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

Percentage Accurate: 74.2% → 82.6%

Time: 20.1s

Alternatives: 26

Speedup: 0.5×

• 58.1% 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: 74.2% 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: 82.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (-
          (* j (- (* a c) (* y i)))
          (- (* x (- (* t a) (* y z))) (* b (- (* t i) (* z c)))))))
   (if (<= t_1 INFINITY) t_1 (* c (- (* a j) (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (b * ((t * i) - (z * c))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) - Float64(b * Float64(Float64(t * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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))) - ((x * ((t * a) - (y * z))) - (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $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 90.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 50.4%

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

4. Final simplification 83.7%

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

Alternative 2: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(x \cdot \frac{y \cdot z}{j} - y \cdot i\right)\\ \mathbf{elif}\;a \leq 0.0033:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (* y z)) (* b (- (* t i) (* z c))))))
   (if (<= a -2.3e+63)
     (* a (* x (- (* c (/ j x)) t)))
     (if (<= a -1.32e-246)
       t_1
       (if (<= a -6.8e-291)
         (* j (- (* x (/ (* y z) j)) (* y i)))
         (if (<= a 0.0033) 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)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= -2.3e+63) {
		tmp = a * (x * ((c * (j / x)) - t));
	} else if (a <= -1.32e-246) {
		tmp = t_1;
	} else if (a <= -6.8e-291) {
		tmp = j * ((x * ((y * z) / j)) - (y * i));
	} else if (a <= 0.0033) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)))
    if (a <= (-2.3d+63)) then
        tmp = a * (x * ((c * (j / x)) - t))
    else if (a <= (-1.32d-246)) then
        tmp = t_1
    else if (a <= (-6.8d-291)) then
        tmp = j * ((x * ((y * z) / j)) - (y * i))
    else if (a <= 0.0033d0) then
        tmp = t_1
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= -2.3e+63) {
		tmp = a * (x * ((c * (j / x)) - t));
	} else if (a <= -1.32e-246) {
		tmp = t_1;
	} else if (a <= -6.8e-291) {
		tmp = j * ((x * ((y * z) / j)) - (y * i));
	} else if (a <= 0.0033) {
		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)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if a <= -2.3e+63:
		tmp = a * (x * ((c * (j / x)) - t))
	elif a <= -1.32e-246:
		tmp = t_1
	elif a <= -6.8e-291:
		tmp = j * ((x * ((y * z) / j)) - (y * i))
	elif a <= 0.0033:
		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(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= -2.3e+63)
		tmp = Float64(a * Float64(x * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (a <= -1.32e-246)
		tmp = t_1;
	elseif (a <= -6.8e-291)
		tmp = Float64(j * Float64(Float64(x * Float64(Float64(y * z) / j)) - Float64(y * i)));
	elseif (a <= 0.0033)
		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)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (a <= -2.3e+63)
		tmp = a * (x * ((c * (j / x)) - t));
	elseif (a <= -1.32e-246)
		tmp = t_1;
	elseif (a <= -6.8e-291)
		tmp = j * ((x * ((y * z) / j)) - (y * i));
	elseif (a <= 0.0033)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+63], N[(a * N[(x * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.32e-246], t$95$1, If[LessEqual[a, -6.8e-291], N[(j * N[(N[(x * N[(N[(y * z), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0033], t$95$1, N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.29999999999999993e63

   1. Initial program 58.8%

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

   3. Taylor expanded in a around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in x around inf 65.9%

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

      1. associate-/l* 68.2%

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

   8. Simplified 68.2%

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

   if -2.29999999999999993e63 < a < -1.31999999999999989e-246 or -6.80000000000000053e-291 < a < 0.0033

   1. Initial program 83.0%

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

   3. Taylor expanded in j around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. *-commutative 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in a around 0 60.8%

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

   if -1.31999999999999989e-246 < a < -6.80000000000000053e-291

   1. Initial program 81.2%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

      4. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in j around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. unsub-neg 83.5%

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

      4. associate-/l* 83.5%

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

   8. Simplified 83.5%

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

   if 0.0033 < a

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf 66.9%

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

      1. +-commutative 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

   5. Simplified 66.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(x \cdot \frac{y \cdot z}{j} - y \cdot i\right)\\ \mathbf{elif}\;a \leq 0.0033:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -1.15 \cdot 10^{+63}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+152}:\\ \;\;\;\;t\_1 - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= i -1.15e+63)
     (+ t_1 (* b (- (* t i) (* z c))))
     (if (<= i 2.3e+152)
       (- t_1 (+ (* z (* b c)) (* x (- (* t a) (* y z)))))
       (* i (- (* t b) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -1.15e+63) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (i <= 2.3e+152) {
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	} else {
		tmp = i * ((t * b) - (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) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (i <= (-1.15d+63)) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (i <= 2.3d+152) then
        tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))))
    else
        tmp = i * ((t * b) - (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 t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -1.15e+63) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (i <= 2.3e+152) {
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if i <= -1.15e+63:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif i <= 2.3e+152:
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))))
	else:
		tmp = i * ((t * b) - (y * j))
	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 (i <= -1.15e+63)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (i <= 2.3e+152)
		tmp = Float64(t_1 - Float64(Float64(z * Float64(b * c)) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	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 (i <= -1.15e+63)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (i <= 2.3e+152)
		tmp = t_1 - ((z * (b * c)) + (x * ((t * a) - (y * z))));
	else
		tmp = i * ((t * b) - (y * j));
	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[i, -1.15e+63], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e+152], 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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.14999999999999997e63

   1. Initial program 65.7%

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

   3. Taylor expanded in x around 0 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   if -1.14999999999999997e63 < i < 2.29999999999999985e152

   1. Initial program 80.1%

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

   3. Taylor expanded in c around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-*l* 76.8%

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

      4. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if 2.29999999999999985e152 < i

