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

Percentage Accurate: 73.4% → 82.3%

Time: 17.3s

Alternatives: 20

Speedup: 0.5×

• 58.7% 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: 73.4% 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: 82.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* 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 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 = a * ((c * j) - (x * t));
	}
	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 = a * ((c * j) - (x * t));
	}
	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 = a * ((c * j) - (x * t))
	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(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)
	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 = a * ((c * j) - (x * t));
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $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 94.6%

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

   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 a around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

      4. *-commutative 48.9%

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

   5. Simplified 48.9%

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

4. Final simplification 86.8%

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

Alternative 2: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-12} \lor \neg \left(x \leq 3.5 \cdot 10^{+38}\right):\\ \;\;\;\;t\_1 - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= x -3.4e-12) (not (<= x 3.5e+38)))
     (- t_1 (+ (* z (* b c)) (* x (- (* t a) (* y z)))))
     (- t_1 (* b (- (* z c) (* t i)))))))

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 ((x <= -3.4e-12) || !(x <= 3.5e+38)) {
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	} else {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if ((x <= (-3.4d-12)) .or. (.not. (x <= 3.5d+38))) then
        tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))))
    else
        tmp = t_1 - (b * ((z * c) - (t * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -3.4e-12) || !(x <= 3.5e+38)) {
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	} else {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (x <= -3.4e-12) or not (x <= 3.5e+38):
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))))
	else:
		tmp = t_1 - (b * ((z * c) - (t * i)))
	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 ((x <= -3.4e-12) || !(x <= 3.5e+38))
		tmp = Float64(t_1 - Float64(Float64(z * Float64(b * c)) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))));
	else
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	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 ((x <= -3.4e-12) || ~((x <= 3.5e+38)))
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	else
		tmp = t_1 - (b * ((z * c) - (t * i)));
	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[Or[LessEqual[x, -3.4e-12], N[Not[LessEqual[x, 3.5e+38]], $MachinePrecision]], N[(t$95$1 - N[(N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4000000000000001e-12 or 3.50000000000000002e38 < x

   1. Initial program 81.9%

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

   3. Taylor expanded in c around inf 81.4%

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

      1. *-commutative 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*l* 83.9%

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

      4. *-commutative 83.9%

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

   5. Simplified 83.9%

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

   if -3.4000000000000001e-12 < x < 3.50000000000000002e38

   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 76.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-12} \lor \neg \left(x \leq 3.5 \cdot 10^{+38}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.7e+76)
   (* j (* y (- (* a (/ c y)) i)))
   (if (<= j -1.32e-158)
     (- (* x (* y z)) (* z (* b c)))
     (if (<= j 5.5e-131)
       (- (* b (* t i)) (* b (* z c)))
       (if (<= j 4e+106)
         (* x (- (* y z) (* t a)))
         (* j (- (* a c) (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.7e+76) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -1.32e-158) {
		tmp = (x * (y * z)) - (z * (b * c));
	} else if (j <= 5.5e-131) {
		tmp = (b * (t * i)) - (b * (z * c));
	} else if (j <= 4e+106) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.7d+76)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (j <= (-1.32d-158)) then
        tmp = (x * (y * z)) - (z * (b * c))
    else if (j <= 5.5d-131) then
        tmp = (b * (t * i)) - (b * (z * c))
    else if (j <= 4d+106) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.7e+76) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -1.32e-158) {
		tmp = (x * (y * z)) - (z * (b * c));
	} else if (j <= 5.5e-131) {
		tmp = (b * (t * i)) - (b * (z * c));
	} else if (j <= 4e+106) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.7e+76:
		tmp = j * (y * ((a * (c / y)) - i))
	elif j <= -1.32e-158:
		tmp = (x * (y * z)) - (z * (b * c))
	elif j <= 5.5e-131:
		tmp = (b * (t * i)) - (b * (z * c))
	elif j <= 4e+106:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.7e+76)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (j <= -1.32e-158)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(z * Float64(b * c)));
	elseif (j <= 5.5e-131)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(b * Float64(z * c)));
	elseif (j <= 4e+106)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.7e+76)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (j <= -1.32e-158)
		tmp = (x * (y * z)) - (z * (b * c));
	elseif (j <= 5.5e-131)
		tmp = (b * (t * i)) - (b * (z * c));
	elseif (j <= 4e+106)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.7e+76], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.32e-158], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-131], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+106], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.6999999999999999e76

