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

Percentage Accurate: 73.0% → 83.5%

Time: 22.0s

Alternatives: 26

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: 73.0% 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: 83.5% accurate, 0.5× speedup

Math

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

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
     (* c (+ (* a j) (- (* b (* i (/ t c))) (* z 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 = ((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 = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	}
	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 = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	}
	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 = c * ((a * j) + ((b * (i * (t / c))) - (z * b)))
	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(c * Float64(Float64(a * j) + Float64(Float64(b * Float64(i * Float64(t / c))) - Float64(z * b))));
	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 = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	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[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(b * N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $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 91.2%

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

   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 c around inf 24.2%

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

      1. +-commutative 24.2%

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

      2. mul-1-neg 24.2%

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

      3. unsub-neg 24.2%

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

      4. fma-define 24.2%

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

      5. associate-/l* 24.2%

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

      6. *-commutative 24.2%

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

      7. +-commutative 24.2%

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

      8. mul-1-neg 24.2%

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

      9. unsub-neg 24.2%

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

   5. Simplified 35.0%

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

   6. Taylor expanded in c around inf 59.3%

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

      1. *-commutative 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 85.5%

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

Alternative 2: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := t\_1 - a \cdot \left(x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-190}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-99}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (- t_1 (* a (* x t))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -5.6e+34)
     t_3
     (if (<= z -8.6e-169)
       t_2
       (if (<= z 1.06e-190)
         (+ (* j (- (* a c) (* y i))) (* b (* t i)))
         (if (<= z 7e-99)
           (+ (* j (* a c)) t_1)
           (if (<= z 4.9e+55) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = t_1 - (a * (x * t));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.6e+34) {
		tmp = t_3;
	} else if (z <= -8.6e-169) {
		tmp = t_2;
	} else if (z <= 1.06e-190) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (z <= 7e-99) {
		tmp = (j * (a * c)) + t_1;
	} else if (z <= 4.9e+55) {
		tmp = t_2;
	} 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 = b * ((t * i) - (z * c))
    t_2 = t_1 - (a * (x * t))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-5.6d+34)) then
        tmp = t_3
    else if (z <= (-8.6d-169)) then
        tmp = t_2
    else if (z <= 1.06d-190) then
        tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
    else if (z <= 7d-99) then
        tmp = (j * (a * c)) + t_1
    else if (z <= 4.9d+55) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = t_1 - (a * (x * t));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.6e+34) {
		tmp = t_3;
	} else if (z <= -8.6e-169) {
		tmp = t_2;
	} else if (z <= 1.06e-190) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (z <= 7e-99) {
		tmp = (j * (a * c)) + t_1;
	} else if (z <= 4.9e+55) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = t_1 - (a * (x * t))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -5.6e+34:
		tmp = t_3
	elif z <= -8.6e-169:
		tmp = t_2
	elif z <= 1.06e-190:
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
	elif z <= 7e-99:
		tmp = (j * (a * c)) + t_1
	elif z <= 4.9e+55:
		tmp = t_2
	else:
		tmp = t_3
	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(t_1 - Float64(a * Float64(x * t)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -5.6e+34)
		tmp = t_3;
	elseif (z <= -8.6e-169)
		tmp = t_2;
	elseif (z <= 1.06e-190)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(t * i)));
	elseif (z <= 7e-99)
		tmp = Float64(Float64(j * Float64(a * c)) + t_1);
	elseif (z <= 4.9e+55)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = t_1 - (a * (x * t));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -5.6e+34)
		tmp = t_3;
	elseif (z <= -8.6e-169)
		tmp = t_2;
	elseif (z <= 1.06e-190)
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	elseif (z <= 7e-99)
		tmp = (j * (a * c)) + t_1;
	elseif (z <= 4.9e+55)
		tmp = t_2;
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+34], t$95$3, If[LessEqual[z, -8.6e-169], t$95$2, If[LessEqual[z, 1.06e-190], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-99], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 4.9e+55], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.60000000000000016e34 or 4.90000000000000015e55 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if -5.60000000000000016e34 < z < -8.59999999999999967e-169 or 6.9999999999999997e-99 < z < 4.90000000000000015e55

   1. Initial program 82.9%

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

   3. Taylor expanded in j around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in y around 0 78.2%

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

   if -8.59999999999999967e-169 < z < 1.05999999999999997e-190

   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 x around 0 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in c around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. neg-mul-1 70.4%

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

      3. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   if 1.05999999999999997e-190 < z < 6.9999999999999997e-99

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in a around inf 82.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-190}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-99}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-82}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+203}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* b (* t i))))
        (t_3 (- (* x (- (* y z) (* t a))) (* z (* b c)))))
   (if (<= j -3.8e-14)
     t_2
     (if (<= j 1.85e-82)
       t_3
       (if (<= j 6e+66) t_2 (if (<= j 9.2e+203) 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 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * (t * i));
	double t_3 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double tmp;
	if (j <= -3.8e-14) {
		tmp = t_2;
	} else if (j <= 1.85e-82) {
		tmp = t_3;
	} else if (j <= 6e+66) {
		tmp = t_2;
	} else if (j <= 9.2e+203) {
		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 = j * ((a * c) - (y * i))
    t_2 = t_1 + (b * (t * i))
    t_3 = (x * ((y * z) - (t * a))) - (z * (b * c))
    if (j <= (-3.8d-14)) then
        tmp = t_2
    else if (j <= 1.85d-82) then
        tmp = t_3
    else if (j <= 6d+66) then
        tmp = t_2
    else if (j <= 9.2d+203) 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 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * (t * i));
	double t_3 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double tmp;
	if (j <= -3.8e-14) {
		tmp = t_2;
	} else if (j <= 1.85e-82) {
		tmp = t_3;
	} else if (j <= 6e+66) {
		tmp = t_2;
	} else if (j <= 9.2e+203) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (b * (t * i))
	t_3 = (x * ((y * z) - (t * a))) - (z * (b * c))
	tmp = 0
	if j <= -3.8e-14:
		tmp = t_2
	elif j <= 1.85e-82:
		tmp = t_3
	elif j <= 6e+66:
		tmp = t_2
	elif j <= 9.2e+203:
		tmp = t_3
	else:
		tmp = t_1
	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(t_1 + Float64(b * Float64(t * i)))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)))
	tmp = 0.0
	if (j <= -3.8e-14)
		tmp = t_2;
	elseif (j <= 1.85e-82)
		tmp = t_3;
	elseif (j <= 6e+66)
		tmp = t_2;
	elseif (j <= 9.2e+203)
		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 = j * ((a * c) - (y * i));
	t_2 = t_1 + (b * (t * i));
	t_3 = (x * ((y * z) - (t * a))) - (z * (b * c));
	tmp = 0.0;
	if (j <= -3.8e-14)
		tmp = t_2;
	elseif (j <= 1.85e-82)
		tmp = t_3;
	elseif (j <= 6e+66)
		tmp = t_2;
	elseif (j <= 9.2e+203)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e-14], t$95$2, If[LessEqual[j, 1.85e-82], t$95$3, If[LessEqual[j, 6e+66], t$95$2, If[LessEqual[j, 9.2e+203], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.8000000000000002e-14 or 1.85e-82 < j < 6.00000000000000005e66