   1. Initial program 57.4%

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

   3. Taylor expanded in i around inf 83.2%

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

      1. distribute-lft-out-- 83.2%

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

      2. *-commutative 83.2%

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

   5. Simplified 83.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - t \cdot b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.15 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(z \cdot \left(b \cdot c\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-295}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;t \leq 10^{+16}:\\ \;\;\;\;t\_2 + t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_3 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= t -1.2e+103)
     (* t (- (* b i) (* x a)))
     (if (<= t -2.3e-295)
       (+ t_2 t_1)
       (if (<= t 1e+16) (+ t_2 t_3) (+ t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -1.2e+103) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -2.3e-295) {
		tmp = t_2 + t_1;
	} else if (t <= 1e+16) {
		tmp = t_2 + t_3;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (t <= (-1.2d+103)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= (-2.3d-295)) then
        tmp = t_2 + t_1
    else if (t <= 1d+16) then
        tmp = t_2 + t_3
    else
        tmp = t_3 + 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 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -1.2e+103) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -2.3e-295) {
		tmp = t_2 + t_1;
	} else if (t <= 1e+16) {
		tmp = t_2 + t_3;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if t <= -1.2e+103:
		tmp = t * ((b * i) - (x * a))
	elif t <= -2.3e-295:
		tmp = t_2 + t_1
	elif t <= 1e+16:
		tmp = t_2 + t_3
	else:
		tmp = t_3 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (t <= -1.2e+103)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= -2.3e-295)
		tmp = Float64(t_2 + t_1);
	elseif (t <= 1e+16)
		tmp = Float64(t_2 + t_3);
	else
		tmp = Float64(t_3 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (t <= -1.2e+103)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= -2.3e-295)
		tmp = t_2 + t_1;
	elseif (t <= 1e+16)
		tmp = t_2 + t_3;
	else
		tmp = t_3 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+103], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e-295], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[t, 1e+16], N[(t$95$2 + t$95$3), $MachinePrecision], N[(t$95$3 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1999999999999999e103

   1. Initial program 59.4%

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

   3. Taylor expanded in t around inf 79.2%

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

      1. distribute-lft-out-- 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in t around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. *-commutative 79.2%

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

      3. distribute-rgt-neg-out 79.2%

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

      4. neg-mul-1 79.2%

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

      5. *-commutative 79.2%

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

      6. distribute-lft-out-- 79.2%

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

      7. mul-1-neg 79.2%

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

      8. distribute-lft-neg-out 79.2%

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

      9. cancel-sign-sub 79.2%

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

      10. +-commutative 79.2%

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

      11. *-commutative 79.2%

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

      12. mul-1-neg 79.2%

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

      13. unsub-neg 79.2%

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

   8. Simplified 79.2%

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

   if -1.1999999999999999e103 < t < -2.3e-295

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if -2.3e-295 < t < 1e16

   1. Initial program 95.8%

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

   3. Taylor expanded in b around 0 85.8%

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

   if 1e16 < t

   1. Initial program 67.8%

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

   3. Taylor expanded in j around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. *-commutative 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 10^{+16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -5.8e+116)
     t_1
     (if (<= y -8e-137)
       (* t (- (* b i) (* x a)))
       (if (<= y 1.95e-134)
         (* c (- (* a j) (* z b)))
         (if (<= y 3.2e+27) (* a (- (* c j) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.8e+116) {
		tmp = t_1;
	} else if (y <= -8e-137) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.95e-134) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 3.2e+27) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-5.8d+116)) then
        tmp = t_1
    else if (y <= (-8d-137)) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1.95d-134) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 3.2d+27) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.8e+116) {
		tmp = t_1;
	} else if (y <= -8e-137) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.95e-134) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 3.2e+27) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5.8e+116:
		tmp = t_1
	elif y <= -8e-137:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1.95e-134:
		tmp = c * ((a * j) - (z * b))
	elif y <= 3.2e+27:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.8e+116)
		tmp = t_1;
	elseif (y <= -8e-137)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1.95e-134)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 3.2e+27)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5.8e+116)
		tmp = t_1;
	elseif (y <= -8e-137)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1.95e-134)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 3.2e+27)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+116], t$95$1, If[LessEqual[y, -8e-137], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-134], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+27], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8000000000000003e116 or 3.20000000000000015e27 < y

   1. Initial program 71.7%

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

   3. Taylor expanded in y around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -5.8000000000000003e116 < y < -7.99999999999999982e-137

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf 59.4%

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

      1. distribute-lft-out-- 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0 59.4%