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf 68.1%

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

   4. Taylor expanded in y around inf 68.1%

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

      1. associate-/l* 68.2%

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

   6. Simplified 68.2%

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

   if -1.6999999999999999e76 < j < -1.3200000000000001e-158

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 46.3%

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

   4. Taylor expanded in x around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. +-commutative 46.0%

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

      3. sub-neg 46.0%

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

      4. associate-*r* 49.8%

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

      5. *-commutative 49.8%

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

   6. Simplified 49.8%

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

   if -1.3200000000000001e-158 < j < 5.4999999999999997e-131

   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 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in i around 0 79.7%

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

   7. Taylor expanded in x around 0 60.2%

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

   if 5.4999999999999997e-131 < j < 4.00000000000000036e106

   1. Initial program 78.2%

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

   3. Taylor expanded in j around 0 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around inf 55.7%

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

   if 4.00000000000000036e106 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -1.76 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -1.45e+56)
     (* j (* y (- (* a (/ c y)) i)))
     (if (<= j -1.76e-158)
       t_1
       (if (<= j 6.2e-140)
         (- (* b (* t i)) (* b (* z c)))
         (if (<= j 1.16e+107) t_1 (* j (- (* a c) (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.45e+56) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -1.76e-158) {
		tmp = t_1;
	} else if (j <= 6.2e-140) {
		tmp = (b * (t * i)) - (b * (z * c));
	} else if (j <= 1.16e+107) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-1.45d+56)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (j <= (-1.76d-158)) then
        tmp = t_1
    else if (j <= 6.2d-140) then
        tmp = (b * (t * i)) - (b * (z * c))
    else if (j <= 1.16d+107) then
        tmp = t_1
    else
        tmp = j * ((a * c) - (y * 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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.45e+56) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -1.76e-158) {
		tmp = t_1;
	} else if (j <= 6.2e-140) {
		tmp = (b * (t * i)) - (b * (z * c));
	} else if (j <= 1.16e+107) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -1.45e+56:
		tmp = j * (y * ((a * (c / y)) - i))
	elif j <= -1.76e-158:
		tmp = t_1
	elif j <= 6.2e-140:
		tmp = (b * (t * i)) - (b * (z * c))
	elif j <= 1.16e+107:
		tmp = t_1
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -1.45e+56)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (j <= -1.76e-158)
		tmp = t_1;
	elseif (j <= 6.2e-140)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(b * Float64(z * c)));
	elseif (j <= 1.16e+107)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -1.45e+56)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (j <= -1.76e-158)
		tmp = t_1;
	elseif (j <= 6.2e-140)
		tmp = (b * (t * i)) - (b * (z * c));
	elseif (j <= 1.16e+107)
		tmp = t_1;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.45e+56], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.76e-158], t$95$1, If[LessEqual[j, 6.2e-140], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e+107], t$95$1, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.45000000000000004e56

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 67.1%

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

   4. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

   if -1.45000000000000004e56 < j < -1.76e-158 or 6.1999999999999998e-140 < j < 1.1600000000000001e107

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf 52.5%

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

   if -1.76e-158 < j < 6.1999999999999998e-140

   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 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in i around 0 79.7%