   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 x around 0 73.9%

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

      1. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in c around 0 66.6%

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

      1. associate-*r* 66.6%

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

      2. neg-mul-1 66.6%

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

      3. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   if -3.8000000000000002e-14 < j < 1.85e-82 or 6.00000000000000005e66 < j < 9.1999999999999996e203

   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 j around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in c around inf 67.5%

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

      1. *-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*l* 70.0%

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

      4. *-commutative 70.0%

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

   8. Simplified 68.0%

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

   if 9.1999999999999996e203 < j

   1. Initial program 56.5%

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

   3. Taylor expanded in x around 0 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in j around inf 87.6%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.85e+138)
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
   (if (<= b 2e+52)
     (- (* j (- (* a c) (* y i))) (+ (* z (* b c)) (* x (- (* t a) (* y z)))))
     (* c (+ (* a j) (- (* b (* i (/ t c))) (* z b)))))))

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 <= -1.85e+138) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (b <= 2e+52) {
		tmp = (j * ((a * c) - (y * i))) - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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) :: tmp
    if (b <= (-1.85d+138)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else if (b <= 2d+52) then
        tmp = (j * ((a * c) - (y * i))) - ((z * (b * c)) + (x * ((t * a) - (y * z))))
    else
        tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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 tmp;
	if (b <= -1.85e+138) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (b <= 2e+52) {
		tmp = (j * ((a * c) - (y * i))) - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.85e+138:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	elif b <= 2e+52:
		tmp = (j * ((a * c) - (y * i))) - ((z * (b * c)) + (x * ((t * a) - (y * z))))
	else:
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.85e+138)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (b <= 2e+52)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(Float64(z * Float64(b * c)) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))));
	else
		tmp = Float64(c * Float64(Float64(a * j) + Float64(Float64(b * Float64(i * Float64(t / c))) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.85e+138)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	elseif (b <= 2e+52)
		tmp = (j * ((a * c) - (y * i))) - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	else
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.85e+138], 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], If[LessEqual[b, 2e+52], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(b * N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8499999999999999e138

   1. Initial program 72.8%

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

   3. Taylor expanded in j around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -1.8499999999999999e138 < b < 2e52

   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 c around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*l* 79.5%

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

      4. *-commutative 79.5%

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

   5. Simplified 79.5%

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

   if 2e52 < b

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. fma-define 65.1%

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

      5. associate-/l* 65.1%

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

      6. *-commutative 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. unsub-neg 65.1%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in c around inf 80.4%

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

      1. *-commutative 80.4%

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

   8. Simplified 80.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -7.4e+19)
     t_2
     (if (<= b -1.6e-128)
       t_1
       (if (<= b -1.15e-289)
         (* j (- (* a c) (* y i)))
         (if (<= b 1.5e-241)
           t_1
           (if (<= b 6.5e+53) (* a (- (* c j) (* x t))) 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 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.4e+19) {
		tmp = t_2;
	} else if (b <= -1.6e-128) {
		tmp = t_1;
	} else if (b <= -1.15e-289) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.5e-241) {
		tmp = t_1;
	} else if (b <= 6.5e+53) {
		tmp = a * ((c * j) - (x * t));
	} 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 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-7.4d+19)) then
        tmp = t_2
    else if (b <= (-1.6d-128)) then
        tmp = t_1
    else if (b <= (-1.15d-289)) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 1.5d-241) then
        tmp = t_1
    else if (b <= 6.5d+53) then
        tmp = a * ((c * j) - (x * t))
    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 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.4e+19) {
		tmp = t_2;
	} else if (b <= -1.6e-128) {
		tmp = t_1;
	} else if (b <= -1.15e-289) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.5e-241) {
		tmp = t_1;
	} else if (b <= 6.5e+53) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.4e+19:
		tmp = t_2
	elif b <= -1.6e-128:
		tmp = t_1
	elif b <= -1.15e-289:
		tmp = j * ((a * c) - (y * i))
	elif b <= 1.5e-241:
		tmp = t_1
	elif b <= 6.5e+53:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.4e+19)
		tmp = t_2;
	elseif (b <= -1.6e-128)
		tmp = t_1;
	elseif (b <= -1.15e-289)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 1.5e-241)
		tmp = t_1;
	elseif (b <= 6.5e+53)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.4e+19)
		tmp = t_2;
	elseif (b <= -1.6e-128)
		tmp = t_1;
	elseif (b <= -1.15e-289)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 1.5e-241)
		tmp = t_1;
	elseif (b <= 6.5e+53)
		tmp = a * ((c * j) - (x * t));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+19], t$95$2, If[LessEqual[b, -1.6e-128], t$95$1, If[LessEqual[b, -1.15e-289], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-241], t$95$1, If[LessEqual[b, 6.5e+53], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.4e19 or 6.50000000000000017e53 < b

   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 b around inf 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -7.4e19 < b < -1.5999999999999999e-128 or -1.1500000000000001e-289 < b < 1.5e-241

