
   12. Step-by-step derivation

       1. associate-/l* 88.3%

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

   13. Simplified 88.3%

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

   if -7.6000000000000004e-107 < c < 4.00000000000000009e144

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 80.7%

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

   4. Taylor expanded in c around 0 74.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 74.3%

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

      1. associate-*r* 74.3%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 74.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 74.3%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 74.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 74.3%

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

      6. *-commutative 74.3%

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

      7. unsub-neg 74.3%

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

   7. Simplified 74.3%

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

   if 4.00000000000000009e144 < c

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 46.7%

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

   4. Taylor expanded in c around 0 66.7%

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

   5. Taylor expanded in a around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. *-commutative 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

   7. Simplified 83.6%

      \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+192}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -0.00013:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-107}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+217}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -510000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+163}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+242}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (* c (- b)))))
   (if (<= b -1.2e+217)
     (* i (* t b))
     (if (<= b -1.05e+179)
       t_1
       (if (<= b -6.2e+93)
         (* t (* b i))
         (if (<= b -510000.0)
           t_2
           (if (<= b 2.5e+33)
             t_1
             (if (<= b 1.14e+141)
               t_2
               (if (<= b 6.2e+163)
                 (* (* i j) (- y))
                 (if (<= b 1.4e+242) (* y (* x z)) (* b (* z (- c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * (c * -b);
	double tmp;
	if (b <= -1.2e+217) {
		tmp = i * (t * b);
	} else if (b <= -1.05e+179) {
		tmp = t_1;
	} else if (b <= -6.2e+93) {
		tmp = t * (b * i);
	} else if (b <= -510000.0) {
		tmp = t_2;
	} else if (b <= 2.5e+33) {
		tmp = t_1;
	} else if (b <= 1.14e+141) {
		tmp = t_2;
	} else if (b <= 6.2e+163) {
		tmp = (i * j) * -y;
	} else if (b <= 1.4e+242) {
		tmp = y * (x * z);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * (c * -b)
    if (b <= (-1.2d+217)) then
        tmp = i * (t * b)
    else if (b <= (-1.05d+179)) then
        tmp = t_1
    else if (b <= (-6.2d+93)) then
        tmp = t * (b * i)
    else if (b <= (-510000.0d0)) then
        tmp = t_2
    else if (b <= 2.5d+33) then
        tmp = t_1
    else if (b <= 1.14d+141) then
        tmp = t_2
    else if (b <= 6.2d+163) then
        tmp = (i * j) * -y
    else if (b <= 1.4d+242) then
        tmp = y * (x * z)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * (c * -b);
	double tmp;
	if (b <= -1.2e+217) {
		tmp = i * (t * b);
	} else if (b <= -1.05e+179) {
		tmp = t_1;
	} else if (b <= -6.2e+93) {
		tmp = t * (b * i);
	} else if (b <= -510000.0) {
		tmp = t_2;
	} else if (b <= 2.5e+33) {
		tmp = t_1;
	} else if (b <= 1.14e+141) {
		tmp = t_2;
	} else if (b <= 6.2e+163) {
		tmp = (i * j) * -y;
	} else if (b <= 1.4e+242) {
		tmp = y * (x * z);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * (c * -b)
	tmp = 0
	if b <= -1.2e+217:
		tmp = i * (t * b)
	elif b <= -1.05e+179:
		tmp = t_1
	elif b <= -6.2e+93:
		tmp = t * (b * i)
	elif b <= -510000.0:
		tmp = t_2
	elif b <= 2.5e+33:
		tmp = t_1
	elif b <= 1.14e+141:
		tmp = t_2
	elif b <= 6.2e+163:
		tmp = (i * j) * -y
	elif b <= 1.4e+242:
		tmp = y * (x * z)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(c * Float64(-b)))
	tmp = 0.0
	if (b <= -1.2e+217)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -1.05e+179)
		tmp = t_1;
	elseif (b <= -6.2e+93)
		tmp = Float64(t * Float64(b * i));
	elseif (b <= -510000.0)
		tmp = t_2;
	elseif (b <= 2.5e+33)
		tmp = t_1;
	elseif (b <= 1.14e+141)
		tmp = t_2;
	elseif (b <= 6.2e+163)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (b <= 1.4e+242)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = z * (c * -b);
	tmp = 0.0;
	if (b <= -1.2e+217)
		tmp = i * (t * b);
	elseif (b <= -1.05e+179)
		tmp = t_1;
	elseif (b <= -6.2e+93)
		tmp = t * (b * i);
	elseif (b <= -510000.0)
		tmp = t_2;
	elseif (b <= 2.5e+33)
		tmp = t_1;
	elseif (b <= 1.14e+141)
		tmp = t_2;
	elseif (b <= 6.2e+163)
		tmp = (i * j) * -y;
	elseif (b <= 1.4e+242)
		tmp = y * (x * z);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+217], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e+179], t$95$1, If[LessEqual[b, -6.2e+93], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -510000.0], t$95$2, If[LessEqual[b, 2.5e+33], t$95$1, If[LessEqual[b, 1.14e+141], t$95$2, If[LessEqual[b, 6.2e+163], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[b, 1.4e+242], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.1999999999999999e217

   1. Initial program 49.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 50.0%

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

      1. distribute-lft-out-- 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in j around 0 50.1%

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

      1. neg-mul-1 50.1%

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

      2. distribute-rgt-neg-in 50.1%

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

   8. Simplified 50.1%

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

   if -1.1999999999999999e217 < b < -1.0499999999999999e179 or -5.1e5 < b < 2.49999999999999986e33

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -1.0499999999999999e179 < b < -6.20000000000000038e93

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 63.5%

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

   4. Taylor expanded in c around 0 66.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-*r* 50.7%

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

   7. Simplified 50.7%

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

   if -6.20000000000000038e93 < b < -5.1e5 or 2.49999999999999986e33 < b < 1.14000000000000003e141

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 51.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in y around 0 51.3%

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

      1. neg-mul-1 51.3%

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

      2. distribute-rgt-neg-in 51.3%

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

   8. Simplified 51.3%

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

   if 1.14000000000000003e141 < b < 6.20000000000000057e163

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 76.0%

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

      1. associate-*r* 76.0%

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

      2. neg-mul-1 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in c around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. associate-*r* 75.4%

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

      3. distribute-rgt-neg-in 75.4%

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

   8. Simplified 75.4%

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

   if 6.20000000000000057e163 < b < 1.4e242

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 67.2%

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

   4. Taylor expanded in c around 0 62.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in z around inf 45.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-*r* 50.8%

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

   7. Simplified 50.8%

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

   if 1.4e242 < b

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.7%

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

      2. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. distribute-rgt-neg-in 63.1%