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

   7. Taylor expanded in x around 0 60.2%

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

   if 1.1600000000000001e107 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -1.76 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -1.2e+56)
     (* j (* y (- (* a (/ c y)) i)))
     (if (<= j -9.2e-159)
       t_1
       (if (<= j 2.6e-143)
         (* b (- (* t i) (* z c)))
         (if (<= j 4.2e+106) t_1 (* j (- (* a c) (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.2e+56) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -9.2e-159) {
		tmp = t_1;
	} else if (j <= 2.6e-143) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.2e+106) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-1.2d+56)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (j <= (-9.2d-159)) then
        tmp = t_1
    else if (j <= 2.6d-143) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 4.2d+106) then
        tmp = t_1
    else
        tmp = j * ((a * c) - (y * 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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.2e+56) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -9.2e-159) {
		tmp = t_1;
	} else if (j <= 2.6e-143) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.2e+106) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -1.2e+56:
		tmp = j * (y * ((a * (c / y)) - i))
	elif j <= -9.2e-159:
		tmp = t_1
	elif j <= 2.6e-143:
		tmp = b * ((t * i) - (z * c))
	elif j <= 4.2e+106:
		tmp = t_1
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -1.2e+56)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (j <= -9.2e-159)
		tmp = t_1;
	elseif (j <= 2.6e-143)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 4.2e+106)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -1.2e+56)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (j <= -9.2e-159)
		tmp = t_1;
	elseif (j <= 2.6e-143)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 4.2e+106)
		tmp = t_1;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e+56], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.2e-159], t$95$1, If[LessEqual[j, 2.6e-143], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+106], t$95$1, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.20000000000000007e56

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 67.1%

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

   4. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

   if -1.20000000000000007e56 < j < -9.19999999999999914e-159 or 2.59999999999999987e-143 < j < 4.2000000000000001e106

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf 52.5%

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

   if -9.19999999999999914e-159 < j < 2.59999999999999987e-143

   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 b around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if 4.2000000000000001e106 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.1e+55)
     t_2
     (if (<= j -1.02e-158)
       t_1
       (if (<= j 5.2e-140)
         (* b (- (* t i) (* z c)))
         (if (<= j 6.2e+106) 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.1e+55) {
		tmp = t_2;
	} else if (j <= -1.02e-158) {
		tmp = t_1;
	} else if (j <= 5.2e-140) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 6.2e+106) {
		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 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-2.1d+55)) then
        tmp = t_2
    else if (j <= (-1.02d-158)) then
        tmp = t_1
    else if (j <= 5.2d-140) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 6.2d+106) 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.1e+55) {
		tmp = t_2;
	} else if (j <= -1.02e-158) {
		tmp = t_1;
	} else if (j <= 5.2e-140) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 6.2e+106) {
		tmp = t_1;
	} 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 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.1e+55:
		tmp = t_2
	elif j <= -1.02e-158:
		tmp = t_1
	elif j <= 5.2e-140:
		tmp = b * ((t * i) - (z * c))
	elif j <= 6.2e+106:
		tmp = t_1
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.1e+55)
		tmp = t_2;
	elseif (j <= -1.02e-158)
		tmp = t_1;
	elseif (j <= 5.2e-140)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 6.2e+106)
		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 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.1e+55)
		tmp = t_2;
	elseif (j <= -1.02e-158)
		tmp = t_1;
	elseif (j <= 5.2e-140)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 6.2e+106)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.1e+55], t$95$2, If[LessEqual[j, -1.02e-158], t$95$1, If[LessEqual[j, 5.2e-140], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.1000000000000001e55 or 6.1999999999999999e106 < j

   1. Initial program 81.0%

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

   3. Taylor expanded in j around inf 76.4%

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

   if -2.1000000000000001e55 < j < -1.0199999999999999e-158 or 5.1999999999999996e-140 < j < 6.1999999999999999e106

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf 52.5%

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

   if -1.0199999999999999e-158 < j < 5.1999999999999996e-140

   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 b around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

   5. Simplified 60.1%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 7.1 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -7.5e+100)
     (- t_1 (* b (- (* z c) (* t i))))
     (if (<= j 7.1e+106)
       (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
       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 <= -7.5e+100) {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	} else if (j <= 7.1e+106) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} 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 <= (-7.5d+100)) then
        tmp = t_1 - (b * ((z * c) - (t * i)))
    else if (j <= 7.1d+106) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    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 <= -7.5e+100) {
		tmp = t_1 - (b * ((z * c) - (t * i)));
	} else if (j <= 7.1e+106) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} 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 <= -7.5e+100:
		tmp = t_1 - (b * ((z * c) - (t * i)))
	elif j <= 7.1e+106:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	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 <= -7.5e+100)
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	elseif (j <= 7.1e+106)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	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 <= -7.5e+100)
		tmp = t_1 - (b * ((z * c) - (t * i)));
	elseif (j <= 7.1e+106)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	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, -7.5e+100], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.1e+106], 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], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.49999999999999983e100