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

      1. mul-1-neg 59.4%

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

      2. *-commutative 59.4%

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

      3. distribute-rgt-neg-out 59.4%

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

      4. neg-mul-1 59.4%

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

      5. *-commutative 59.4%

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

      6. distribute-lft-out-- 59.4%

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

      7. mul-1-neg 59.4%

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

      8. distribute-lft-neg-out 59.4%

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

      9. cancel-sign-sub 59.4%

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

      10. +-commutative 59.4%

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

      11. *-commutative 59.4%

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

      12. mul-1-neg 59.4%

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

      13. unsub-neg 59.4%

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

   8. Simplified 59.4%

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

   if -7.99999999999999982e-137 < y < 1.95e-134

   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 c around inf 50.1%

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

   if 1.95e-134 < y < 3.20000000000000015e27

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.75 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -9.2e+61)
     t_1
     (if (<= a -3.75e-47)
       (* x (* y z))
       (if (<= a -3.8e-207)
         (* t (* b i))
         (if (<= a 3.5e-187) (* y (* i (- j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9.2e+61) {
		tmp = t_1;
	} else if (a <= -3.75e-47) {
		tmp = x * (y * z);
	} else if (a <= -3.8e-207) {
		tmp = t * (b * i);
	} else if (a <= 3.5e-187) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-9.2d+61)) then
        tmp = t_1
    else if (a <= (-3.75d-47)) then
        tmp = x * (y * z)
    else if (a <= (-3.8d-207)) then
        tmp = t * (b * i)
    else if (a <= 3.5d-187) then
        tmp = y * (i * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9.2e+61) {
		tmp = t_1;
	} else if (a <= -3.75e-47) {
		tmp = x * (y * z);
	} else if (a <= -3.8e-207) {
		tmp = t * (b * i);
	} else if (a <= 3.5e-187) {
		tmp = y * (i * -j);
	} 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 <= -9.2e+61:
		tmp = t_1
	elif a <= -3.75e-47:
		tmp = x * (y * z)
	elif a <= -3.8e-207:
		tmp = t * (b * i)
	elif a <= 3.5e-187:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9.2e+61)
		tmp = t_1;
	elseif (a <= -3.75e-47)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -3.8e-207)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 3.5e-187)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -9.2e+61)
		tmp = t_1;
	elseif (a <= -3.75e-47)
		tmp = x * (y * z);
	elseif (a <= -3.8e-207)
		tmp = t * (b * i);
	elseif (a <= 3.5e-187)
		tmp = y * (i * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+61], t$95$1, If[LessEqual[a, -3.75e-47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-207], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-187], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.1999999999999998e61 or 3.49999999999999979e-187 < a

   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 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   if -9.1999999999999998e61 < a < -3.74999999999999984e-47

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

      4. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in z around inf 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   if -3.74999999999999984e-47 < a < -3.8e-207

   1. Initial program 80.9%

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

   3. Taylor expanded in t around inf 58.4%

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

      1. distribute-lft-out-- 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in a around 0 50.8%

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

      1. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if -3.8e-207 < a < 3.49999999999999979e-187

   1. Initial program 86.7%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around 0 37.5%

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

      1. mul-1-neg 37.5%

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

      2. distribute-lft-neg-out 37.5%

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

      3. *-commutative 37.5%

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

   8. Simplified 37.5%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.75 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+65} \lor \neg \left(i \leq 2.8 \cdot 10^{+142}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -8.6e+65) (not (<= i 2.8e+142)))
   (* i (- (* t b) (* y j)))
   (+ (* j (- (* a c) (* y 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 ((i <= -8.6e+65) || !(i <= 2.8e+142)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (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 ((i <= (-8.6d+65)) .or. (.not. (i <= 2.8d+142))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (j * ((a * c) - (y * i))) + (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 ((i <= -8.6e+65) || !(i <= 2.8e+142)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -8.6e+65) or not (i <= 2.8e+142):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -8.6e+65) || !(i <= 2.8e+142))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + 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 ((i <= -8.6e+65) || ~((i <= 2.8e+142)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -8.6e+65], N[Not[LessEqual[i, 2.8e+142]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -8.60000000000000091e65 or 2.8e142 < i

   1. Initial program 60.4%

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

   3. Taylor expanded in i around inf 74.8%

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

      1. distribute-lft-out-- 74.8%

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

      2. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -8.60000000000000091e65 < i < 2.8e142

   1. Initial program 81.1%

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

   3. Taylor expanded in b around 0 71.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+65} \lor \neg \left(i \leq 2.8 \cdot 10^{+142}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+141}:\\ \;\;\;\;t\_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= b -8.5e+94)
     (+ (* x (* y z)) t_1)
     (if (<= b 1.42e+141) (+ t_2 (* x (- (* y z) (* t a)))) (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -8.5e+94) {
		tmp = (x * (y * z)) + t_1;
	} else if (b <= 1.42e+141) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (b <= (-8.5d+94)) then
        tmp = (x * (y * z)) + t_1
    else if (b <= 1.42d+141) then
        tmp = t_2 + (x * ((y * z) - (t * a)))
    else
        tmp = t_2 + 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 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -8.5e+94) {
		tmp = (x * (y * z)) + t_1;
	} else if (b <= 1.42e+141) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if b <= -8.5e+94:
		tmp = (x * (y * z)) + t_1
	elif b <= 1.42e+141:
		tmp = t_2 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -8.5e+94)
		tmp = Float64(Float64(x * Float64(y * z)) + t_1);
	elseif (b <= 1.42e+141)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (b <= -8.5e+94)
		tmp = (x * (y * z)) + t_1;
	elseif (b <= 1.42e+141)
		tmp = t_2 + (x * ((y * z) - (t * a)));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+94], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 1.42e+141], N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.50000000000000054e94