   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 j around inf 65.5%

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

   4. Taylor expanded in x around -inf 61.6%

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

      1. *-commutative 61.6%

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

   6. Simplified 61.6%

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

   if -1.5999999999999999e-128 < b < -1.1500000000000001e-289

   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 0 63.2%

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

      1. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in j around inf 64.2%

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

   if 1.5e-241 < b < 6.50000000000000017e53

   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 a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+138}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq -7600000000:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= b -7.5e+138)
     (- t_1 (* a (* x t)))
     (if (<= b -7600000000.0)
       (+ t_2 t_1)
       (if (<= b 4.7e+58)
         (- t_2 (* x (- (* t a) (* y z))))
         (* c (+ (* a j) (- (* b (* i (/ t c))) (* z 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 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -7.5e+138) {
		tmp = t_1 - (a * (x * t));
	} else if (b <= -7600000000.0) {
		tmp = t_2 + t_1;
	} else if (b <= 4.7e+58) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (b <= (-7.5d+138)) then
        tmp = t_1 - (a * (x * t))
    else if (b <= (-7600000000.0d0)) then
        tmp = t_2 + t_1
    else if (b <= 4.7d+58) then
        tmp = t_2 - (x * ((t * a) - (y * z)))
    else
        tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -7.5e+138) {
		tmp = t_1 - (a * (x * t));
	} else if (b <= -7600000000.0) {
		tmp = t_2 + t_1;
	} else if (b <= 4.7e+58) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if b <= -7.5e+138:
		tmp = t_1 - (a * (x * t))
	elif b <= -7600000000.0:
		tmp = t_2 + t_1
	elif b <= 4.7e+58:
		tmp = t_2 - (x * ((t * a) - (y * z)))
	else:
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -7.5e+138)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (b <= -7600000000.0)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 4.7e+58)
		tmp = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(c * Float64(Float64(a * j) + Float64(Float64(b * Float64(i * Float64(t / c))) - Float64(z * 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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (b <= -7.5e+138)
		tmp = t_1 - (a * (x * t));
	elseif (b <= -7600000000.0)
		tmp = t_2 + t_1;
	elseif (b <= 4.7e+58)
		tmp = t_2 - (x * ((t * a) - (y * z)));
	else
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+138], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7600000000.0], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 4.7e+58], N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(b * N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.4999999999999999e138

   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 j around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around 0 79.9%

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

   if -7.4999999999999999e138 < b < -7.6e9

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 75.6%

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

      1. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -7.6e9 < b < 4.69999999999999972e58

   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 b around 0 77.5%

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

   if 4.69999999999999972e58 < b

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. fma-define 65.1%

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

      5. associate-/l* 65.1%

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

      6. *-commutative 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. unsub-neg 65.1%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in c around inf 80.4%

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

      1. *-commutative 80.4%

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

   8. Simplified 80.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq -7600000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8.2 \cdot 10^{-14}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+182}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -8.2e-14)
     (+ t_1 (* b (* t i)))
     (if (<= j 2.3e-174)
       (- (* x (- (* y z) (* t a))) (* z (* b c)))
       (if (<= j 6e+182)
         (* c (+ (* a j) (- (* b (* i (/ t c))) (* z b))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -8.2e-14) {
		tmp = t_1 + (b * (t * i));
	} else if (j <= 2.3e-174) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else if (j <= 6e+182) {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	} 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 = j * ((a * c) - (y * i))
    if (j <= (-8.2d-14)) then
        tmp = t_1 + (b * (t * i))
    else if (j <= 2.3d-174) then
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    else if (j <= 6d+182) then
        tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -8.2e-14) {
		tmp = t_1 + (b * (t * i));
	} else if (j <= 2.3e-174) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else if (j <= 6e+182) {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -8.2e-14:
		tmp = t_1 + (b * (t * i))
	elif j <= 2.3e-174:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	elif j <= 6e+182:
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (j <= -8.2e-14)
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	elseif (j <= 2.3e-174)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	elseif (j <= 6e+182)
		tmp = Float64(c * Float64(Float64(a * j) + Float64(Float64(b * Float64(i * Float64(t / c))) - Float64(z * b))));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (j <= -8.2e-14)
		tmp = t_1 + (b * (t * i));
	elseif (j <= 2.3e-174)
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	elseif (j <= 6e+182)
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.2e-14], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-174], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e+182], N[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(b * N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.2000000000000004e-14

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 72.6%

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

      1. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in c around 0 65.4%

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

      1. associate-*r* 65.4%

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

      2. neg-mul-1 65.4%

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

      3. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   if -8.2000000000000004e-14 < j < 2.2999999999999999e-174

   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 j around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in c around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-*l* 69.6%

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

      4. *-commutative 69.6%

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

   8. Simplified 70.5%

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

   if 2.2999999999999999e-174 < j < 6.0000000000000004e182

   1. Initial program 73.7%

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

   3. Taylor expanded in c around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. fma-define 66.9%

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

      5. associate-/l* 64.5%

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

      6. *-commutative 64.5%

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

      7. +-commutative 64.5%

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

      8. mul-1-neg 64.5%

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

      9. unsub-neg 64.5%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in c around inf 63.4%

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

      1. *-commutative 63.4%

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

   8. Simplified 63.4%

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

   if 6.0000000000000004e182 < j

   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 x around 0 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in j around inf 85.9%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+182}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.54 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.45e+16)
     t_2
     (if (<= b -1.02e-149)
       t_1
       (if (<= b -1.54e-291)
         (* j (- (* a c) (* y i)))
         (if (<= b 1.6e+63) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_2;
	} else if (b <= -1.02e-149) {
		tmp = t_1;
	} else if (b <= -1.54e-291) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.6e+63) {
		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 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.45d+16)) then
        tmp = t_2
    else if (b <= (-1.02d-149)) then
        tmp = t_1
    else if (b <= (-1.54d-291)) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 1.6d+63) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_2;
	} else if (b <= -1.02e-149) {
		tmp = t_1;
	} else if (b <= -1.54e-291) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.6e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.45e+16:
		tmp = t_2
	elif b <= -1.02e-149:
		tmp = t_1
	elif b <= -1.54e-291:
		tmp = j * ((a * c) - (y * i))
	elif b <= 1.6e+63:
		tmp = t_1
	else:
		tmp = t_2
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.45e+16)
		tmp = t_2;
	elseif (b <= -1.02e-149)
		tmp = t_1;
	elseif (b <= -1.54e-291)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 1.6e+63)
		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 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.45e+16)
		tmp = t_2;
	elseif (b <= -1.02e-149)
		tmp = t_1;
	elseif (b <= -1.54e-291)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 1.6e+63)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+16], t$95$2, If[LessEqual[b, -1.02e-149], t$95$1, If[LessEqual[b, -1.54e-291], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.45e16 or 1.60000000000000006e63 < b

   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 b around inf 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -1.45e16 < b < -1.0200000000000001e-149 or -1.53999999999999995e-291 < b < 1.60000000000000006e63

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. mul-1-neg 57.6%

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

      3. unsub-neg 57.6%

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

   5. Simplified 57.6%

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

   if -1.0200000000000001e-149 < b < -1.53999999999999995e-291

   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 x around 0 59.0%

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

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in j around inf 62.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.54 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.2e-27)
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
   (if (<= b 1.4e+62)
     (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
     (* c (+ (* a j) (- (* b (* i (/ t c))) (* z b)))))))