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 79.5%

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

   if -7.49999999999999983e100 < j < 7.1000000000000003e106

   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 j around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   if 7.1000000000000003e106 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 7.1 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.25e+71)
   (- (* b (* t i)) (* x (- (* t a) (* y z))))
   (if (<= x 1.65e+59)
     (- (* j (- (* a c) (* y i))) (* b (- (* z c) (* t i))))
     (* x (- (* y z) (* t a))))))

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 <= -1.25e+71) {
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	} else if (x <= 1.65e+59) {
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-1.25d+71)) then
        tmp = (b * (t * i)) - (x * ((t * a) - (y * z)))
    else if (x <= 1.65d+59) then
        tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.25e+71) {
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	} else if (x <= 1.65e+59) {
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.25e+71:
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)))
	elif x <= 1.65e+59:
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.25e+71)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (x <= 1.65e+59)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.25e+71)
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	elseif (x <= 1.65e+59)
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.25e+71], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+59], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999993e71

   1. Initial program 83.8%

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

   3. Taylor expanded in j around 0 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%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in i around 0 77.8%

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

   7. Taylor expanded in c around 0 75.8%

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

   if -1.24999999999999993e71 < x < 1.65e59

   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 x around 0 75.8%

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

   if 1.65e59 < x

   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 j around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around inf 76.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -7e+144)
     t_1
     (if (<= c 3.2e-230)
       (* z (* x y))
       (if (<= c 1.2e-108)
         (* j (* i (- y)))
         (if (<= c 4.4e-51) (* b (* t i)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -7e+144) {
		tmp = t_1;
	} else if (c <= 3.2e-230) {
		tmp = z * (x * y);
	} else if (c <= 1.2e-108) {
		tmp = j * (i * -y);
	} else if (c <= 4.4e-51) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (c <= (-7d+144)) then
        tmp = t_1
    else if (c <= 3.2d-230) then
        tmp = z * (x * y)
    else if (c <= 1.2d-108) then
        tmp = j * (i * -y)
    else if (c <= 4.4d-51) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -7e+144) {
		tmp = t_1;
	} else if (c <= 3.2e-230) {
		tmp = z * (x * y);
	} else if (c <= 1.2e-108) {
		tmp = j * (i * -y);
	} else if (c <= 4.4e-51) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -7e+144:
		tmp = t_1
	elif c <= 3.2e-230:
		tmp = z * (x * y)
	elif c <= 1.2e-108:
		tmp = j * (i * -y)
	elif c <= 4.4e-51:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -7e+144)
		tmp = t_1;
	elseif (c <= 3.2e-230)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.2e-108)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (c <= 4.4e-51)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (c <= -7e+144)
		tmp = t_1;
	elseif (c <= 3.2e-230)
		tmp = z * (x * y);
	elseif (c <= 1.2e-108)
		tmp = j * (i * -y);
	elseif (c <= 4.4e-51)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+144], t$95$1, If[LessEqual[c, 3.2e-230], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.2e-108], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.4e-51], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.9999999999999996e144 or 4.4e-51 < c