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

      3. distribute-lft-neg-in 63.1%

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

   8. Simplified 63.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(-c\right) \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+217}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+179}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -510000:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+163}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+242}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot j\right) \cdot \left(-y\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-166}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i j) (- y))) (t_2 (* x (* t (- a)))))
   (if (<= a -3.9e+133)
     t_2
     (if (<= a -4.3e+68)
       t_1
       (if (<= a -1.26e+29)
         t_2
         (if (<= a -2.65e-166)
           (* z (* c (- b)))
           (if (<= a -4.4e-200)
             (* x (* y z))
             (if (<= a -2.85e-285)
               t_1
               (if (<= a 5.6e-216)
                 (* y (* x z))
                 (if (<= a 4e+202) t_1 (* t (* x (- a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * j) * -y;
	double t_2 = x * (t * -a);
	double tmp;
	if (a <= -3.9e+133) {
		tmp = t_2;
	} else if (a <= -4.3e+68) {
		tmp = t_1;
	} else if (a <= -1.26e+29) {
		tmp = t_2;
	} else if (a <= -2.65e-166) {
		tmp = z * (c * -b);
	} else if (a <= -4.4e-200) {
		tmp = x * (y * z);
	} else if (a <= -2.85e-285) {
		tmp = t_1;
	} else if (a <= 5.6e-216) {
		tmp = y * (x * z);
	} else if (a <= 4e+202) {
		tmp = t_1;
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * j) * -y
    t_2 = x * (t * -a)
    if (a <= (-3.9d+133)) then
        tmp = t_2
    else if (a <= (-4.3d+68)) then
        tmp = t_1
    else if (a <= (-1.26d+29)) then
        tmp = t_2
    else if (a <= (-2.65d-166)) then
        tmp = z * (c * -b)
    else if (a <= (-4.4d-200)) then
        tmp = x * (y * z)
    else if (a <= (-2.85d-285)) then
        tmp = t_1
    else if (a <= 5.6d-216) then
        tmp = y * (x * z)
    else if (a <= 4d+202) then
        tmp = t_1
    else
        tmp = t * (x * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * j) * -y;
	double t_2 = x * (t * -a);
	double tmp;
	if (a <= -3.9e+133) {
		tmp = t_2;
	} else if (a <= -4.3e+68) {
		tmp = t_1;
	} else if (a <= -1.26e+29) {
		tmp = t_2;
	} else if (a <= -2.65e-166) {
		tmp = z * (c * -b);
	} else if (a <= -4.4e-200) {
		tmp = x * (y * z);
	} else if (a <= -2.85e-285) {
		tmp = t_1;
	} else if (a <= 5.6e-216) {
		tmp = y * (x * z);
	} else if (a <= 4e+202) {
		tmp = t_1;
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * j) * -y
	t_2 = x * (t * -a)
	tmp = 0
	if a <= -3.9e+133:
		tmp = t_2
	elif a <= -4.3e+68:
		tmp = t_1
	elif a <= -1.26e+29:
		tmp = t_2
	elif a <= -2.65e-166:
		tmp = z * (c * -b)
	elif a <= -4.4e-200:
		tmp = x * (y * z)
	elif a <= -2.85e-285:
		tmp = t_1
	elif a <= 5.6e-216:
		tmp = y * (x * z)
	elif a <= 4e+202:
		tmp = t_1
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * j) * Float64(-y))
	t_2 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (a <= -3.9e+133)
		tmp = t_2;
	elseif (a <= -4.3e+68)
		tmp = t_1;
	elseif (a <= -1.26e+29)
		tmp = t_2;
	elseif (a <= -2.65e-166)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (a <= -4.4e-200)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -2.85e-285)
		tmp = t_1;
	elseif (a <= 5.6e-216)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 4e+202)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * j) * -y;
	t_2 = x * (t * -a);
	tmp = 0.0;
	if (a <= -3.9e+133)
		tmp = t_2;
	elseif (a <= -4.3e+68)
		tmp = t_1;
	elseif (a <= -1.26e+29)
		tmp = t_2;
	elseif (a <= -2.65e-166)
		tmp = z * (c * -b);
	elseif (a <= -4.4e-200)
		tmp = x * (y * z);
	elseif (a <= -2.85e-285)
		tmp = t_1;
	elseif (a <= 5.6e-216)
		tmp = y * (x * z);
	elseif (a <= 4e+202)
		tmp = t_1;
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+133], t$95$2, If[LessEqual[a, -4.3e+68], t$95$1, If[LessEqual[a, -1.26e+29], t$95$2, If[LessEqual[a, -2.65e-166], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e-200], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.85e-285], t$95$1, If[LessEqual[a, 5.6e-216], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+202], t$95$1, N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.90000000000000014e133 or -4.3000000000000001e68 < a < -1.26e29

   1. Initial program 64.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 60.5%

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

   4. Taylor expanded in c around 0 58.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around inf 54.4%

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

      1. +-commutative 54.4%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} + -1 \cdot j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

      5. associate-/l* 56.7%

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

   7. Simplified 56.7%

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

   8. Taylor expanded in a around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. *-commutative 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-*r* 59.3%

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

      5. distribute-rgt-neg-in 59.3%

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

   10. Simplified 59.3%

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

   if -3.90000000000000014e133 < a < -4.3000000000000001e68 or -4.40000000000000027e-200 < a < -2.85000000000000013e-285 or 5.6e-216 < a < 3.9999999999999996e202

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. neg-mul-1 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in c around 0 37.4%

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

      1. mul-1-neg 37.4%

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

      2. associate-*r* 38.9%

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

      3. distribute-rgt-neg-in 38.9%

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

   8. Simplified 38.9%

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

   if -1.26e29 < a < -2.64999999999999998e-166

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 55.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around 0 44.8%

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

      1. neg-mul-1 44.8%

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

      2. distribute-rgt-neg-in 44.8%

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

   8. Simplified 44.8%

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

   if -2.64999999999999998e-166 < a < -4.40000000000000027e-200

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in y around inf 83.2%

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

   if -2.85000000000000013e-285 < a < 5.6e-216

   1. Initial program 62.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 62.4%

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

   4. Taylor expanded in c around 0 71.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in z around inf 35.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.5%

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

      2. *-commutative 39.5%

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

      3. associate-*r* 44.1%

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

   7. Simplified 44.1%

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

   if 3.9999999999999996e202 < a

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.8%

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

      1. distribute-lft-out-- 55.8%

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

      2. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in a around inf 25.5%

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

      1. mul-1-neg 25.5%

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

      2. *-commutative 25.5%

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

      3. associate-*r* 42.0%

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

      4. *-commutative 42.0%

         \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

      5. distribute-rgt-neg-out 42.0%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right)} \]

      6. *-commutative 42.0%

         \[\leadsto t \cdot \left(-\color{blue}{x \cdot a}\right) \]