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 <= -4.2e-27) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (b <= 1.4e+62) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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) :: tmp
    if (b <= (-4.2d-27)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else if (b <= 1.4d+62) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else
        tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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 tmp;
	if (b <= -4.2e-27) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (b <= 1.4e+62) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.2e-27:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	elif b <= 1.4e+62:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	else:
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.2e-27)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (b <= 1.4e+62)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(c * Float64(Float64(a * j) + Float64(Float64(b * Float64(i * Float64(t / c))) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.2e-27)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	elseif (b <= 1.4e+62)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	else
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.2e-27], 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], If[LessEqual[b, 1.4e+62], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(b * N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.20000000000000031e-27

   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 j around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -4.20000000000000031e-27 < b < 1.40000000000000007e62

   1. Initial program 73.7%

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

   3. Taylor expanded in b around 0 77.4%

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

   if 1.40000000000000007e62 < b

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. fma-define 65.1%

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

      5. associate-/l* 65.1%

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

      6. *-commutative 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. unsub-neg 65.1%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in c around inf 80.4%

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

      1. *-commutative 80.4%

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

   8. Simplified 80.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -9.5e+114)
   (- (* b (- (* t i) (* z c))) (* a (* x t)))
   (if (<= b 1.35e+55)
     (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
     (* c (+ (* a j) (- (* b (* i (/ t c))) (* z b)))))))

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 <= -9.5e+114) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else if (b <= 1.35e+55) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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) :: tmp
    if (b <= (-9.5d+114)) then
        tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
    else if (b <= 1.35d+55) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else
        tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * 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 tmp;
	if (b <= -9.5e+114) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else if (b <= 1.35e+55) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -9.5e+114:
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
	elif b <= 1.35e+55:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	else:
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -9.5e+114)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	elseif (b <= 1.35e+55)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(c * Float64(Float64(a * j) + Float64(Float64(b * Float64(i * Float64(t / c))) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -9.5e+114)
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	elseif (b <= 1.35e+55)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	else
		tmp = c * ((a * j) + ((b * (i * (t / c))) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -9.5e+114], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+55], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(b * N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5000000000000001e114

   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 j around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in y around 0 76.2%

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

   if -9.5000000000000001e114 < b < 1.34999999999999988e55

   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 b around 0 75.2%

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

   if 1.34999999999999988e55 < b

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. fma-define 65.1%

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

      5. associate-/l* 65.1%

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

      6. *-commutative 65.1%

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

      7. +-commutative 65.1%

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

      8. mul-1-neg 65.1%

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

      9. unsub-neg 65.1%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in c around inf 80.4%

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

      1. *-commutative 80.4%

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

   8. Simplified 80.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(b \cdot \left(i \cdot \frac{t}{c}\right) - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b)))))
   (if (<= b -6.8e+67)
     t_1
     (if (<= b -1.7e-128)
       (* x (* t (- a)))
       (if (<= b -1.8e-298)
         (* y (* i (- j)))
         (if (<= b 2.2e+60) (* a (* x (- t))) 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 = z * (c * -b);
	double tmp;
	if (b <= -6.8e+67) {
		tmp = t_1;
	} else if (b <= -1.7e-128) {
		tmp = x * (t * -a);
	} else if (b <= -1.8e-298) {
		tmp = y * (i * -j);
	} else if (b <= 2.2e+60) {
		tmp = a * (x * -t);
	} 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 = z * (c * -b)
    if (b <= (-6.8d+67)) then
        tmp = t_1
    else if (b <= (-1.7d-128)) then
        tmp = x * (t * -a)
    else if (b <= (-1.8d-298)) then
        tmp = y * (i * -j)
    else if (b <= 2.2d+60) then
        tmp = a * (x * -t)
    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 = z * (c * -b);
	double tmp;
	if (b <= -6.8e+67) {
		tmp = t_1;
	} else if (b <= -1.7e-128) {
		tmp = x * (t * -a);
	} else if (b <= -1.8e-298) {
		tmp = y * (i * -j);
	} else if (b <= 2.2e+60) {
		tmp = a * (x * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	tmp = 0
	if b <= -6.8e+67:
		tmp = t_1
	elif b <= -1.7e-128:
		tmp = x * (t * -a)
	elif b <= -1.8e-298:
		tmp = y * (i * -j)
	elif b <= 2.2e+60:
		tmp = a * (x * -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	tmp = 0.0
	if (b <= -6.8e+67)
		tmp = t_1;
	elseif (b <= -1.7e-128)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (b <= -1.8e-298)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= 2.2e+60)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	tmp = 0.0;
	if (b <= -6.8e+67)
		tmp = t_1;
	elseif (b <= -1.7e-128)
		tmp = x * (t * -a);
	elseif (b <= -1.8e-298)
		tmp = y * (i * -j);
	elseif (b <= 2.2e+60)
		tmp = a * (x * -t);
	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[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+67], t$95$1, If[LessEqual[b, -1.7e-128], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.8e-298], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+60], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.8000000000000003e67 or 2.19999999999999996e60 < b

   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 z around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. neg-mul-1 50.5%

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

      2. distribute-rgt-neg-in 50.5%

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

   8. Simplified 50.5%

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

   if -6.8000000000000003e67 < b < -1.69999999999999987e-128

   1. Initial program 83.5%

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

   3. Taylor expanded in j around inf 73.2%

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

   4. Taylor expanded in x around -inf 54.2%

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

      1. *-commutative 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in y around 0 35.3%

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

      1. neg-mul-1 35.3%

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

      2. distribute-rgt-neg-in 35.3%

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

   9. Simplified 35.3%

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

   if -1.69999999999999987e-128 < b < -1.80000000000000001e-298

   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 y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in z around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. distribute-lft-neg-out 42.6%

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

      3. *-commutative 42.6%

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

   8. Simplified 42.6%

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

   if -1.80000000000000001e-298 < b < 2.19999999999999996e60

   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 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in c around 0 37.4%