   1. Initial program 69.3%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in c around inf 51.6%

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

   if -6.9999999999999996e144 < c < 3.2e-230

   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 z around inf 45.3%

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

   4. Taylor expanded in x around inf 37.8%

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

   if 3.2e-230 < c < 1.20000000000000009e-108

   1. Initial program 99.9%

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

   3. Taylor expanded in j around inf 55.1%

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

   4. Taylor expanded in a around 0 51.8%

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

      1. neg-mul-1 51.8%

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

      2. distribute-rgt-neg-in 51.8%

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

   6. Simplified 51.8%

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

   if 1.20000000000000009e-108 < c < 4.4e-51

   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 i around -inf 57.7%

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

   4. Taylor expanded in j around 0 51.3%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+144}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.75e+56)
   (* j (* y (- (* a (/ c y)) i)))
   (if (<= j 5.4e+106)
     (- (* b (* t i)) (* x (- (* t a) (* y z))))
     (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.75e+56) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= 5.4e+106) {
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.75d+56)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (j <= 5.4d+106) then
        tmp = (b * (t * i)) - (x * ((t * a) - (y * z)))
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.75e+56) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= 5.4e+106) {
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.75e+56:
		tmp = j * (y * ((a * (c / y)) - i))
	elif j <= 5.4e+106:
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)))
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.75e+56)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (j <= 5.4e+106)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.75e+56)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (j <= 5.4e+106)
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.75e+56], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+106], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.75e56

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 67.1%

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

   4. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

   if -1.75e56 < j < 5.40000000000000012e106

   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 j around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in i around 0 71.7%

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

   7. Taylor expanded in c around 0 66.0%

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

   if 5.40000000000000012e106 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-137}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.9e+110)
     t_1
     (if (<= a -1.06e-137)
       (* z (* x y))
       (if (<= a 4.1e-94) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.9e+110) {
		tmp = t_1;
	} else if (a <= -1.06e-137) {
		tmp = z * (x * y);
	} else if (a <= 4.1e-94) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.9d+110)) then
        tmp = t_1
    else if (a <= (-1.06d-137)) then
        tmp = z * (x * y)
    else if (a <= 4.1d-94) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.9e+110) {
		tmp = t_1;
	} else if (a <= -1.06e-137) {
		tmp = z * (x * y);
	} else if (a <= 4.1e-94) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.9e+110:
		tmp = t_1
	elif a <= -1.06e-137:
		tmp = z * (x * y)
	elif a <= 4.1e-94:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (a <= -1.9e+110)
		tmp = t_1;
	elseif (a <= -1.06e-137)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 4.1e-94)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.9e+110)
		tmp = t_1;
	elseif (a <= -1.06e-137)
		tmp = z * (x * y);
	elseif (a <= 4.1e-94)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+110], t$95$1, If[LessEqual[a, -1.06e-137], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-94], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.89999999999999994e110 or 4.10000000000000001e-94 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

      4. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   if -1.89999999999999994e110 < a < -1.06000000000000005e-137

   1. Initial program 83.2%

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

   3. Taylor expanded in z around inf 62.1%

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

   4. Taylor expanded in x around inf 47.4%

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

   if -1.06000000000000005e-137 < a < 4.10000000000000001e-94

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. *-commutative 54.5%

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

   5. Simplified 54.5%

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

Alternative 12: 41.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.1e+112)
     t_1
     (if (<= a -1.75e-247)
       (* z (* x y))
       (if (<= a 5.3e-101) (* t (* b i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.1e+112) {
		tmp = t_1;
	} else if (a <= -1.75e-247) {
		tmp = z * (x * y);
	} else if (a <= 5.3e-101) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-2.1d+112)) then
        tmp = t_1
    else if (a <= (-1.75d-247)) then
        tmp = z * (x * y)
    else if (a <= 5.3d-101) then
        tmp = t * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.1e+112) {
		tmp = t_1;
	} else if (a <= -1.75e-247) {
		tmp = z * (x * y);
	} else if (a <= 5.3e-101) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.1e+112:
		tmp = t_1
	elif a <= -1.75e-247:
		tmp = z * (x * y)
	elif a <= 5.3e-101:
		tmp = t * (b * i)
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (a <= -2.1e+112)
		tmp = t_1;
	elseif (a <= -1.75e-247)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 5.3e-101)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.1e+112)
		tmp = t_1;
	elseif (a <= -1.75e-247)
		tmp = z * (x * y);
	elseif (a <= 5.3e-101)
		tmp = t * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+112], t$95$1, If[LessEqual[a, -1.75e-247], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e-101], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0999999999999999e112 or 5.3000000000000003e-101 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

      4. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   if -2.0999999999999999e112 < a < -1.75e-247