      7. distribute-rgt-neg-in 42.0%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-166}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-285}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+202}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 390:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))) (t_2 (* i (* y (- j)))))
   (if (<= a -8e+28)
     (* x (* t (- a)))
     (if (<= a -6.6e-80)
       t_1
       (if (<= a -2.2e-106)
         t_2
         (if (<= a -3.9e-157)
           t_1
           (if (<= a -2.6e-173)
             (* z (* x y))
             (if (<= a 390.0)
               t_2
               (if (<= a 1.8e+72)
                 (* a (* t (- x)))
                 (if (<= a 3.9e+202) t_2 (* t (* x (- a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = i * (y * -j);
	double tmp;
	if (a <= -8e+28) {
		tmp = x * (t * -a);
	} else if (a <= -6.6e-80) {
		tmp = t_1;
	} else if (a <= -2.2e-106) {
		tmp = t_2;
	} else if (a <= -3.9e-157) {
		tmp = t_1;
	} else if (a <= -2.6e-173) {
		tmp = z * (x * y);
	} else if (a <= 390.0) {
		tmp = t_2;
	} else if (a <= 1.8e+72) {
		tmp = a * (t * -x);
	} else if (a <= 3.9e+202) {
		tmp = t_2;
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (c * -b)
    t_2 = i * (y * -j)
    if (a <= (-8d+28)) then
        tmp = x * (t * -a)
    else if (a <= (-6.6d-80)) then
        tmp = t_1
    else if (a <= (-2.2d-106)) then
        tmp = t_2
    else if (a <= (-3.9d-157)) then
        tmp = t_1
    else if (a <= (-2.6d-173)) then
        tmp = z * (x * y)
    else if (a <= 390.0d0) then
        tmp = t_2
    else if (a <= 1.8d+72) then
        tmp = a * (t * -x)
    else if (a <= 3.9d+202) then
        tmp = t_2
    else
        tmp = t * (x * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = i * (y * -j);
	double tmp;
	if (a <= -8e+28) {
		tmp = x * (t * -a);
	} else if (a <= -6.6e-80) {
		tmp = t_1;
	} else if (a <= -2.2e-106) {
		tmp = t_2;
	} else if (a <= -3.9e-157) {
		tmp = t_1;
	} else if (a <= -2.6e-173) {
		tmp = z * (x * y);
	} else if (a <= 390.0) {
		tmp = t_2;
	} else if (a <= 1.8e+72) {
		tmp = a * (t * -x);
	} else if (a <= 3.9e+202) {
		tmp = t_2;
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	t_2 = i * (y * -j)
	tmp = 0
	if a <= -8e+28:
		tmp = x * (t * -a)
	elif a <= -6.6e-80:
		tmp = t_1
	elif a <= -2.2e-106:
		tmp = t_2
	elif a <= -3.9e-157:
		tmp = t_1
	elif a <= -2.6e-173:
		tmp = z * (x * y)
	elif a <= 390.0:
		tmp = t_2
	elif a <= 1.8e+72:
		tmp = a * (t * -x)
	elif a <= 3.9e+202:
		tmp = t_2
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (a <= -8e+28)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (a <= -6.6e-80)
		tmp = t_1;
	elseif (a <= -2.2e-106)
		tmp = t_2;
	elseif (a <= -3.9e-157)
		tmp = t_1;
	elseif (a <= -2.6e-173)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 390.0)
		tmp = t_2;
	elseif (a <= 1.8e+72)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= 3.9e+202)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (a <= -8e+28)
		tmp = x * (t * -a);
	elseif (a <= -6.6e-80)
		tmp = t_1;
	elseif (a <= -2.2e-106)
		tmp = t_2;
	elseif (a <= -3.9e-157)
		tmp = t_1;
	elseif (a <= -2.6e-173)
		tmp = z * (x * y);
	elseif (a <= 390.0)
		tmp = t_2;
	elseif (a <= 1.8e+72)
		tmp = a * (t * -x);
	elseif (a <= 3.9e+202)
		tmp = t_2;
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+28], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-80], t$95$1, If[LessEqual[a, -2.2e-106], t$95$2, If[LessEqual[a, -3.9e-157], t$95$1, If[LessEqual[a, -2.6e-173], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 390.0], t$95$2, If[LessEqual[a, 1.8e+72], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+202], t$95$2, N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.99999999999999967e28

   1. Initial program 67.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 64.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 57.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around inf 55.3%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot j + \frac{b \cdot t}{y}\right)\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]
   6. Step-by-step derivation

      1. +-commutative 55.3%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} + -1 \cdot j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. mul-1-neg 55.3%

         \[\leadsto i \cdot \left(y \cdot \left(\frac{b \cdot t}{y} + \color{blue}{\left(-j\right)}\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. unsub-neg 55.3%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} - j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. *-commutative 55.3%

         \[\leadsto i \cdot \left(y \cdot \left(\frac{\color{blue}{t \cdot b}}{y} - j\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. associate-/l* 57.1%

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{t \cdot \frac{b}{y}} - j\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Simplified 57.1%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(t \cdot \frac{b}{y} - j\right)\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   8. Taylor expanded in a around inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 41.8%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. *-commutative 41.8%

         \[\leadsto -\color{blue}{\left(x \cdot t\right)} \cdot a \]

      4. associate-*r* 48.1%

         \[\leadsto -\color{blue}{x \cdot \left(t \cdot a\right)} \]

      5. distribute-rgt-neg-in 48.1%

         \[\leadsto \color{blue}{x \cdot \left(-t \cdot a\right)} \]

   10. Simplified 48.1%

       \[\leadsto \color{blue}{x \cdot \left(-t \cdot a\right)} \]

   if -7.99999999999999967e28 < a < -6.5999999999999999e-80 or -2.19999999999999994e-106 < a < -3.89999999999999999e-157

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 56.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 56.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 46.5%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 46.5%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 46.5%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 46.5%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   if -6.5999999999999999e-80 < a < -2.19999999999999994e-106 or -2.60000000000000003e-173 < a < 390 or 1.80000000000000017e72 < a < 3.89999999999999983e202

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 56.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 56.6%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. neg-mul-1 56.6%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 56.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in c around 0 41.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 41.0%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 41.0%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if -3.89999999999999999e-157 < a < -2.60000000000000003e-173

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 66.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 66.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 100.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 100.0%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if 390 < a < 1.80000000000000017e72

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0 30.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 30.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. mul-1-neg 30.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

   8. Simplified 30.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]

   if 3.89999999999999983e202 < a

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 55.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 55.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around inf 25.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.5%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 25.5%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. associate-*r* 42.0%

         \[\leadsto -\color{blue}{t \cdot \left(x \cdot a\right)} \]

      4. *-commutative 42.0%

         \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

      5. distribute-rgt-neg-out 42.0%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right)} \]

      6. *-commutative 42.0%

         \[\leadsto t \cdot \left(-\color{blue}{x \cdot a}\right) \]