   1. Initial program 64.1%

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

   3. Taylor expanded in j around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in a around 0 72.5%

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

   if -8.50000000000000054e94 < b < 1.42000000000000005e141

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0 71.6%

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

   if 1.42000000000000005e141 < b

   1. Initial program 68.4%

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

   3. Taylor expanded in x around 0 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+228}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -9.8e+42)
   (* x (* y z))
   (if (<= y -2.05e-156)
     (* i (* t b))
     (if (<= y 6e-9)
       (* c (* a j))
       (if (<= y 3e+228) (* (* y j) (- i)) (* y (* x z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9.8e+42) {
		tmp = x * (y * z);
	} else if (y <= -2.05e-156) {
		tmp = i * (t * b);
	} else if (y <= 6e-9) {
		tmp = c * (a * j);
	} else if (y <= 3e+228) {
		tmp = (y * j) * -i;
	} else {
		tmp = y * (x * z);
	}
	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 (y <= (-9.8d+42)) then
        tmp = x * (y * z)
    else if (y <= (-2.05d-156)) then
        tmp = i * (t * b)
    else if (y <= 6d-9) then
        tmp = c * (a * j)
    else if (y <= 3d+228) then
        tmp = (y * j) * -i
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9.8e+42) {
		tmp = x * (y * z);
	} else if (y <= -2.05e-156) {
		tmp = i * (t * b);
	} else if (y <= 6e-9) {
		tmp = c * (a * j);
	} else if (y <= 3e+228) {
		tmp = (y * j) * -i;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -9.8e+42:
		tmp = x * (y * z)
	elif y <= -2.05e-156:
		tmp = i * (t * b)
	elif y <= 6e-9:
		tmp = c * (a * j)
	elif y <= 3e+228:
		tmp = (y * j) * -i
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -9.8e+42)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -2.05e-156)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 6e-9)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 3e+228)
		tmp = Float64(Float64(y * j) * Float64(-i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -9.8e+42)
		tmp = x * (y * z);
	elseif (y <= -2.05e-156)
		tmp = i * (t * b);
	elseif (y <= 6e-9)
		tmp = c * (a * j);
	elseif (y <= 3e+228)
		tmp = (y * j) * -i;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -9.8e+42], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-156], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-9], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+228], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.8000000000000004e42

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 61.3%

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

      1. +-commutative 61.3%

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

      2. mul-1-neg 61.3%

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

      3. unsub-neg 61.3%

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

      4. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in z around inf 38.5%

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

      1. *-commutative 38.5%

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

   8. Simplified 38.5%

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

   if -9.8000000000000004e42 < y < -2.0500000000000001e-156

   1. Initial program 84.2%

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

   3. Taylor expanded in i around inf 58.7%

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

      1. distribute-lft-out-- 58.7%

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

      2. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in j around 0 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if -2.0500000000000001e-156 < y < 5.99999999999999996e-9

   1. Initial program 74.5%

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

   3. Taylor expanded in a around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in c around inf 32.2%

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

      1. *-commutative 32.2%

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

   8. Simplified 32.2%

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

   9. Taylor expanded in a around 0 32.2%

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

       1. *-commutative 32.2%

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

       2. associate-*l* 35.4%

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

       3. *-commutative 35.4%

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

   11. Simplified 35.4%

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

   if 5.99999999999999996e-9 < y < 3.0000000000000001e228

   1. Initial program 78.5%

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

   3. Taylor expanded in i around inf 48.1%

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

      1. distribute-lft-out-- 48.1%

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

      2. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in j around inf 41.9%

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

      1. associate-*r* 41.9%

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

      2. mul-1-neg 41.9%

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

   8. Simplified 41.9%

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

   if 3.0000000000000001e228 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

      4. *-commutative 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in z around inf 60.5%

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

      1. *-commutative 60.5%

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

   8. Simplified 60.5%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+228}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.06 \cdot 10^{+66} \lor \neg \left(i \leq 4.7 \cdot 10^{-23}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.06e+66) (not (<= i 4.7e-23)))
   (* i (- (* t b) (* y j)))
   (- (* x (- (* y z) (* t a))) (* z (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.06e+66) || !(i <= 4.7e-23)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.06d+66)) .or. (.not. (i <= 4.7d-23))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.06e+66) || !(i <= 4.7e-23)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.06e+66) or not (i <= 4.7e-23):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.06e+66) || !(i <= 4.7e-23))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.06e+66) || ~((i <= 4.7e-23)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.06e+66], N[Not[LessEqual[i, 4.7e-23]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.06000000000000004e66 or 4.7000000000000001e-23 < i

   1. Initial program 70.6%

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

   3. Taylor expanded in i around inf 70.1%

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

      1. distribute-lft-out-- 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -1.06000000000000004e66 < i < 4.7000000000000001e-23

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in i around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

   8. Simplified 62.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.06 \cdot 10^{+66} \lor \neg \left(i \leq 4.7 \cdot 10^{-23}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+63} \lor \neg \left(i \leq 1.9 \cdot 10^{-22}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -4.4e+63) (not (<= i 1.9e-22)))
   (* i (- (* t b) (* y j)))
   (- (* x (- (* y z) (* t a))) (* b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.4e+63) || !(i <= 1.9e-22)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-4.4d+63)) .or. (.not. (i <= 1.9d-22))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.4e+63) || !(i <= 1.9e-22)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -4.4e+63) or not (i <= 1.9e-22):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -4.4e+63) || !(i <= 1.9e-22))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * 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 ((i <= -4.4e+63) || ~((i <= 1.9e-22)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -4.4e+63], N[Not[LessEqual[i, 1.9e-22]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.3999999999999997e63 or 1.90000000000000012e-22 < i

   1. Initial program 70.6%

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

   3. Taylor expanded in i around inf 70.1%

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

      1. distribute-lft-out-- 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -4.3999999999999997e63 < i < 1.90000000000000012e-22

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in i around 0 60.8%

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

      1. *-commutative 60.8%

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

   8. Simplified 60.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+63} \lor \neg \left(i \leq 1.9 \cdot 10^{-22}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.32 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -4e+62)
     t_1
     (if (<= i 2.32e-231)
       (* x (- (* y z) (* t a)))
       (if (<= i 1.3e-26) (* c (- (* a j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4e+62) {
		tmp = t_1;
	} else if (i <= 2.32e-231) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.3e-26) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-4d+62)) then
        tmp = t_1
    else if (i <= 2.32d-231) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 1.3d-26) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4e+62) {
		tmp = t_1;
	} else if (i <= 2.32e-231) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.3e-26) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4e+62:
		tmp = t_1
	elif i <= 2.32e-231:
		tmp = x * ((y * z) - (t * a))
	elif i <= 1.3e-26:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4e+62)
		tmp = t_1;
	elseif (i <= 2.32e-231)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 1.3e-26)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4e+62)
		tmp = t_1;
	elseif (i <= 2.32e-231)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 1.3e-26)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+62], t$95$1, If[LessEqual[i, 2.32e-231], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-26], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.00000000000000014e62 or 1.30000000000000005e-26 < i