   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 z around inf 58.8%

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

   4. Taylor expanded in x around inf 40.9%

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

   if -1.75e-247 < a < 5.3000000000000003e-101

   1. Initial program 80.4%

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

   3. Taylor expanded in i around -inf 48.6%

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

   4. Taylor expanded in j around 0 38.9%

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

      1. associate-*r* 41.9%

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

   6. Simplified 41.9%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.04:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4.8e+55)
   (* j (* a c))
   (if (<= j 0.04)
     (* x (* y z))
     (if (<= j 1.2e+211) (* a (* c j)) (* (- i) (* y 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 (j <= -4.8e+55) {
		tmp = j * (a * c);
	} else if (j <= 0.04) {
		tmp = x * (y * z);
	} else if (j <= 1.2e+211) {
		tmp = a * (c * j);
	} else {
		tmp = -i * (y * 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 (j <= (-4.8d+55)) then
        tmp = j * (a * c)
    else if (j <= 0.04d0) then
        tmp = x * (y * z)
    else if (j <= 1.2d+211) then
        tmp = a * (c * j)
    else
        tmp = -i * (y * 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 (j <= -4.8e+55) {
		tmp = j * (a * c);
	} else if (j <= 0.04) {
		tmp = x * (y * z);
	} else if (j <= 1.2e+211) {
		tmp = a * (c * j);
	} else {
		tmp = -i * (y * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -4.8e+55:
		tmp = j * (a * c)
	elif j <= 0.04:
		tmp = x * (y * z)
	elif j <= 1.2e+211:
		tmp = a * (c * j)
	else:
		tmp = -i * (y * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4.8e+55)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 0.04)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.2e+211)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(Float64(-i) * Float64(y * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -4.8e+55)
		tmp = j * (a * c);
	elseif (j <= 0.04)
		tmp = x * (y * z);
	elseif (j <= 1.2e+211)
		tmp = a * (c * j);
	else
		tmp = -i * (y * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4.8e+55], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.04], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+211], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.7999999999999998e55

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 67.1%

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

   4. Taylor expanded in a around inf 53.6%

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

      1. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   if -4.7999999999999998e55 < j < 0.0400000000000000008

   1. Initial program 76.1%

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

   3. Taylor expanded in j around 0 73.2%

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

      1. *-commutative 73.2%

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

      2. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in b around inf 69.0%

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

   7. Taylor expanded in y around inf 31.1%

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

   if 0.0400000000000000008 < j < 1.20000000000000009e211

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around inf 54.5%

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

   if 1.20000000000000009e211 < j

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf 84.5%

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

   4. Taylor expanded in a around 0 72.3%

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

      1. associate-*r* 72.3%

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

      2. neg-mul-1 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.04:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.7e+110)
   (* a (* c j))
   (if (<= a -2.55e-246)
     (* z (* x y))
     (if (<= a 6e-93) (* t (* b 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 (a <= -1.7e+110) {
		tmp = a * (c * j);
	} else if (a <= -2.55e-246) {
		tmp = z * (x * y);
	} else if (a <= 6e-93) {
		tmp = t * (b * 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 (a <= (-1.7d+110)) then
        tmp = a * (c * j)
    else if (a <= (-2.55d-246)) then
        tmp = z * (x * y)
    else if (a <= 6d-93) then
        tmp = t * (b * 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 (a <= -1.7e+110) {
		tmp = a * (c * j);
	} else if (a <= -2.55e-246) {
		tmp = z * (x * y);
	} else if (a <= 6e-93) {
		tmp = t * (b * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.7e+110:
		tmp = a * (c * j)
	elif a <= -2.55e-246:
		tmp = z * (x * y)
	elif a <= 6e-93:
		tmp = t * (b * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.7e+110)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -2.55e-246)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 6e-93)
		tmp = Float64(t * Float64(b * 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 (a <= -1.7e+110)
		tmp = a * (c * j);
	elseif (a <= -2.55e-246)
		tmp = z * (x * y);
	elseif (a <= 6e-93)
		tmp = t * (b * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.7e+110], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-246], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-93], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7000000000000001e110