      7. distribute-rgt-neg-in 42.0%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-106}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-157}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 390:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i\right)\\ t_4 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-222}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j)))
        (t_2 (* j (* a c)))
        (t_3 (* t (* b i)))
        (t_4 (* z (* x y))))
   (if (<= x -8.6e+33)
     t_4
     (if (<= x -2.5e-60)
       t_1
       (if (<= x -7.8e-91)
         t_3
         (if (<= x -1.8e-101)
           t_1
           (if (<= x -1.95e-222)
             t_3
             (if (<= x -3.5e-273)
               t_2
               (if (<= x 4.5e-248)
                 (* b (* t i))
                 (if (<= x 9.5e-52) t_2 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = j * (a * c);
	double t_3 = t * (b * i);
	double t_4 = z * (x * y);
	double tmp;
	if (x <= -8.6e+33) {
		tmp = t_4;
	} else if (x <= -2.5e-60) {
		tmp = t_1;
	} else if (x <= -7.8e-91) {
		tmp = t_3;
	} else if (x <= -1.8e-101) {
		tmp = t_1;
	} else if (x <= -1.95e-222) {
		tmp = t_3;
	} else if (x <= -3.5e-273) {
		tmp = t_2;
	} else if (x <= 4.5e-248) {
		tmp = b * (t * i);
	} else if (x <= 9.5e-52) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = j * (a * c)
    t_3 = t * (b * i)
    t_4 = z * (x * y)
    if (x <= (-8.6d+33)) then
        tmp = t_4
    else if (x <= (-2.5d-60)) then
        tmp = t_1
    else if (x <= (-7.8d-91)) then
        tmp = t_3
    else if (x <= (-1.8d-101)) then
        tmp = t_1
    else if (x <= (-1.95d-222)) then
        tmp = t_3
    else if (x <= (-3.5d-273)) then
        tmp = t_2
    else if (x <= 4.5d-248) then
        tmp = b * (t * i)
    else if (x <= 9.5d-52) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = j * (a * c);
	double t_3 = t * (b * i);
	double t_4 = z * (x * y);
	double tmp;
	if (x <= -8.6e+33) {
		tmp = t_4;
	} else if (x <= -2.5e-60) {
		tmp = t_1;
	} else if (x <= -7.8e-91) {
		tmp = t_3;
	} else if (x <= -1.8e-101) {
		tmp = t_1;
	} else if (x <= -1.95e-222) {
		tmp = t_3;
	} else if (x <= -3.5e-273) {
		tmp = t_2;
	} else if (x <= 4.5e-248) {
		tmp = b * (t * i);
	} else if (x <= 9.5e-52) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = j * (a * c)
	t_3 = t * (b * i)
	t_4 = z * (x * y)
	tmp = 0
	if x <= -8.6e+33:
		tmp = t_4
	elif x <= -2.5e-60:
		tmp = t_1
	elif x <= -7.8e-91:
		tmp = t_3
	elif x <= -1.8e-101:
		tmp = t_1
	elif x <= -1.95e-222:
		tmp = t_3
	elif x <= -3.5e-273:
		tmp = t_2
	elif x <= 4.5e-248:
		tmp = b * (t * i)
	elif x <= 9.5e-52:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(j * Float64(a * c))
	t_3 = Float64(t * Float64(b * i))
	t_4 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -8.6e+33)
		tmp = t_4;
	elseif (x <= -2.5e-60)
		tmp = t_1;
	elseif (x <= -7.8e-91)
		tmp = t_3;
	elseif (x <= -1.8e-101)
		tmp = t_1;
	elseif (x <= -1.95e-222)
		tmp = t_3;
	elseif (x <= -3.5e-273)
		tmp = t_2;
	elseif (x <= 4.5e-248)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 9.5e-52)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = j * (a * c);
	t_3 = t * (b * i);
	t_4 = z * (x * y);
	tmp = 0.0;
	if (x <= -8.6e+33)
		tmp = t_4;
	elseif (x <= -2.5e-60)
		tmp = t_1;
	elseif (x <= -7.8e-91)
		tmp = t_3;
	elseif (x <= -1.8e-101)
		tmp = t_1;
	elseif (x <= -1.95e-222)
		tmp = t_3;
	elseif (x <= -3.5e-273)
		tmp = t_2;
	elseif (x <= 4.5e-248)
		tmp = b * (t * i);
	elseif (x <= 9.5e-52)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+33], t$95$4, If[LessEqual[x, -2.5e-60], t$95$1, If[LessEqual[x, -7.8e-91], t$95$3, If[LessEqual[x, -1.8e-101], t$95$1, If[LessEqual[x, -1.95e-222], t$95$3, If[LessEqual[x, -3.5e-273], t$95$2, If[LessEqual[x, 4.5e-248], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-52], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.60000000000000057e33 or 9.50000000000000007e-52 < x

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 48.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 40.7%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 40.7%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -8.60000000000000057e33 < x < -2.5000000000000001e-60 or -7.79999999999999987e-91 < x < -1.8e-101

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 55.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 55.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 32.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 32.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.5000000000000001e-60 < x < -7.79999999999999987e-91 or -1.8e-101 < x < -1.95e-222

   1. Initial program 63.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 72.3%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 59.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.1%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 39.1%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 42.2%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 42.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -1.95e-222 < x < -3.49999999999999992e-273 or 4.4999999999999996e-248 < x < 9.50000000000000007e-52

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 40.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 40.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 32.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 34.6%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -3.49999999999999992e-273 < x < 4.4999999999999996e-248

   1. Initial program 91.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 64.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 27.6%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 27.6%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 27.6%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   8. Simplified 27.6%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   9. Taylor expanded in i around 0 27.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 27.2%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 27.2%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-82}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -6.2e-21)
     t_2
     (if (<= x -2.3e-48)
       (* b (* z (- c)))
       (if (<= x -6e-82)
         (* i (- (* t b) (* y j)))
         (if (<= x -9e-147)
           t_1
           (if (<= x -8.6e-221)
             (* b (- (* t i) (* z c)))
             (if (<= x 7.4e-53)
               t_1
               (if (<= x 9.5e+51) (* y (- (* x z) (* i j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.2e-21) {
		tmp = t_2;
	} else if (x <= -2.3e-48) {
		tmp = b * (z * -c);
	} else if (x <= -6e-82) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= -9e-147) {
		tmp = t_1;
	} else if (x <= -8.6e-221) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 7.4e-53) {
		tmp = t_1;
	} else if (x <= 9.5e+51) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-6.2d-21)) then
        tmp = t_2
    else if (x <= (-2.3d-48)) then
        tmp = b * (z * -c)
    else if (x <= (-6d-82)) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= (-9d-147)) then
        tmp = t_1
    else if (x <= (-8.6d-221)) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 7.4d-53) then
        tmp = t_1
    else if (x <= 9.5d+51) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.2e-21) {
		tmp = t_2;
	} else if (x <= -2.3e-48) {
		tmp = b * (z * -c);
	} else if (x <= -6e-82) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= -9e-147) {
		tmp = t_1;
	} else if (x <= -8.6e-221) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 7.4e-53) {
		tmp = t_1;
	} else if (x <= 9.5e+51) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6.2e-21:
		tmp = t_2
	elif x <= -2.3e-48:
		tmp = b * (z * -c)
	elif x <= -6e-82:
		tmp = i * ((t * b) - (y * j))
	elif x <= -9e-147:
		tmp = t_1
	elif x <= -8.6e-221:
		tmp = b * ((t * i) - (z * c))
	elif x <= 7.4e-53:
		tmp = t_1
	elif x <= 9.5e+51:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6.2e-21)
		tmp = t_2;
	elseif (x <= -2.3e-48)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -6e-82)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= -9e-147)
		tmp = t_1;
	elseif (x <= -8.6e-221)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 7.4e-53)
		tmp = t_1;
	elseif (x <= 9.5e+51)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -6.2e-21)
		tmp = t_2;
	elseif (x <= -2.3e-48)
		tmp = b * (z * -c);
	elseif (x <= -6e-82)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= -9e-147)
		tmp = t_1;
	elseif (x <= -8.6e-221)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 7.4e-53)
		tmp = t_1;
	elseif (x <= 9.5e+51)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e-21], t$95$2, If[LessEqual[x, -2.3e-48], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-82], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-147], t$95$1, If[LessEqual[x, -8.6e-221], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-53], t$95$1, If[LessEqual[x, 9.5e+51], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.1999999999999997e-21 or 9.4999999999999999e51 < x