   1. Initial program 70.6%

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

   3. Taylor expanded in i around inf 70.1%

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

      1. distribute-lft-out-- 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -4.00000000000000014e62 < i < 2.3199999999999999e-231

   1. Initial program 78.8%

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

   3. Taylor expanded in j around 0 64.2%

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

      1. *-commutative 64.2%

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

      2. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in i around 0 64.9%

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

      1. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in x around inf 58.2%

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

   if 2.3199999999999999e-231 < i < 1.30000000000000005e-26

   1. Initial program 80.1%

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

   3. Taylor expanded in c around inf 56.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+62}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.32 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6400000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-248}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -6400000000000.0)
     t_1
     (if (<= a 1e-248)
       (* b (- (* t i) (* z c)))
       (if (<= a 4.3e-180) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6400000000000.0) {
		tmp = t_1;
	} else if (a <= 1e-248) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.3e-180) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-6400000000000.0d0)) then
        tmp = t_1
    else if (a <= 1d-248) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 4.3d-180) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6400000000000.0) {
		tmp = t_1;
	} else if (a <= 1e-248) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.3e-180) {
		tmp = x * (y * z);
	} 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 <= -6400000000000.0:
		tmp = t_1
	elif a <= 1e-248:
		tmp = b * ((t * i) - (z * c))
	elif a <= 4.3e-180:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6400000000000.0)
		tmp = t_1;
	elseif (a <= 1e-248)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 4.3e-180)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6400000000000.0)
		tmp = t_1;
	elseif (a <= 1e-248)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 4.3e-180)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6400000000000.0], t$95$1, If[LessEqual[a, 1e-248], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-180], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.4e12 or 4.2999999999999996e-180 < a

   1. Initial program 71.0%

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

   3. Taylor expanded in a around inf 57.3%

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

      1. +-commutative 57.3%

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

      2. mul-1-neg 57.3%

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

      3. unsub-neg 57.3%

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

   5. Simplified 57.3%

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

   if -6.4e12 < a < 9.9999999999999998e-249

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 48.3%

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

      1. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   if 9.9999999999999998e-249 < a < 4.2999999999999996e-180

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. +-commutative 66.2%

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

      2. mul-1-neg 66.2%

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

      3. unsub-neg 66.2%

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

      4. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in z around inf 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6400000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 10^{-248}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-304}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))))
   (if (<= t -7.5e+100)
     t_1
     (if (<= t -2.7e-304)
       (* (* y j) (- i))
       (if (<= t 1.26e+104) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (t <= -7.5e+100) {
		tmp = t_1;
	} else if (t <= -2.7e-304) {
		tmp = (y * j) * -i;
	} else if (t <= 1.26e+104) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x * -a)
    if (t <= (-7.5d+100)) then
        tmp = t_1
    else if (t <= (-2.7d-304)) then
        tmp = (y * j) * -i
    else if (t <= 1.26d+104) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (t <= -7.5e+100) {
		tmp = t_1;
	} else if (t <= -2.7e-304) {
		tmp = (y * j) * -i;
	} else if (t <= 1.26e+104) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	tmp = 0
	if t <= -7.5e+100:
		tmp = t_1
	elif t <= -2.7e-304:
		tmp = (y * j) * -i
	elif t <= 1.26e+104:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (t <= -7.5e+100)
		tmp = t_1;
	elseif (t <= -2.7e-304)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (t <= 1.26e+104)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * -a);
	tmp = 0.0;
	if (t <= -7.5e+100)
		tmp = t_1;
	elseif (t <= -2.7e-304)
		tmp = (y * j) * -i;
	elseif (t <= 1.26e+104)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+100], t$95$1, If[LessEqual[t, -2.7e-304], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[t, 1.26e+104], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999983e100 or 1.25999999999999994e104 < t

   1. Initial program 63.9%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. distribute-lft-out-- 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in a around inf 49.8%

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

      1. associate-*r* 49.8%

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

      2. neg-mul-1 49.8%

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

   8. Simplified 49.8%

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

   if -7.49999999999999983e100 < t < -2.7000000000000001e-304

   1. Initial program 72.3%

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

   3. Taylor expanded in i around inf 44.7%

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

      1. distribute-lft-out-- 44.7%

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

      2. *-commutative 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in j around inf 36.5%

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

      1. associate-*r* 36.5%

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

      2. mul-1-neg 36.5%

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

   8. Simplified 36.5%

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

   if -2.7000000000000001e-304 < t < 1.25999999999999994e104

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

      4. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in z around inf 35.0%

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

      1. *-commutative 35.0%

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

   8. Simplified 35.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-304}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.9e+43)
   (* x (* y z))
   (if (<= y -3e-156)
     (* i (* t b))
     (if (<= y 6e+27) (* c (* a j)) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.9e+43) {
		tmp = x * (y * z);
	} else if (y <= -3e-156) {
		tmp = i * (t * b);
	} else if (y <= 6e+27) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	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 (y <= (-3.9d+43)) then
        tmp = x * (y * z)
    else if (y <= (-3d-156)) then
        tmp = i * (t * b)
    else if (y <= 6d+27) then
        tmp = c * (a * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.9e+43) {
		tmp = x * (y * z);
	} else if (y <= -3e-156) {
		tmp = i * (t * b);
	} else if (y <= 6e+27) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.9e+43:
		tmp = x * (y * z)
	elif y <= -3e-156:
		tmp = i * (t * b)
	elif y <= 6e+27:
		tmp = c * (a * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.9e+43)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3e-156)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 6e+27)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.9e+43)
		tmp = x * (y * z);
	elseif (y <= -3e-156)
		tmp = i * (t * b);
	elseif (y <= 6e+27)
		tmp = c * (a * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.9e+43], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-156], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+27], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.9000000000000001e43