   1. Initial program 72.4%

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

   3. Taylor expanded in a around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in c around inf 59.5%

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

   if -1.7000000000000001e110 < a < -2.54999999999999984e-246

   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 z around inf 58.8%

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

   4. Taylor expanded in x around inf 40.9%

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

   if -2.54999999999999984e-246 < a < 6.0000000000000003e-93

   1. Initial program 80.4%

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

   3. Taylor expanded in i around -inf 48.6%

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

   4. Taylor expanded in j around 0 38.9%

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

      1. associate-*r* 41.9%

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

   6. Simplified 41.9%

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

   if 6.0000000000000003e-93 < a

   1. Initial program 74.1%

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

   3. Taylor expanded in j around inf 58.2%

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

   4. Taylor expanded in a around inf 41.1%

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

      1. *-commutative 41.1%

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

   6. Simplified 41.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -2e+142)
     t_1
     (if (<= c 1.95e-218)
       (* z (* x y))
       (if (<= c 7.4e-51) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -2e+142) {
		tmp = t_1;
	} else if (c <= 1.95e-218) {
		tmp = z * (x * y);
	} else if (c <= 7.4e-51) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (c <= (-2d+142)) then
        tmp = t_1
    else if (c <= 1.95d-218) then
        tmp = z * (x * y)
    else if (c <= 7.4d-51) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -2e+142) {
		tmp = t_1;
	} else if (c <= 1.95e-218) {
		tmp = z * (x * y);
	} else if (c <= 7.4e-51) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -2e+142:
		tmp = t_1
	elif c <= 1.95e-218:
		tmp = z * (x * y)
	elif c <= 7.4e-51:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -2e+142)
		tmp = t_1;
	elseif (c <= 1.95e-218)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 7.4e-51)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (c <= -2e+142)
		tmp = t_1;
	elseif (c <= 1.95e-218)
		tmp = z * (x * y);
	elseif (c <= 7.4e-51)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+142], t$95$1, If[LessEqual[c, 1.95e-218], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.4e-51], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.0000000000000001e142 or 7.39999999999999946e-51 < c

   1. Initial program 69.3%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in c around inf 51.6%

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

   if -2.0000000000000001e142 < c < 1.95e-218

   1. Initial program 81.5%

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

   3. Taylor expanded in z around inf 46.4%

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

   4. Taylor expanded in x around inf 39.1%

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

   if 1.95e-218 < c < 7.39999999999999946e-51

   1. Initial program 94.7%

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

   3. Taylor expanded in i around -inf 54.5%

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

   4. Taylor expanded in j around 0 34.3%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -6.2e+111)
   (* a (* c j))
   (if (<= a 7.2e-228)
     (* x (* y z))
     (if (<= a 4.4e-102) (* 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 (a <= -6.2e+111) {
		tmp = a * (c * j);
	} else if (a <= 7.2e-228) {
		tmp = x * (y * z);
	} else if (a <= 4.4e-102) {
		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 (a <= (-6.2d+111)) then
        tmp = a * (c * j)
    else if (a <= 7.2d-228) then
        tmp = x * (y * z)
    else if (a <= 4.4d-102) 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 (a <= -6.2e+111) {
		tmp = a * (c * j);
	} else if (a <= 7.2e-228) {
		tmp = x * (y * z);
	} else if (a <= 4.4e-102) {
		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 a <= -6.2e+111:
		tmp = a * (c * j)
	elif a <= 7.2e-228:
		tmp = x * (y * z)
	elif a <= 4.4e-102:
		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 (a <= -6.2e+111)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= 7.2e-228)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 4.4e-102)
		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 (a <= -6.2e+111)
		tmp = a * (c * j);
	elseif (a <= 7.2e-228)
		tmp = x * (y * z);
	elseif (a <= 4.4e-102)
		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[LessEqual[a, -6.2e+111], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-228], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-102], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.2000000000000001e111