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -6.1999999999999997e-21 < x < -2.3000000000000001e-48

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 67.6%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 67.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 83.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 83.6%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. distribute-rgt-neg-in 83.6%

         \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      3. distribute-lft-neg-in 83.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

   8. Simplified 83.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(-c\right) \cdot z\right)} \]

   if -2.3000000000000001e-48 < x < -5.9999999999999998e-82

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 83.3%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 83.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 83.3%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]
   6. Step-by-step derivation

      1. associate-*r* 83.3%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 83.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 83.3%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 83.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 83.3%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. *-commutative 83.3%

         \[\leadsto i \cdot \left(t \cdot b + \left(-\color{blue}{y \cdot j}\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. unsub-neg 83.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Simplified 83.3%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   8. Taylor expanded in y around 0 83.1%

      \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 83.1%

         \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. distribute-rgt-neg-in 83.1%

         \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      3. distribute-rgt-neg-in 83.1%

         \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   10. Simplified 83.1%

       \[\leadsto i \cdot \left(t \cdot b - y \cdot j\right) + \color{blue}{a \cdot \left(t \cdot \left(-x\right)\right)} \]

   11. Taylor expanded in i around inf 66.8%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]
   12. Step-by-step derivation

       1. *-commutative 66.8%

          \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   13. Simplified 66.8%

       \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   if -5.9999999999999998e-82 < x < -8.99999999999999946e-147 or -8.5999999999999996e-221 < x < 7.39999999999999965e-53

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 63.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -8.99999999999999946e-147 < x < -8.5999999999999996e-221

   1. Initial program 59.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 71.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 7.39999999999999965e-53 < x < 9.4999999999999999e51

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 59.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 59.5%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-82}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))) (t_2 (* z (* x y))))
   (if (<= x -4.4e+58)
     t_2
     (if (<= x -3.8e-19)
       (* a (* t (- x)))
       (if (<= x -4.4e-55)
         (* b (* z (- c)))
         (if (<= x -5.1e-104)
           (* t (* b i))
           (if (<= x -2.6e-220)
             t_1
             (if (<= x 1.38e-204)
               (* j (* a c))
               (if (<= x 1.1e-57) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -4.4e+58) {
		tmp = t_2;
	} else if (x <= -3.8e-19) {
		tmp = a * (t * -x);
	} else if (x <= -4.4e-55) {
		tmp = b * (z * -c);
	} else if (x <= -5.1e-104) {
		tmp = t * (b * i);
	} else if (x <= -2.6e-220) {
		tmp = t_1;
	} else if (x <= 1.38e-204) {
		tmp = j * (a * c);
	} else if (x <= 1.1e-57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (c * -b)
    t_2 = z * (x * y)
    if (x <= (-4.4d+58)) then
        tmp = t_2
    else if (x <= (-3.8d-19)) then
        tmp = a * (t * -x)
    else if (x <= (-4.4d-55)) then
        tmp = b * (z * -c)
    else if (x <= (-5.1d-104)) then
        tmp = t * (b * i)
    else if (x <= (-2.6d-220)) then
        tmp = t_1
    else if (x <= 1.38d-204) then
        tmp = j * (a * c)
    else if (x <= 1.1d-57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -4.4e+58) {
		tmp = t_2;
	} else if (x <= -3.8e-19) {
		tmp = a * (t * -x);
	} else if (x <= -4.4e-55) {
		tmp = b * (z * -c);
	} else if (x <= -5.1e-104) {
		tmp = t * (b * i);
	} else if (x <= -2.6e-220) {
		tmp = t_1;
	} else if (x <= 1.38e-204) {
		tmp = j * (a * c);
	} else if (x <= 1.1e-57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -4.4e+58:
		tmp = t_2
	elif x <= -3.8e-19:
		tmp = a * (t * -x)
	elif x <= -4.4e-55:
		tmp = b * (z * -c)
	elif x <= -5.1e-104:
		tmp = t * (b * i)
	elif x <= -2.6e-220:
		tmp = t_1
	elif x <= 1.38e-204:
		tmp = j * (a * c)
	elif x <= 1.1e-57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -4.4e+58)
		tmp = t_2;
	elseif (x <= -3.8e-19)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (x <= -4.4e-55)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -5.1e-104)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= -2.6e-220)
		tmp = t_1;
	elseif (x <= 1.38e-204)
		tmp = Float64(j * Float64(a * c));
	elseif (x <= 1.1e-57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -4.4e+58)
		tmp = t_2;
	elseif (x <= -3.8e-19)
		tmp = a * (t * -x);
	elseif (x <= -4.4e-55)
		tmp = b * (z * -c);
	elseif (x <= -5.1e-104)
		tmp = t * (b * i);
	elseif (x <= -2.6e-220)
		tmp = t_1;
	elseif (x <= 1.38e-204)
		tmp = j * (a * c);
	elseif (x <= 1.1e-57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.4e+58], t$95$2, If[LessEqual[x, -3.8e-19], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.4e-55], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.1e-104], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-220], t$95$1, If[LessEqual[x, 1.38e-204], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-57], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.4000000000000001e58 or 1.09999999999999999e-57 < x

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 47.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 39.6%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.6%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 39.6%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -4.4000000000000001e58 < x < -3.8e-19

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 67.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 67.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 67.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 67.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 67.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0 48.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. mul-1-neg 48.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

   8. Simplified 48.7%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]

   if -3.8e-19 < x < -4.3999999999999999e-55

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 72.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 85.9%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. distribute-rgt-neg-in 85.9%

         \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      3. distribute-lft-neg-in 85.9%

         \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

   8. Simplified 85.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(-c\right) \cdot z\right)} \]

   if -4.3999999999999999e-55 < x < -5.09999999999999992e-104

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 84.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 76.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.2%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 35.2%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 43.1%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -5.09999999999999992e-104 < x < -2.6e-220 or 1.3799999999999999e-204 < x < 1.09999999999999999e-57

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 37.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 37.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 38.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 38.0%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 38.0%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 38.0%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   if -2.6e-220 < x < 1.3799999999999999e-204