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

      1. associate-*r* 37.4%

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

      2. neg-mul-1 37.4%

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

   8. Simplified 37.4%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-298}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= c -5.5e+113)
     t_1
     (if (<= c -7.5e-112)
       (* t (* b i))
       (if (<= c 6.4e-120)
         (* z (* x y))
         (if (<= c 3.5e+84) (* y (* 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 = j * (a * c);
	double tmp;
	if (c <= -5.5e+113) {
		tmp = t_1;
	} else if (c <= -7.5e-112) {
		tmp = t * (b * i);
	} else if (c <= 6.4e-120) {
		tmp = z * (x * y);
	} else if (c <= 3.5e+84) {
		tmp = y * (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 = j * (a * c)
    if (c <= (-5.5d+113)) then
        tmp = t_1
    else if (c <= (-7.5d-112)) then
        tmp = t * (b * i)
    else if (c <= 6.4d-120) then
        tmp = z * (x * y)
    else if (c <= 3.5d+84) then
        tmp = y * (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 = j * (a * c);
	double tmp;
	if (c <= -5.5e+113) {
		tmp = t_1;
	} else if (c <= -7.5e-112) {
		tmp = t * (b * i);
	} else if (c <= 6.4e-120) {
		tmp = z * (x * y);
	} else if (c <= 3.5e+84) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if c <= -5.5e+113:
		tmp = t_1
	elif c <= -7.5e-112:
		tmp = t * (b * i)
	elif c <= 6.4e-120:
		tmp = z * (x * y)
	elif c <= 3.5e+84:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (c <= -5.5e+113)
		tmp = t_1;
	elseif (c <= -7.5e-112)
		tmp = Float64(t * Float64(b * i));
	elseif (c <= 6.4e-120)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 3.5e+84)
		tmp = Float64(y * Float64(i * Float64(-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 = j * (a * c);
	tmp = 0.0;
	if (c <= -5.5e+113)
		tmp = t_1;
	elseif (c <= -7.5e-112)
		tmp = t * (b * i);
	elseif (c <= 6.4e-120)
		tmp = z * (x * y);
	elseif (c <= 3.5e+84)
		tmp = y * (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[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e+113], t$95$1, If[LessEqual[c, -7.5e-112], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.4e-120], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+84], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.5000000000000001e113 or 3.4999999999999999e84 < c

   1. Initial program 53.8%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in c around inf 44.4%

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

      1. associate-*r* 47.6%

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

      2. *-commutative 47.6%

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

      3. *-commutative 47.6%

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

      4. *-commutative 47.6%

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

   8. Simplified 47.6%

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

   if -5.5000000000000001e113 < c < -7.5000000000000002e-112

   1. Initial program 82.2%

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

   3. Taylor expanded in j around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in i around inf 26.9%

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

      1. *-commutative 26.9%

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

      2. *-commutative 26.9%

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

      3. associate-*l* 28.6%

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

      4. *-commutative 28.6%

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

   8. Simplified 28.6%

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

   if -7.5000000000000002e-112 < c < 6.3999999999999999e-120

   1. Initial program 87.0%

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

   3. Taylor expanded in z around inf 46.1%

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

      1. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in y around inf 42.1%

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

      1. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 6.3999999999999999e-120 < c < 3.4999999999999999e84

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 37.6%

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

      1. +-commutative 37.6%

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

      2. mul-1-neg 37.6%

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

      3. unsub-neg 37.6%

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

      4. *-commutative 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in z around 0 37.4%

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

      1. mul-1-neg 37.4%

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

      2. distribute-lft-neg-out 37.4%

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

      3. *-commutative 37.4%

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

   8. Simplified 37.4%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+113}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.7 \cdot 10^{+49} \lor \neg \left(x \leq 1.95 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -8.7e+49) (not (<= x 1.95e-17)))
   (- (* x (- (* y z) (* t a))) (* z (* b c)))
   (+ (* j (* a c)) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -8.7e+49) || !(x <= 1.95e-17)) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else {
		tmp = (j * (a * c)) + (b * ((t * i) - (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) :: tmp
    if ((x <= (-8.7d+49)) .or. (.not. (x <= 1.95d-17))) then
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    else
        tmp = (j * (a * c)) + (b * ((t * i) - (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 tmp;
	if ((x <= -8.7e+49) || !(x <= 1.95e-17)) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -8.7e+49) or not (x <= 1.95e-17):
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	else:
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -8.7e+49) || !(x <= 1.95e-17))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	else
		tmp = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -8.7e+49) || ~((x <= 1.95e-17)))
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	else
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -8.7e+49], N[Not[LessEqual[x, 1.95e-17]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7e49 or 1.94999999999999995e-17 < x

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 0 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in c around inf 70.4%

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

      1. *-commutative 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*l* 79.9%

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

      4. *-commutative 79.9%

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

   8. Simplified 72.1%

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

   if -8.7e49 < x < 1.94999999999999995e-17

   1. Initial program 71.2%

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

   3. Taylor expanded in x around 0 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around inf 59.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.7 \cdot 10^{+49} \lor \neg \left(x \leq 1.95 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - a \cdot \frac{t}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -8.2e+50)
   (* x (- (* y z) (* t a)))
   (if (<= x 3.35e+68)
     (+ (* j (* a c)) (* b (- (* t i) (* z c))))
     (* x (* y (- z (* a (/ t y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -8.2e+50) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= 3.35e+68) {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = x * (y * (z - (a * (t / y))));
	}
	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 (x <= (-8.2d+50)) then
        tmp = x * ((y * z) - (t * a))
    else if (x <= 3.35d+68) then
        tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
    else
        tmp = x * (y * (z - (a * (t / y))))
    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 (x <= -8.2e+50) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= 3.35e+68) {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = x * (y * (z - (a * (t / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -8.2e+50:
		tmp = x * ((y * z) - (t * a))
	elif x <= 3.35e+68:
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
	else:
		tmp = x * (y * (z - (a * (t / y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -8.2e+50)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (x <= 3.35e+68)
		tmp = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(x * Float64(y * Float64(z - Float64(a * Float64(t / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -8.2e+50)
		tmp = x * ((y * z) - (t * a));
	elseif (x <= 3.35e+68)
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	else
		tmp = x * (y * (z - (a * (t / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -8.2e+50], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.35e+68], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2000000000000002e50

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 67.3%

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

   4. Taylor expanded in x around -inf 69.4%

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

      1. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if -8.2000000000000002e50 < x < 3.3499999999999999e68

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in a around inf 58.0%

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

   if 3.3499999999999999e68 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in j around inf 67.6%

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

   4. Taylor expanded in x around -inf 71.8%

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

      1. *-commutative 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in y around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. associate-/l* 73.8%