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 61.3%

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

      1. +-commutative 61.3%

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

      2. mul-1-neg 61.3%

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

      3. unsub-neg 61.3%

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

      4. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in z around inf 38.5%

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

      1. *-commutative 38.5%

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

   8. Simplified 38.5%

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

   if -3.9000000000000001e43 < y < -3e-156

   1. Initial program 84.2%

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

   3. Taylor expanded in i around inf 58.7%

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

      1. distribute-lft-out-- 58.7%

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

      2. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in j around 0 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if -3e-156 < y < 5.99999999999999953e27

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in c around inf 30.9%

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

      1. *-commutative 30.9%

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

   8. Simplified 30.9%

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

   9. Taylor expanded in a around 0 30.9%

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

       1. *-commutative 30.9%

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

       2. associate-*l* 32.9%

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

       3. *-commutative 32.9%

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

   11. Simplified 32.9%

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

   if 5.99999999999999953e27 < y

   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 y around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in z around inf 31.4%

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

      1. *-commutative 31.4%

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

   8. Simplified 31.4%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -8.5e+42)
   (* b (* t i))
   (if (<= i -2.1e-262)
     (* y (* x z))
     (if (<= i 1.22e+17) (* c (* a j)) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -8.5e+42) {
		tmp = b * (t * i);
	} else if (i <= -2.1e-262) {
		tmp = y * (x * z);
	} else if (i <= 1.22e+17) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-8.5d+42)) then
        tmp = b * (t * i)
    else if (i <= (-2.1d-262)) then
        tmp = y * (x * z)
    else if (i <= 1.22d+17) then
        tmp = c * (a * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -8.5e+42) {
		tmp = b * (t * i);
	} else if (i <= -2.1e-262) {
		tmp = y * (x * z);
	} else if (i <= 1.22e+17) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -8.5e+42:
		tmp = b * (t * i)
	elif i <= -2.1e-262:
		tmp = y * (x * z)
	elif i <= 1.22e+17:
		tmp = c * (a * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -8.5e+42)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= -2.1e-262)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.22e+17)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -8.5e+42)
		tmp = b * (t * i);
	elseif (i <= -2.1e-262)
		tmp = y * (x * z);
	elseif (i <= 1.22e+17)
		tmp = c * (a * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -8.5e+42], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.1e-262], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.22e+17], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.5000000000000003e42

   1. Initial program 65.8%

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

   3. Taylor expanded in t around inf 49.8%

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

      1. distribute-lft-out-- 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in a around 0 45.7%

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

   if -8.5000000000000003e42 < i < -2.1e-262

   1. Initial program 79.6%

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

   3. Taylor expanded in y around inf 40.7%

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

      1. +-commutative 40.7%

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

      2. mul-1-neg 40.7%

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

      3. unsub-neg 40.7%

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

      4. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in z around inf 28.0%

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

      1. *-commutative 28.0%

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

   8. Simplified 28.0%

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

   if -2.1e-262 < i < 1.22e17

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in c around inf 32.5%

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

      1. *-commutative 32.5%

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

   8. Simplified 32.5%

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

   9. Taylor expanded in a around 0 32.5%

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

       1. *-commutative 32.5%

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

       2. associate-*l* 33.8%

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

       3. *-commutative 33.8%

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

   11. Simplified 33.8%

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

   if 1.22e17 < i

   1. Initial program 71.9%

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

   3. Taylor expanded in t around inf 49.9%

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

      1. distribute-lft-out-- 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in a around 0 38.7%

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

      1. *-commutative 38.7%

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

   8. Simplified 38.7%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -760000000 \lor \neg \left(x \leq 1.2 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -760000000.0) (not (<= x 1.2e+82)))
   (* x (- (* y z) (* t a)))
   (* c (- (* a j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -760000000.0) || !(x <= 1.2e+82)) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-760000000.0d0)) .or. (.not. (x <= 1.2d+82))) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -760000000.0) || !(x <= 1.2e+82)) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -760000000.0) or not (x <= 1.2e+82):
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -760000000.0) || !(x <= 1.2e+82))
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -760000000.0) || ~((x <= 1.2e+82)))
		tmp = x * ((y * z) - (t * a));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -760000000.0], N[Not[LessEqual[x, 1.2e+82]], $MachinePrecision]], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6e8 or 1.19999999999999999e82 < x

   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 0 70.6%

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

      1. *-commutative 70.6%

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

      2. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in i around 0 66.6%

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

      1. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in x around inf 66.9%

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

   if -7.6e8 < x < 1.19999999999999999e82

   1. Initial program 71.5%

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

   3. Taylor expanded in c around inf 44.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -760000000 \lor \neg \left(x \leq 1.2 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+81} \lor \neg \left(c \leq 5.8 \cdot 10^{-50}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.5e+81) (not (<= c 5.8e-50)))
   (* c (- (* a j) (* z b)))
   (* t (- (* b i) (* x 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 ((c <= -3.5e+81) || !(c <= 5.8e-50)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.5d+81)) .or. (.not. (c <= 5.8d-50))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.5e+81) || !(c <= 5.8e-50)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.5e+81) or not (c <= 5.8e-50):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.5e+81) || !(c <= 5.8e-50))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.5e+81) || ~((c <= 5.8e-50)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.5e+81], N[Not[LessEqual[c, 5.8e-50]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.5e81 or 5.80000000000000016e-50 < c

   1. Initial program 69.2%

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

   3. Taylor expanded in c around inf 56.1%

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

   if -3.5e81 < c < 5.80000000000000016e-50

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf 51.2%

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

      1. distribute-lft-out-- 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in t around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. *-commutative 51.2%