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 28.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 28.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 28.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 28.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 28.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 28.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 28.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.7%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 32.7%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-220}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))) (t_2 (* z (* x y))))
   (if (<= x -7e+61)
     t_2
     (if (<= x -1.15e-19)
       (* x (* t (- a)))
       (if (<= x -3.1e-55)
         (* b (* z (- c)))
         (if (<= x -1.46e-103)
           (* t (* b i))
           (if (<= x -2.05e-218)
             t_1
             (if (<= x 1.35e-204)
               (* j (* a c))
               (if (<= x 2.7e-57) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -7e+61) {
		tmp = t_2;
	} else if (x <= -1.15e-19) {
		tmp = x * (t * -a);
	} else if (x <= -3.1e-55) {
		tmp = b * (z * -c);
	} else if (x <= -1.46e-103) {
		tmp = t * (b * i);
	} else if (x <= -2.05e-218) {
		tmp = t_1;
	} else if (x <= 1.35e-204) {
		tmp = j * (a * c);
	} else if (x <= 2.7e-57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (c * -b)
    t_2 = z * (x * y)
    if (x <= (-7d+61)) then
        tmp = t_2
    else if (x <= (-1.15d-19)) then
        tmp = x * (t * -a)
    else if (x <= (-3.1d-55)) then
        tmp = b * (z * -c)
    else if (x <= (-1.46d-103)) then
        tmp = t * (b * i)
    else if (x <= (-2.05d-218)) then
        tmp = t_1
    else if (x <= 1.35d-204) then
        tmp = j * (a * c)
    else if (x <= 2.7d-57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -7e+61) {
		tmp = t_2;
	} else if (x <= -1.15e-19) {
		tmp = x * (t * -a);
	} else if (x <= -3.1e-55) {
		tmp = b * (z * -c);
	} else if (x <= -1.46e-103) {
		tmp = t * (b * i);
	} else if (x <= -2.05e-218) {
		tmp = t_1;
	} else if (x <= 1.35e-204) {
		tmp = j * (a * c);
	} else if (x <= 2.7e-57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -7e+61:
		tmp = t_2
	elif x <= -1.15e-19:
		tmp = x * (t * -a)
	elif x <= -3.1e-55:
		tmp = b * (z * -c)
	elif x <= -1.46e-103:
		tmp = t * (b * i)
	elif x <= -2.05e-218:
		tmp = t_1
	elif x <= 1.35e-204:
		tmp = j * (a * c)
	elif x <= 2.7e-57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -7e+61)
		tmp = t_2;
	elseif (x <= -1.15e-19)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -3.1e-55)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= -1.46e-103)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= -2.05e-218)
		tmp = t_1;
	elseif (x <= 1.35e-204)
		tmp = Float64(j * Float64(a * c));
	elseif (x <= 2.7e-57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -7e+61)
		tmp = t_2;
	elseif (x <= -1.15e-19)
		tmp = x * (t * -a);
	elseif (x <= -3.1e-55)
		tmp = b * (z * -c);
	elseif (x <= -1.46e-103)
		tmp = t * (b * i);
	elseif (x <= -2.05e-218)
		tmp = t_1;
	elseif (x <= 1.35e-204)
		tmp = j * (a * c);
	elseif (x <= 2.7e-57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+61], t$95$2, If[LessEqual[x, -1.15e-19], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-55], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.46e-103], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.05e-218], t$95$1, If[LessEqual[x, 1.35e-204], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-57], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.00000000000000036e61 or 2.7000000000000002e-57 < x

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 47.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 47.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 39.6%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.6%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 39.6%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -7.00000000000000036e61 < x < -1.1499999999999999e-19

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 75.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 72.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around inf 60.3%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot j + \frac{b \cdot t}{y}\right)\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]
   6. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} + -1 \cdot j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. mul-1-neg 60.3%

         \[\leadsto i \cdot \left(y \cdot \left(\frac{b \cdot t}{y} + \color{blue}{\left(-j\right)}\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. unsub-neg 60.3%

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{b \cdot t}{y} - j\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. *-commutative 60.3%

         \[\leadsto i \cdot \left(y \cdot \left(\frac{\color{blue}{t \cdot b}}{y} - j\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. associate-/l* 60.3%

         \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{t \cdot \frac{b}{y}} - j\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Simplified 60.3%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(t \cdot \frac{b}{y} - j\right)\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   8. Taylor expanded in a around inf 48.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 48.7%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 48.7%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. *-commutative 48.7%

         \[\leadsto -\color{blue}{\left(x \cdot t\right)} \cdot a \]

      4. associate-*r* 48.6%

         \[\leadsto -\color{blue}{x \cdot \left(t \cdot a\right)} \]

      5. distribute-rgt-neg-in 48.6%

         \[\leadsto \color{blue}{x \cdot \left(-t \cdot a\right)} \]

   10. Simplified 48.6%

       \[\leadsto \color{blue}{x \cdot \left(-t \cdot a\right)} \]

   if -1.1499999999999999e-19 < x < -3.09999999999999997e-55

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 72.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 85.9%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. distribute-rgt-neg-in 85.9%

         \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      3. distribute-lft-neg-in 85.9%

         \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

   8. Simplified 85.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(-c\right) \cdot z\right)} \]

   if -3.09999999999999997e-55 < x < -1.46e-103

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 84.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 76.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.2%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 35.2%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 43.1%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -1.46e-103 < x < -2.0499999999999999e-218 or 1.34999999999999996e-204 < x < 2.7000000000000002e-57

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 37.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 37.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 38.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 38.0%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 38.0%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 38.0%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   if -2.0499999999999999e-218 < x < 1.34999999999999996e-204

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 28.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 28.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 28.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 28.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 28.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 28.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 28.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.7%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 32.7%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* z (* x y))))
   (if (<= x -5.6e+34)
     t_2
     (if (<= x -5.1e-39)
       t_1
       (if (<= x -1.3e-220)
         (* t (* b i))
         (if (<= x 1.8e-204)
           (* j (* a c))
           (if (<= x 1.8e-57) t_1 (if (<= x 1.45e-42) (* b (* t i)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -5.6e+34) {
		tmp = t_2;
	} else if (x <= -5.1e-39) {
		tmp = t_1;
	} else if (x <= -1.3e-220) {
		tmp = t * (b * i);
	} else if (x <= 1.8e-204) {
		tmp = j * (a * c);
	} else if (x <= 1.8e-57) {
		tmp = t_1;
	} else if (x <= 1.45e-42) {
		tmp = b * (t * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = z * (x * y)
    if (x <= (-5.6d+34)) then
        tmp = t_2
    else if (x <= (-5.1d-39)) then
        tmp = t_1
    else if (x <= (-1.3d-220)) then
        tmp = t * (b * i)
    else if (x <= 1.8d-204) then
        tmp = j * (a * c)
    else if (x <= 1.8d-57) then
        tmp = t_1
    else if (x <= 1.45d-42) then
        tmp = b * (t * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -5.6e+34) {
		tmp = t_2;
	} else if (x <= -5.1e-39) {
		tmp = t_1;
	} else if (x <= -1.3e-220) {
		tmp = t * (b * i);
	} else if (x <= 1.8e-204) {
		tmp = j * (a * c);
	} else if (x <= 1.8e-57) {
		tmp = t_1;
	} else if (x <= 1.45e-42) {
		tmp = b * (t * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -5.6e+34:
		tmp = t_2
	elif x <= -5.1e-39:
		tmp = t_1
	elif x <= -1.3e-220:
		tmp = t * (b * i)
	elif x <= 1.8e-204:
		tmp = j * (a * c)
	elif x <= 1.8e-57:
		tmp = t_1
	elif x <= 1.45e-42:
		tmp = b * (t * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -5.6e+34)
		tmp = t_2;
	elseif (x <= -5.1e-39)
		tmp = t_1;
	elseif (x <= -1.3e-220)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 1.8e-204)
		tmp = Float64(j * Float64(a * c));
	elseif (x <= 1.8e-57)
		tmp = t_1;
	elseif (x <= 1.45e-42)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -5.6e+34)
		tmp = t_2;
	elseif (x <= -5.1e-39)
		tmp = t_1;
	elseif (x <= -1.3e-220)
		tmp = t * (b * i);
	elseif (x <= 1.8e-204)
		tmp = j * (a * c);
	elseif (x <= 1.8e-57)
		tmp = t_1;
	elseif (x <= 1.45e-42)
		tmp = b * (t * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+34], t$95$2, If[LessEqual[x, -5.1e-39], t$95$1, If[LessEqual[x, -1.3e-220], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-204], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-57], t$95$1, If[LessEqual[x, 1.45e-42], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.60000000000000016e34 or 1.4500000000000001e-42 < x