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

   9. Simplified 73.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - a \cdot \frac{t}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.65e+50)
   (* x (* t (- a)))
   (if (<= x -5.8e-263)
     (* b (* t i))
     (if (<= x 2.3e+68) (* j (* a c)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.65e+50) {
		tmp = x * (t * -a);
	} else if (x <= -5.8e-263) {
		tmp = b * (t * i);
	} else if (x <= 2.3e+68) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-1.65d+50)) then
        tmp = x * (t * -a)
    else if (x <= (-5.8d-263)) then
        tmp = b * (t * i)
    else if (x <= 2.3d+68) then
        tmp = j * (a * c)
    else
        tmp = z * (x * y)
    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 (x <= -1.65e+50) {
		tmp = x * (t * -a);
	} else if (x <= -5.8e-263) {
		tmp = b * (t * i);
	} else if (x <= 2.3e+68) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.65e+50:
		tmp = x * (t * -a)
	elif x <= -5.8e-263:
		tmp = b * (t * i)
	elif x <= 2.3e+68:
		tmp = j * (a * c)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.65e+50)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -5.8e-263)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 2.3e+68)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.65e+50)
		tmp = x * (t * -a);
	elseif (x <= -5.8e-263)
		tmp = b * (t * i);
	elseif (x <= 2.3e+68)
		tmp = j * (a * c);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.65e+50], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-263], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+68], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.65e50

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 67.3%

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

   4. Taylor expanded in x around -inf 69.4%

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

      1. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in y around 0 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-rgt-neg-in 49.3%

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

   9. Simplified 49.3%

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

   if -1.65e50 < x < -5.80000000000000007e-263

   1. Initial program 75.1%

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

   3. Taylor expanded in j around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in i around inf 30.5%

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

      1. *-commutative 30.5%

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

   8. Simplified 30.5%

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

   if -5.80000000000000007e-263 < x < 2.3e68

   1. Initial program 68.2%

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

   3. Taylor expanded in a around inf 32.3%

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

      1. +-commutative 32.3%

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

      2. mul-1-neg 32.3%

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

      3. unsub-neg 32.3%

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

   5. Simplified 32.3%

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

   6. Taylor expanded in c around inf 27.9%

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

      1. associate-*r* 30.3%

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

      2. *-commutative 30.3%

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

      3. *-commutative 30.3%

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

      4. *-commutative 30.3%

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

   8. Simplified 30.3%

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

   if 2.3e68 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 53.6%

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

      1. *-commutative 53.6%

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

   8. Simplified 53.6%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.01 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= c -3.4e+114)
     t_1
     (if (<= c -1.01e-112)
       (* t (* b i))
       (if (<= c 6.6e-39) (* 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 = j * (a * c);
	double tmp;
	if (c <= -3.4e+114) {
		tmp = t_1;
	} else if (c <= -1.01e-112) {
		tmp = t * (b * i);
	} else if (c <= 6.6e-39) {
		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 = j * (a * c)
    if (c <= (-3.4d+114)) then
        tmp = t_1
    else if (c <= (-1.01d-112)) then
        tmp = t * (b * i)
    else if (c <= 6.6d-39) 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 = j * (a * c);
	double tmp;
	if (c <= -3.4e+114) {
		tmp = t_1;
	} else if (c <= -1.01e-112) {
		tmp = t * (b * i);
	} else if (c <= 6.6e-39) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if c <= -3.4e+114:
		tmp = t_1
	elif c <= -1.01e-112:
		tmp = t * (b * i)
	elif c <= 6.6e-39:
		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(j * Float64(a * c))
	tmp = 0.0
	if (c <= -3.4e+114)
		tmp = t_1;
	elseif (c <= -1.01e-112)
		tmp = Float64(t * Float64(b * i));
	elseif (c <= 6.6e-39)
		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 = j * (a * c);
	tmp = 0.0;
	if (c <= -3.4e+114)
		tmp = t_1;
	elseif (c <= -1.01e-112)
		tmp = t * (b * i);
	elseif (c <= 6.6e-39)
		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[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.4e+114], t$95$1, If[LessEqual[c, -1.01e-112], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.6e-39], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.4000000000000001e114 or 6.5999999999999997e-39 < c

   1. Initial program 58.5%

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

   3. Taylor expanded in a around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in c around inf 41.3%

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

      1. associate-*r* 43.9%

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

      2. *-commutative 43.9%

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

      3. *-commutative 43.9%

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

      4. *-commutative 43.9%

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

   8. Simplified 43.9%

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

   if -3.4000000000000001e114 < c < -1.01e-112

   1. Initial program 82.2%

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

   3. Taylor expanded in j around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in i around inf 26.9%

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

      1. *-commutative 26.9%

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

      2. *-commutative 26.9%

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

      3. associate-*l* 28.6%

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

      4. *-commutative 28.6%

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

   8. Simplified 28.6%

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

   if -1.01e-112 < c < 6.5999999999999997e-39

   1. Initial program 88.6%

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

   3. Taylor expanded in z around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq -1.01 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;c \leq -2.3 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= c -2.3e+113)
     t_1
     (if (<= c -7.6e-112) (* t (* b i)) (if (<= c 5e-39) (* x (* y 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 = j * (a * c);
	double tmp;
	if (c <= -2.3e+113) {
		tmp = t_1;
	} else if (c <= -7.6e-112) {
		tmp = t * (b * i);
	} else if (c <= 5e-39) {
		tmp = x * (y * 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 = j * (a * c)
    if (c <= (-2.3d+113)) then
        tmp = t_1
    else if (c <= (-7.6d-112)) then
        tmp = t * (b * i)
    else if (c <= 5d-39) then
        tmp = x * (y * 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 = j * (a * c);
	double tmp;
	if (c <= -2.3e+113) {
		tmp = t_1;
	} else if (c <= -7.6e-112) {
		tmp = t * (b * i);
	} else if (c <= 5e-39) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if c <= -2.3e+113:
		tmp = t_1
	elif c <= -7.6e-112:
		tmp = t * (b * i)
	elif c <= 5e-39:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (c <= -2.3e+113)
		tmp = t_1;
	elseif (c <= -7.6e-112)
		tmp = Float64(t * Float64(b * i));
	elseif (c <= 5e-39)
		tmp = Float64(x * Float64(y * 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 = j * (a * c);
	tmp = 0.0;
	if (c <= -2.3e+113)
		tmp = t_1;
	elseif (c <= -7.6e-112)
		tmp = t * (b * i);
	elseif (c <= 5e-39)
		tmp = x * (y * 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[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.3e+113], t$95$1, If[LessEqual[c, -7.6e-112], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e-39], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.29999999999999997e113 or 4.9999999999999998e-39 < c