   1. Initial program 72.4%

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

   3. Taylor expanded in a around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in c around inf 59.5%

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

   if -6.2000000000000001e111 < a < 7.2000000000000004e-228

   1. Initial program 85.6%

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

   3. Taylor expanded in j around 0 69.2%

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

      1. *-commutative 69.2%

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

      2. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in b around inf 68.4%

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

   7. Taylor expanded in y around inf 37.1%

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

   if 7.2000000000000004e-228 < a < 4.40000000000000026e-102

   1. Initial program 74.1%

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

   3. Taylor expanded in i around -inf 48.4%

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

   4. Taylor expanded in j around 0 48.0%

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

   if 4.40000000000000026e-102 < a

   1. Initial program 74.1%

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

   3. Taylor expanded in j around inf 58.2%

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

   4. Taylor expanded in a around inf 41.1%

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

      1. *-commutative 41.1%

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

   6. Simplified 41.1%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+61} \lor \neg \left(j \leq 0.85\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.2e+61) (not (<= j 0.85)))
   (* j (- (* a c) (* y i)))
   (* 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 ((j <= -6.2e+61) || !(j <= 0.85)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = 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 ((j <= (-6.2d+61)) .or. (.not. (j <= 0.85d0))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = 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 ((j <= -6.2e+61) || !(j <= 0.85)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.2e+61) or not (j <= 0.85):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.2e+61) || !(j <= 0.85))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = 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 ((j <= -6.2e+61) || ~((j <= 0.85)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.2e+61], N[Not[LessEqual[j, 0.85]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.1999999999999998e61 or 0.849999999999999978 < j

   1. Initial program 80.2%

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

   3. Taylor expanded in j around inf 72.5%

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

   if -6.1999999999999998e61 < j < 0.849999999999999978

   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 b around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. *-commutative 47.8%

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

   5. Simplified 47.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+61} \lor \neg \left(j \leq 0.85\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+55} \lor \neg \left(j \leq 0.017\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3.6e+55) (not (<= j 0.017))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3.6e+55) || !(j <= 0.017)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-3.6d+55)) .or. (.not. (j <= 0.017d0))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3.6e+55) || !(j <= 0.017)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -3.6e+55) or not (j <= 0.017):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -3.6e+55) || !(j <= 0.017))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -3.6e+55) || ~((j <= 0.017)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -3.6e+55], N[Not[LessEqual[j, 0.017]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.59999999999999987e55 or 0.017000000000000001 < j

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in c around inf 50.1%

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

   if -3.59999999999999987e55 < j < 0.017000000000000001

   1. Initial program 76.1%

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

   3. Taylor expanded in i around -inf 34.7%

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

   4. Taylor expanded in j around 0 28.5%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+55} \lor \neg \left(j \leq 0.017\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.0054:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.9e+55)
   (* j (* a c))
   (if (<= j 0.0054) (* 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 (j <= -2.9e+55) {
		tmp = j * (a * c);
	} else if (j <= 0.0054) {
		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 (j <= (-2.9d+55)) then
        tmp = j * (a * c)
    else if (j <= 0.0054d0) 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 (j <= -2.9e+55) {
		tmp = j * (a * c);
	} else if (j <= 0.0054) {
		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 j <= -2.9e+55:
		tmp = j * (a * c)
	elif j <= 0.0054:
		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 (j <= -2.9e+55)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 0.0054)
		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 (j <= -2.9e+55)
		tmp = j * (a * c);
	elseif (j <= 0.0054)
		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[LessEqual[j, -2.9e+55], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.0054], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.8999999999999999e55

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 67.1%

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

   4. Taylor expanded in a around inf 53.6%

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

      1. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   if -2.8999999999999999e55 < j < 0.0054000000000000003

   1. Initial program 76.1%

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

   3. Taylor expanded in i around -inf 34.7%

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

   4. Taylor expanded in j around 0 28.5%

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

   if 0.0054000000000000003 < j

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in c around inf 48.4%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.0054:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.9% 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 78.4%

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

3. Taylor expanded in a around inf 41.3%

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

   1. +-commutative 41.3%

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

   2. mul-1-neg 41.3%

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

   3. unsub-neg 41.3%

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

   4. *-commutative 41.3%

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

5. Simplified 41.3%

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

6. Taylor expanded in c around inf 29.0%

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

Developer Target 1: 59.7% 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 2024135 
(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)))))