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 47.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 47.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 40.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.0%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 40.0%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -5.60000000000000016e34 < x < -5.09999999999999988e-39 or 1.79999999999999982e-204 < x < 1.8000000000000001e-57

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 38.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 38.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 38.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 38.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 36.6%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. distribute-rgt-neg-in 36.6%

         \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

      3. distribute-lft-neg-in 36.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

   8. Simplified 36.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(-c\right) \cdot z\right)} \]

   if -5.09999999999999988e-39 < x < -1.3e-220

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 71.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 57.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around inf 35.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.7%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 35.7%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

      3. associate-*r* 38.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   7. Simplified 38.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]

   if -1.3e-220 < x < 1.79999999999999982e-204

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 28.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 28.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 28.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 28.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 28.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 28.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 28.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 33.5%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if 1.8000000000000001e-57 < x < 1.4500000000000001e-42

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 35.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 35.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 35.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 35.1%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 35.1%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 35.1%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   8. Simplified 35.1%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   9. Taylor expanded in i around 0 35.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.2%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 35.2%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.4e+205)
   (* j (* a c))
   (if (<= c -3.7e+121)
     (- (* j (- (* a c) (* y i))) (* b (* z c)))
     (if (<= c 1.55e+143)
       (+ (* x (- (* y z) (* t a))) (* i (- (* t b) (* y j))))
       (- (* c (- (* a j) (* z b))) (* a (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.4e+205) {
		tmp = j * (a * c);
	} else if (c <= -3.7e+121) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (c <= 1.55e+143) {
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)));
	} else {
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: tmp
    if (c <= (-2.4d+205)) then
        tmp = j * (a * c)
    else if (c <= (-3.7d+121)) then
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    else if (c <= 1.55d+143) then
        tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))
    else
        tmp = (c * ((a * j) - (z * b))) - (a * (x * 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 tmp;
	if (c <= -2.4e+205) {
		tmp = j * (a * c);
	} else if (c <= -3.7e+121) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (c <= 1.55e+143) {
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)));
	} else {
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.4e+205:
		tmp = j * (a * c)
	elif c <= -3.7e+121:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	elif c <= 1.55e+143:
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))
	else:
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.4e+205)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= -3.7e+121)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (c <= 1.55e+143)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(i * Float64(Float64(t * b) - Float64(y * j))));
	else
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) - Float64(a * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.4e+205)
		tmp = j * (a * c);
	elseif (c <= -3.7e+121)
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	elseif (c <= 1.55e+143)
		tmp = (x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)));
	else
		tmp = (c * ((a * j) - (z * b))) - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.4e+205], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.7e+121], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e+143], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.39999999999999986e205

   1. Initial program 22.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 62.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 62.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 62.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 62.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 62.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 69.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 74.0%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 74.0%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -2.39999999999999986e205 < c < -3.70000000000000013e121

   1. Initial program 70.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 71.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 71.4%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. neg-mul-1 71.4%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if -3.70000000000000013e121 < c < 1.54999999999999995e143

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 78.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 71.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in b around 0 71.5%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]
   6. Step-by-step derivation

      1. associate-*r* 71.5%

         \[\leadsto i \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot y} + b \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      2. +-commutative 71.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + \left(-1 \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

      3. *-commutative 71.5%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} + \left(-1 \cdot j\right) \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      4. associate-*r* 71.5%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      5. mul-1-neg 71.5%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      6. *-commutative 71.5%

         \[\leadsto i \cdot \left(t \cdot b + \left(-\color{blue}{y \cdot j}\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right) \]

      7. unsub-neg 71.5%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   7. Simplified 71.5%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   if 1.54999999999999995e143 < c

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 46.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 66.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]

   5. Taylor expanded in a around inf 83.6%

      \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 83.6%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      2. *-commutative 83.6%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) \]

      3. distribute-rgt-neg-in 83.6%

         \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

   7. Simplified 83.6%

      \[\leadsto c \cdot \left(a \cdot j - b \cdot z\right) + \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+188} \lor \neg \left(b \leq -4.1 \cdot 10^{+176}\right) \land \left(b \leq -7.3 \cdot 10^{+87} \lor \neg \left(b \leq 2.4 \cdot 10^{+32}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.3e+188)
         (and (not (<= b -4.1e+176))
              (or (<= b -7.3e+87) (not (<= b 2.4e+32)))))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.3e+188) || (!(b <= -4.1e+176) && ((b <= -7.3e+87) || !(b <= 2.4e+32)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: tmp
    if ((b <= (-3.3d+188)) .or. (.not. (b <= (-4.1d+176))) .and. (b <= (-7.3d+87)) .or. (.not. (b <= 2.4d+32))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * 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 tmp;
	if ((b <= -3.3e+188) || (!(b <= -4.1e+176) && ((b <= -7.3e+87) || !(b <= 2.4e+32)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.3e+188) or (not (b <= -4.1e+176) and ((b <= -7.3e+87) or not (b <= 2.4e+32))):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.3e+188) || (!(b <= -4.1e+176) && ((b <= -7.3e+87) || !(b <= 2.4e+32))))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.3e+188) || (~((b <= -4.1e+176)) && ((b <= -7.3e+87) || ~((b <= 2.4e+32)))))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.3e+188], And[N[Not[LessEqual[b, -4.1e+176]], $MachinePrecision], Or[LessEqual[b, -7.3e+87], N[Not[LessEqual[b, 2.4e+32]], $MachinePrecision]]]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.29999999999999983e188 or -4.0999999999999999e176 < b < -7.29999999999999997e87 or 2.39999999999999991e32 < b

   1. Initial program 70.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 62.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -3.29999999999999983e188 < b < -4.0999999999999999e176 or -7.29999999999999997e87 < b < 2.39999999999999991e32