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

      3. distribute-rgt-neg-out 51.2%

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

      4. neg-mul-1 51.2%

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

      5. *-commutative 51.2%

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

      6. distribute-lft-out-- 51.2%

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

      7. mul-1-neg 51.2%

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

      8. distribute-lft-neg-out 51.2%

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

      9. cancel-sign-sub 51.2%

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

      10. +-commutative 51.2%

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

      11. *-commutative 51.2%

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

      12. mul-1-neg 51.2%

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

      13. unsub-neg 51.2%

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

   8. Simplified 51.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+81} \lor \neg \left(c \leq 5.8 \cdot 10^{-50}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+97} \lor \neg \left(t \leq 5.5 \cdot 10^{+19}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.15e+97) (not (<= t 5.5e+19)))
   (* (* x t) (- a))
   (* y (* i (- 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 ((t <= -1.15e+97) || !(t <= 5.5e+19)) {
		tmp = (x * t) * -a;
	} else {
		tmp = y * (i * -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 ((t <= (-1.15d+97)) .or. (.not. (t <= 5.5d+19))) then
        tmp = (x * t) * -a
    else
        tmp = y * (i * -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 ((t <= -1.15e+97) || !(t <= 5.5e+19)) {
		tmp = (x * t) * -a;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.15e+97) or not (t <= 5.5e+19):
		tmp = (x * t) * -a
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.15e+97) || !(t <= 5.5e+19))
		tmp = Float64(Float64(x * t) * Float64(-a));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.15e+97) || ~((t <= 5.5e+19)))
		tmp = (x * t) * -a;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.15e+97], N[Not[LessEqual[t, 5.5e+19]], $MachinePrecision]], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15000000000000003e97 or 5.5e19 < t

   1. Initial program 63.3%

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

   3. Taylor expanded in a around inf 53.5%

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

      1. +-commutative 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in c around 0 47.3%

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

      1. associate-*r* 47.3%

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

      2. neg-mul-1 47.3%

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

   8. Simplified 47.3%

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

   if -1.15000000000000003e97 < t < 5.5e19

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around 0 36.0%

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

      1. mul-1-neg 36.0%

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

      2. distribute-lft-neg-out 36.0%

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

      3. *-commutative 36.0%

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

   8. Simplified 36.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+97} \lor \neg \left(t \leq 5.5 \cdot 10^{+19}\right):\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{+97} \lor \neg \left(t \leq 4.55 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.46e+97) (not (<= t 4.55e+18)))
   (* t (* x (- a)))
   (* y (* i (- 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 ((t <= -1.46e+97) || !(t <= 4.55e+18)) {
		tmp = t * (x * -a);
	} else {
		tmp = y * (i * -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 ((t <= (-1.46d+97)) .or. (.not. (t <= 4.55d+18))) then
        tmp = t * (x * -a)
    else
        tmp = y * (i * -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 ((t <= -1.46e+97) || !(t <= 4.55e+18)) {
		tmp = t * (x * -a);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.46e+97) or not (t <= 4.55e+18):
		tmp = t * (x * -a)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.46e+97) || !(t <= 4.55e+18))
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.46e+97) || ~((t <= 4.55e+18)))
		tmp = t * (x * -a);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.46e+97], N[Not[LessEqual[t, 4.55e+18]], $MachinePrecision]], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.46e97 or 4.55e18 < t

   1. Initial program 63.3%

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

   3. Taylor expanded in t around inf 65.6%

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

      1. distribute-lft-out-- 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in a around inf 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

   8. Simplified 45.0%

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

   if -1.46e97 < t < 4.55e18

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around 0 36.0%

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

      1. mul-1-neg 36.0%

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

      2. distribute-lft-neg-out 36.0%

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

      3. *-commutative 36.0%

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

   8. Simplified 36.0%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{+97} \lor \neg \left(t \leq 4.55 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+57} \lor \neg \left(i \leq 3.15 \cdot 10^{+16}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -8.6e+57) (not (<= i 3.15e+16))) (* b (* t i)) (* c (* a 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 ((i <= -8.6e+57) || !(i <= 3.15e+16)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * 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 ((i <= (-8.6d+57)) .or. (.not. (i <= 3.15d+16))) then
        tmp = b * (t * i)
    else
        tmp = c * (a * 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 ((i <= -8.6e+57) || !(i <= 3.15e+16)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -8.6e+57) or not (i <= 3.15e+16):
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -8.6e+57) || !(i <= 3.15e+16))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -8.6e+57) || ~((i <= 3.15e+16)))
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -8.6e+57], N[Not[LessEqual[i, 3.15e+16]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -8.60000000000000066e57 or 3.15e16 < i

   1. Initial program 70.4%

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

   3. Taylor expanded in t around inf 49.0%

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

      1. distribute-lft-out-- 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in a around 0 40.0%

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

   if -8.60000000000000066e57 < i < 3.15e16

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in c around inf 24.9%

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

      1. *-commutative 24.9%

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

   8. Simplified 24.9%

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

   9. Taylor expanded in a around 0 24.9%

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

       1. *-commutative 24.9%

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

       2. associate-*l* 27.4%

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

       3. *-commutative 27.4%

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

   11. Simplified 27.4%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+57} \lor \neg \left(i \leq 3.15 \cdot 10^{+16}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+58} \lor \neg \left(i \leq 6.8 \cdot 10^{+16}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1e+58) (not (<= i 6.8e+16))) (* 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 ((i <= -1e+58) || !(i <= 6.8e+16)) {
		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 ((i <= (-1d+58)) .or. (.not. (i <= 6.8d+16))) 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 ((i <= -1e+58) || !(i <= 6.8e+16)) {
		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 (i <= -1e+58) or not (i <= 6.8e+16):
		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 ((i <= -1e+58) || !(i <= 6.8e+16))
		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 ((i <= -1e+58) || ~((i <= 6.8e+16)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1e+58], N[Not[LessEqual[i, 6.8e+16]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -9.99999999999999944e57 or 6.8e16 < i