   1. Initial program 58.5%

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

   3. Taylor expanded in a around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in c around inf 41.3%

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

      1. associate-*r* 43.9%

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

      2. *-commutative 43.9%

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

      3. *-commutative 43.9%

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

      4. *-commutative 43.9%

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

   8. Simplified 43.9%

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

   if -2.29999999999999997e113 < c < -7.59999999999999989e-112

   1. Initial program 82.2%

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

   3. Taylor expanded in j around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in i around inf 26.9%

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

      1. *-commutative 26.9%

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

      2. *-commutative 26.9%

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

      3. associate-*l* 28.6%

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

      4. *-commutative 28.6%

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

   8. Simplified 28.6%

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

   if -7.59999999999999989e-112 < c < 4.9999999999999998e-39

   1. Initial program 88.6%

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

   3. Taylor expanded in z around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in y around inf 34.3%

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

Alternative 18: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+21} \lor \neg \left(b \leq 4.1 \cdot 10^{+64}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.3e+21) (not (<= b 4.1e+64)))
   (* 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+21) || !(b <= 4.1e+64)) {
		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+21)) .or. (.not. (b <= 4.1d+64))) 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+21) || !(b <= 4.1e+64)) {
		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+21) or not (b <= 4.1e+64):
		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+21) || !(b <= 4.1e+64))
		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+21) || ~((b <= 4.1e+64)))
		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+21], N[Not[LessEqual[b, 4.1e+64]], $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 < -3.3e21 or 4.09999999999999978e64 < b

   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 b around inf 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -3.3e21 < b < 4.09999999999999978e64

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

   5. Simplified 52.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+21} \lor \neg \left(b \leq 4.1 \cdot 10^{+64}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8.4e+67)
   (* z (* c (- b)))
   (if (<= b 1.95e+65) (* a (- (* c j) (* x t))) (* (* 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 tmp;
	if (b <= -8.4e+67) {
		tmp = z * (c * -b);
	} else if (b <= 1.95e+65) {
		tmp = a * ((c * j) - (x * t));
	} 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) :: tmp
    if (b <= (-8.4d+67)) then
        tmp = z * (c * -b)
    else if (b <= 1.95d+65) then
        tmp = a * ((c * j) - (x * t))
    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 tmp;
	if (b <= -8.4e+67) {
		tmp = z * (c * -b);
	} else if (b <= 1.95e+65) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8.4e+67:
		tmp = z * (c * -b)
	elif b <= 1.95e+65:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8.4e+67)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (b <= 1.95e+65)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8.4e+67)
		tmp = z * (c * -b);
	elseif (b <= 1.95e+65)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8.4e+67], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+65], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.4000000000000005e67

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. neg-mul-1 50.5%

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

      2. distribute-rgt-neg-in 50.5%

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

   8. Simplified 50.5%

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

   if -8.4000000000000005e67 < b < 1.9499999999999999e65

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

   5. Simplified 51.9%

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

   if 1.9499999999999999e65 < b

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 56.7%

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

      1. *-commutative 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in y around 0 50.4%

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

      1. associate-*r* 50.4%

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

      2. neg-mul-1 50.4%

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

   8. Simplified 50.4%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.8e+51)
   (* t (* x (- a)))
   (if (<= x 3.3e+68) (* (* z c) (- b)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.8e+51) {
		tmp = t * (x * -a);
	} else if (x <= 3.3e+68) {
		tmp = (z * c) * -b;
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-1.8d+51)) then
        tmp = t * (x * -a)
    else if (x <= 3.3d+68) then
        tmp = (z * c) * -b
    else
        tmp = z * (x * y)
    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 (x <= -1.8e+51) {
		tmp = t * (x * -a);
	} else if (x <= 3.3e+68) {
		tmp = (z * c) * -b;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.8e+51:
		tmp = t * (x * -a)
	elif x <= 3.3e+68:
		tmp = (z * c) * -b
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.8e+51)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= 3.3e+68)
		tmp = Float64(Float64(z * c) * Float64(-b));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.8e+51)
		tmp = t * (x * -a);
	elseif (x <= 3.3e+68)
		tmp = (z * c) * -b;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.8e+51], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+68], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000005e51

   1. Initial program 76.5%

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

   3. Taylor expanded in a around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in c around inf 56.0%

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

   7. Taylor expanded in c around 0 48.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. 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%

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

      3. *-commutative 48.7%

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

   9. Simplified 48.7%

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

   10. Taylor expanded in a around 0 48.7%

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

       1. *-commutative 48.7%

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

       2. associate-*r* 48.7%

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

       3. associate-*r* 48.7%

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

       4. associate-*l* 49.4%

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

       5. mul-1-neg 49.4%

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

       6. *-commutative 49.4%

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

   12. Simplified 49.4%

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

   if -1.80000000000000005e51 < x < 3.3e68

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 40.5%

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

      1. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in y around 0 33.6%

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

      1. associate-*r* 33.6%

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

      2. neg-mul-1 33.6%

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

   8. Simplified 33.6%

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

   if 3.3e68 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 53.6%

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

      1. *-commutative 53.6%

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

   8. Simplified 53.6%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+68}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -4.6e+50)
   (* x (* t (- a)))
   (if (<= x 2.2e+68) (* (* z c) (- b)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -4.6e+50) {
		tmp = x * (t * -a);
	} else if (x <= 2.2e+68) {
		tmp = (z * c) * -b;
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-4.6d+50)) then
        tmp = x * (t * -a)
    else if (x <= 2.2d+68) then
        tmp = (z * c) * -b
    else
        tmp = z * (x * y)
    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 (x <= -4.6e+50) {
		tmp = x * (t * -a);
	} else if (x <= 2.2e+68) {
		tmp = (z * c) * -b;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -4.6e+50:
		tmp = x * (t * -a)
	elif x <= 2.2e+68:
		tmp = (z * c) * -b
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -4.6e+50)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= 2.2e+68)
		tmp = Float64(Float64(z * c) * Float64(-b));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -4.6e+50)
		tmp = x * (t * -a);
	elseif (x <= 2.2e+68)
		tmp = (z * c) * -b;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -4.6e+50], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+68], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.59999999999999994e50

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 67.3%

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

   4. Taylor expanded in x around -inf 69.4%

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

      1. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in y around 0 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-rgt-neg-in 49.3%