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 45.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+188} \lor \neg \left(b \leq -4.1 \cdot 10^{+176}\right) \land \left(b \leq -7.3 \cdot 10^{+87} \lor \neg \left(b \leq 2.4 \cdot 10^{+32}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 30.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* a (* c j))))
   (if (<= j -3.2e+137)
     t_2
     (if (<= j 3.15e-223)
       t_1
       (if (<= j 3.6e-42) (* x (* y z)) (if (<= j 1.9e+22) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -3.2e+137) {
		tmp = t_2;
	} else if (j <= 3.15e-223) {
		tmp = t_1;
	} else if (j <= 3.6e-42) {
		tmp = x * (y * z);
	} else if (j <= 1.9e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = a * (c * j)
    if (j <= (-3.2d+137)) then
        tmp = t_2
    else if (j <= 3.15d-223) then
        tmp = t_1
    else if (j <= 3.6d-42) then
        tmp = x * (y * z)
    else if (j <= 1.9d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -3.2e+137) {
		tmp = t_2;
	} else if (j <= 3.15e-223) {
		tmp = t_1;
	} else if (j <= 3.6e-42) {
		tmp = x * (y * z);
	} else if (j <= 1.9e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = a * (c * j)
	tmp = 0
	if j <= -3.2e+137:
		tmp = t_2
	elif j <= 3.15e-223:
		tmp = t_1
	elif j <= 3.6e-42:
		tmp = x * (y * z)
	elif j <= 1.9e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -3.2e+137)
		tmp = t_2;
	elseif (j <= 3.15e-223)
		tmp = t_1;
	elseif (j <= 3.6e-42)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.9e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (j <= -3.2e+137)
		tmp = t_2;
	elseif (j <= 3.15e-223)
		tmp = t_1;
	elseif (j <= 3.6e-42)
		tmp = x * (y * z);
	elseif (j <= 1.9e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+137], t$95$2, If[LessEqual[j, 3.15e-223], t$95$1, If[LessEqual[j, 3.6e-42], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e+22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.20000000000000019e137 or 1.9000000000000002e22 < j

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 39.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 39.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 39.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 39.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 39.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 39.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 37.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 37.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -3.20000000000000019e137 < j < 3.14999999999999993e-223 or 3.6000000000000002e-42 < j < 1.9000000000000002e22

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 35.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 35.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 35.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 23.6%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 23.6%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 23.6%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   8. Simplified 23.6%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   9. Taylor expanded in i around 0 27.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 27.1%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 27.1%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 3.14999999999999993e-223 < j < 3.6000000000000002e-42

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.5%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 59.5%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 31.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-223}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.76 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1.2e+137)
     t_1
     (if (<= j 1.5e-122)
       (* b (* t i))
       (if (<= j 3.76e-56) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.2e+137) {
		tmp = t_1;
	} else if (j <= 1.5e-122) {
		tmp = b * (t * i);
	} else if (j <= 3.76e-56) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-1.2d+137)) then
        tmp = t_1
    else if (j <= 1.5d-122) then
        tmp = b * (t * i)
    else if (j <= 3.76d-56) then
        tmp = z * (x * y)
    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 t_1 = a * (c * j);
	double tmp;
	if (j <= -1.2e+137) {
		tmp = t_1;
	} else if (j <= 1.5e-122) {
		tmp = b * (t * i);
	} else if (j <= 3.76e-56) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1.2e+137:
		tmp = t_1
	elif j <= 1.5e-122:
		tmp = b * (t * i)
	elif j <= 3.76e-56:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -1.2e+137)
		tmp = t_1;
	elseif (j <= 1.5e-122)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 3.76e-56)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -1.2e+137)
		tmp = t_1;
	elseif (j <= 1.5e-122)
		tmp = b * (t * i);
	elseif (j <= 3.76e-56)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e+137], t$95$1, If[LessEqual[j, 1.5e-122], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.76e-56], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.19999999999999992e137 or 3.7599999999999998e-56 < j

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 40.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 40.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 34.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 34.4%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -1.19999999999999992e137 < j < 1.50000000000000002e-122

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 34.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 34.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 34.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 23.7%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 23.7%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 23.7%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   8. Simplified 23.7%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   9. Taylor expanded in i around 0 26.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.4%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 26.4%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.50000000000000002e-122 < j < 3.7599999999999998e-56

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 62.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 62.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 62.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 62.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 54.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 54.0%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.76 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 29.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1.15e+138)
     t_1
     (if (<= j 3.2e-132)
       (* b (* t i))
       (if (<= j 2.5e-25) (* y (* x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.15e+138) {
		tmp = t_1;
	} else if (j <= 3.2e-132) {
		tmp = b * (t * i);
	} else if (j <= 2.5e-25) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-1.15d+138)) then
        tmp = t_1
    else if (j <= 3.2d-132) then
        tmp = b * (t * i)
    else if (j <= 2.5d-25) then
        tmp = y * (x * z)
    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 t_1 = a * (c * j);
	double tmp;
	if (j <= -1.15e+138) {
		tmp = t_1;
	} else if (j <= 3.2e-132) {
		tmp = b * (t * i);
	} else if (j <= 2.5e-25) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1.15e+138:
		tmp = t_1
	elif j <= 3.2e-132:
		tmp = b * (t * i)
	elif j <= 2.5e-25:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -1.15e+138)
		tmp = t_1;
	elseif (j <= 3.2e-132)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 2.5e-25)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -1.15e+138)
		tmp = t_1;
	elseif (j <= 3.2e-132)
		tmp = b * (t * i);
	elseif (j <= 2.5e-25)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.15e+138], t$95$1, If[LessEqual[j, 3.2e-132], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-25], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.15000000000000004e138 or 2.49999999999999981e-25 < j

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 41.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 41.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 41.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 35.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 35.4%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -1.15000000000000004e138 < j < 3.2000000000000002e-132

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 33.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 33.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 33.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 23.1%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 23.1%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 23.1%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   8. Simplified 23.1%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   9. Taylor expanded in i around 0 25.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 25.8%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 25.8%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 3.2000000000000002e-132 < j < 2.49999999999999981e-25

   1. Initial program 70.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 65.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around 0 58.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in z around inf 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 45.9%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

      3. associate-*r* 46.0%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   7. Simplified 46.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8.8 \cdot 10^{+136} \lor \neg \left(j \leq 1.42 \cdot 10^{-86}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -8.8e+136) (not (<= j 1.42e-86))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -8.8e+136) || !(j <= 1.42e-86)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: tmp
    if ((j <= (-8.8d+136)) .or. (.not. (j <= 1.42d-86))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -8.8e+136) || !(j <= 1.42e-86)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -8.8e+136) or not (j <= 1.42e-86):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -8.8e+136) || !(j <= 1.42e-86))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -8.8e+136) || ~((j <= 1.42e-86)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -8.8e+136], N[Not[LessEqual[j, 1.42e-86]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -8.7999999999999998e136 or 1.42000000000000001e-86 < j

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 38.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 38.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 38.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 32.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 32.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -8.7999999999999998e136 < j < 1.42000000000000001e-86

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 34.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 34.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 34.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 23.8%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. neg-mul-1 23.8%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 23.8%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   8. Simplified 23.8%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(b \cdot \left(-t\right)\right)}\right) \]

   9. Taylor expanded in i around 0 26.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.4%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   11. Simplified 26.4%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.8 \cdot 10^{+136} \lor \neg \left(j \leq 1.42 \cdot 10^{-86}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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
    code = a * (c * j)
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) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 36.1%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.1%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.1%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 36.1%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 20.8%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-commutative 20.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Simplified 20.8%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Final simplification 20.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 58.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))