   1. Initial program 70.4%

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

   3. Taylor expanded in t around inf 49.0%

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

      1. distribute-lft-out-- 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in a around 0 40.0%

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

   if -9.99999999999999944e57 < i < 6.8e16

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in c around inf 24.9%

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

      1. *-commutative 24.9%

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

   8. Simplified 24.9%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+58} \lor \neg \left(i \leq 6.8 \cdot 10^{+16}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -9e+57)
   (* b (* t i))
   (if (<= i 5.1e+16) (* c (* a j)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -9e+57) {
		tmp = b * (t * i);
	} else if (i <= 5.1e+16) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-9d+57)) then
        tmp = b * (t * i)
    else if (i <= 5.1d+16) then
        tmp = c * (a * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -9e+57) {
		tmp = b * (t * i);
	} else if (i <= 5.1e+16) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -9e+57:
		tmp = b * (t * i)
	elif i <= 5.1e+16:
		tmp = c * (a * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -9e+57)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 5.1e+16)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -9e+57)
		tmp = b * (t * i);
	elseif (i <= 5.1e+16)
		tmp = c * (a * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -9e+57], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.1e+16], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.99999999999999991e57

   1. Initial program 67.5%

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

   3. Taylor expanded in t around inf 47.2%

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

      1. distribute-lft-out-- 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in a around 0 47.5%

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

   if -8.99999999999999991e57 < i < 5.1e16

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in c around inf 24.9%

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

      1. *-commutative 24.9%

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

   8. Simplified 24.9%

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

   9. Taylor expanded in a around 0 24.9%

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

       1. *-commutative 24.9%

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

       2. associate-*l* 27.4%

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

       3. *-commutative 27.4%

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

   11. Simplified 27.4%

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

   if 5.1e16 < i

   1. Initial program 71.9%

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

   3. Taylor expanded in t around inf 49.9%

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

      1. distribute-lft-out-- 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in a around 0 38.7%

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

      1. *-commutative 38.7%

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

   8. Simplified 38.7%

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

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.18 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.18e+58)
   (* b (* t i))
   (if (<= i 4e+16) (* c (* a j)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.18e+58) {
		tmp = b * (t * i);
	} else if (i <= 4e+16) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.18d+58)) then
        tmp = b * (t * i)
    else if (i <= 4d+16) then
        tmp = c * (a * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.18e+58) {
		tmp = b * (t * i);
	} else if (i <= 4e+16) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.18e+58:
		tmp = b * (t * i)
	elif i <= 4e+16:
		tmp = c * (a * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.18e+58)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 4e+16)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.18e+58)
		tmp = b * (t * i);
	elseif (i <= 4e+16)
		tmp = c * (a * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.18e+58], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+16], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.18000000000000003e58

   1. Initial program 67.5%

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

   3. Taylor expanded in t around inf 47.2%

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

      1. distribute-lft-out-- 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in a around 0 47.5%

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

   if -1.18000000000000003e58 < i < 4e16

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in c around inf 24.9%

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

      1. *-commutative 24.9%

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

   8. Simplified 24.9%

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

   9. Taylor expanded in a around 0 24.9%

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

       1. *-commutative 24.9%

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

       2. associate-*l* 27.4%

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

       3. *-commutative 27.4%

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

   11. Simplified 27.4%

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

   if 4e16 < i

   1. Initial program 71.9%

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

   3. Taylor expanded in i around inf 69.2%

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

      1. distribute-lft-out-- 69.2%

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

      2. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in j around 0 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.18 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8e+191) (* a (* x t)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8e+191) {
		tmp = a * (x * t);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-8d+191)) then
        tmp = a * (x * t)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8e+191) {
		tmp = a * (x * t);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8e+191:
		tmp = a * (x * t)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8e+191)
		tmp = Float64(a * Float64(x * t));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8e+191)
		tmp = a * (x * t);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8e+191], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.00000000000000058e191

   1. Initial program 73.0%

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

   3. Taylor expanded in a around inf 25.1%

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

      1. +-commutative 25.1%

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

      2. mul-1-neg 25.1%

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

      3. unsub-neg 25.1%

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

   5. Simplified 25.1%

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

   6. Taylor expanded in c around 0 25.2%

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

      1. associate-*r* 25.2%

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

      2. neg-mul-1 25.2%

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

   8. Simplified 25.2%

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

      1. add-sqr-sqrt 8.9%

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

      2. sqrt-unprod 13.3%

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

      3. sqr-neg 13.3%

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

      4. sqrt-unprod 12.9%

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

      5. add-sqr-sqrt 21.6%

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

      6. *-un-lft-identity 21.6%

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

   10. Applied egg-rr 21.6%

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

       1. *-lft-identity 21.6%

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

   12. Simplified 21.6%

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

   if -8.00000000000000058e191 < b

   1. Initial program 75.7%

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

   3. Taylor expanded in a around inf 40.7%

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

      1. +-commutative 40.7%

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

      2. mul-1-neg 40.7%

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

      3. unsub-neg 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in c around inf 21.7%

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

      1. *-commutative 21.7%

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

   8. Simplified 21.7%

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

4. Final simplification 21.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.6% 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 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 a around inf 39.2%

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

   1. +-commutative 39.2%

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

   2. mul-1-neg 39.2%

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

   3. unsub-neg 39.2%

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

5. Simplified 39.2%

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

6. Taylor expanded in c around inf 19.7%

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

   1. *-commutative 19.7%

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

8. Simplified 19.7%

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

9. Final simplification 19.7%

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

Developer Target 1: 60.3% 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 2024144 
(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)))))