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

   9. Simplified 49.3%

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

   if -4.59999999999999994e50 < x < 2.19999999999999987e68

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 40.5%

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

      1. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in y around 0 33.6%

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

      1. associate-*r* 33.6%

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

      2. neg-mul-1 33.6%

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

   8. Simplified 33.6%

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

   if 2.19999999999999987e68 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 53.6%

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

      1. *-commutative 53.6%

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

   8. Simplified 53.6%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+68}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.26e+51)
   (* x (* t (- a)))
   (if (<= x 2.3e+68) (* z (* c (- b))) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.26e+51) {
		tmp = x * (t * -a);
	} else if (x <= 2.3e+68) {
		tmp = z * (c * -b);
	} else {
		tmp = z * (x * y);
	}
	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 (x <= (-1.26d+51)) then
        tmp = x * (t * -a)
    else if (x <= 2.3d+68) then
        tmp = z * (c * -b)
    else
        tmp = z * (x * y)
    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 (x <= -1.26e+51) {
		tmp = x * (t * -a);
	} else if (x <= 2.3e+68) {
		tmp = z * (c * -b);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.26e+51:
		tmp = x * (t * -a)
	elif x <= 2.3e+68:
		tmp = z * (c * -b)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.26e+51)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= 2.3e+68)
		tmp = Float64(z * Float64(c * Float64(-b)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.26e+51)
		tmp = x * (t * -a);
	elseif (x <= 2.3e+68)
		tmp = z * (c * -b);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.26e+51], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+68], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25999999999999997e51

   1. Initial program 76.5%

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

   3. Taylor expanded in j around inf 67.3%

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

   4. Taylor expanded in x around -inf 69.4%

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

      1. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in y around 0 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-rgt-neg-in 49.3%

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

   9. Simplified 49.3%

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

   if -1.25999999999999997e51 < x < 2.3e68

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 40.5%

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

      1. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in y around 0 31.9%

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

      1. neg-mul-1 31.9%

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

      2. distribute-rgt-neg-in 31.9%

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

   8. Simplified 31.9%

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

   if 2.3e68 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 53.6%

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

      1. *-commutative 53.6%

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

   8. Simplified 53.6%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.2 \cdot 10^{+40} \lor \neg \left(i \leq 1.1 \cdot 10^{+89}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.2e+40) (not (<= i 1.1e+89))) (* b (* t i)) (* j (* a c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.2e+40) || !(i <= 1.1e+89)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * 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) :: tmp
    if ((i <= (-2.2d+40)) .or. (.not. (i <= 1.1d+89))) then
        tmp = b * (t * i)
    else
        tmp = j * (a * 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 tmp;
	if ((i <= -2.2e+40) || !(i <= 1.1e+89)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.2e+40) or not (i <= 1.1e+89):
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.2e+40) || !(i <= 1.1e+89))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2.2e+40) || ~((i <= 1.1e+89)))
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.2e+40], N[Not[LessEqual[i, 1.1e+89]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.1999999999999999e40 or 1.1e89 < i

   1. Initial program 68.9%

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

   3. Taylor expanded in j around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in i around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   if -2.1999999999999999e40 < i < 1.1e89

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in c around inf 28.4%

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

      1. associate-*r* 29.0%

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

      2. *-commutative 29.0%

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

      3. *-commutative 29.0%

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

      4. *-commutative 29.0%

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

   8. Simplified 29.0%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.2 \cdot 10^{+40} \lor \neg \left(i \leq 1.1 \cdot 10^{+89}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+112} \lor \neg \left(b \leq 1.15 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -8.6e+112) (not (<= b 1.15e+14))) (* b (* t i)) (* 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 tmp;
	if ((b <= -8.6e+112) || !(b <= 1.15e+14)) {
		tmp = b * (t * i);
	} 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) :: tmp
    if ((b <= (-8.6d+112)) .or. (.not. (b <= 1.15d+14))) then
        tmp = b * (t * i)
    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 tmp;
	if ((b <= -8.6e+112) || !(b <= 1.15e+14)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -8.6e+112) or not (b <= 1.15e+14):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -8.6e+112) || !(b <= 1.15e+14))
		tmp = Float64(b * Float64(t * i));
	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)
	tmp = 0.0;
	if ((b <= -8.6e+112) || ~((b <= 1.15e+14)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -8.6e+112], N[Not[LessEqual[b, 1.15e+14]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.59999999999999966e112 or 1.15e14 < b

   1. Initial program 69.0%

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

   3. Taylor expanded in j around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in i around inf 38.8%

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

      1. *-commutative 38.8%

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

   8. Simplified 38.8%

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

   if -8.59999999999999966e112 < b < 1.15e14

   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 a around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in c around inf 28.7%

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

      1. *-commutative 28.7%

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

   8. Simplified 28.7%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+112} \lor \neg \left(b \leq 1.15 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.4e+113)
   (* b (* t i))
   (if (<= b 1e+14) (* a (* c j)) (* t (* b 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 (b <= -5.4e+113) {
		tmp = b * (t * i);
	} else if (b <= 1e+14) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * 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 (b <= (-5.4d+113)) then
        tmp = b * (t * i)
    else if (b <= 1d+14) then
        tmp = a * (c * j)
    else
        tmp = t * (b * 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 (b <= -5.4e+113) {
		tmp = b * (t * i);
	} else if (b <= 1e+14) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.4e+113:
		tmp = b * (t * i)
	elif b <= 1e+14:
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.4e+113)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 1e+14)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.4e+113)
		tmp = b * (t * i);
	elseif (b <= 1e+14)
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.4e+113], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+14], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.40000000000000022e113

   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 j around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in i around inf 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

   if -5.40000000000000022e113 < b < 1e14

   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 a around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in c around inf 28.7%

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

      1. *-commutative 28.7%

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

   8. Simplified 28.7%

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

   if 1e14 < b

   1. Initial program 66.9%

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

   3. Taylor expanded in j around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in i around inf 39.0%

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

      1. *-commutative 39.0%

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

      2. *-commutative 39.0%

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

      3. associate-*l* 42.0%

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

      4. *-commutative 42.0%

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

   8. Simplified 42.0%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.0% 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 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 a around inf 39.7%

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

   1. +-commutative 39.7%

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

   2. mul-1-neg 39.7%

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

   3. unsub-neg 39.7%

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

5. Simplified 39.7%

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

6. Taylor expanded in c around inf 23.2%

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

   1. *-commutative 23.2%

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

8. Simplified 23.2%

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

9. Final simplification 23.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 59.0% 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 2024157 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))