Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 82.5%

Time: 18.1s

Alternatives: 24

Speedup: 0.5×

• 58.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (c * ((x * (y / c)) - 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[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(c * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - 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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 90.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in c around inf 55.6%

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

      1. associate-/l* 55.6%

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

   8. Simplified 55.6%

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

4. Final simplification 84.0%

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

Alternative 2: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) + t\_1\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-118}:\\ \;\;\;\;\left(t\_1 - i \cdot \left(y \cdot j\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+48}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -7.5e+120)
     (+ (* j (* y (- (/ (* t c) y) i))) t_1)
     (if (<= j -1.6e-118)
       (+ (- t_1 (* i (* y j))) (* a (* b i)))
       (if (<= j 2.9e+48)
         (+ t_1 (* b (- (* a i) (* z c))))
         (+ (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -7.5e+120) {
		tmp = (j * (y * (((t * c) / y) - i))) + t_1;
	} else if (j <= -1.6e-118) {
		tmp = (t_1 - (i * (y * j))) + (a * (b * i));
	} else if (j <= 2.9e+48) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-7.5d+120)) then
        tmp = (j * (y * (((t * c) / y) - i))) + t_1
    else if (j <= (-1.6d-118)) then
        tmp = (t_1 - (i * (y * j))) + (a * (b * i))
    else if (j <= 2.9d+48) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (j * ((t * c) - (y * i))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -7.5e+120) {
		tmp = (j * (y * (((t * c) / y) - i))) + t_1;
	} else if (j <= -1.6e-118) {
		tmp = (t_1 - (i * (y * j))) + (a * (b * i));
	} else if (j <= 2.9e+48) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -7.5e+120:
		tmp = (j * (y * (((t * c) / y) - i))) + t_1
	elif j <= -1.6e-118:
		tmp = (t_1 - (i * (y * j))) + (a * (b * i))
	elif j <= 2.9e+48:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (j * ((t * c) - (y * i))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -7.5e+120)
		tmp = Float64(Float64(j * Float64(y * Float64(Float64(Float64(t * c) / y) - i))) + t_1);
	elseif (j <= -1.6e-118)
		tmp = Float64(Float64(t_1 - Float64(i * Float64(y * j))) + Float64(a * Float64(b * i)));
	elseif (j <= 2.9e+48)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -7.5e+120)
		tmp = (j * (y * (((t * c) / y) - i))) + t_1;
	elseif (j <= -1.6e-118)
		tmp = (t_1 - (i * (y * j))) + (a * (b * i));
	elseif (j <= 2.9e+48)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (j * ((t * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.5e+120], N[(N[(j * N[(y * N[(N[(N[(t * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, -1.6e-118], N[(N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e+48], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.5000000000000006e120

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 78.0%

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

   4. Taylor expanded in y around inf 80.8%

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

   if -7.5000000000000006e120 < j < -1.60000000000000002e-118

   1. Initial program 71.0%

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

   3. Taylor expanded in c around 0 69.0%

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

   if -1.60000000000000002e-118 < j < 2.8999999999999999e48

   1. Initial program 74.3%

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

   3. Taylor expanded in j around 0 74.7%

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

   if 2.8999999999999999e48 < j

   1. Initial program 74.2%

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

   3. Taylor expanded in b around 0 84.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-118}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+132}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+142}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.3e+132)
   (* z (- (* x y) (* b c)))
   (if (<= z -2.4e-241)
     (+ (* j (- (* t c) (* y i))) (* x (* y z)))
     (if (<= z 2.7e+142)
       (- (* j (* y (- (/ (* t c) y) i))) (* x (* t a)))
       (* z (* c (- (* x (/ y c)) b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e+132) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -2.4e-241) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (z <= 2.7e+142) {
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a));
	} else {
		tmp = z * (c * ((x * (y / c)) - b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.3d+132)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-2.4d-241)) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (z <= 2.7d+142) then
        tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a))
    else
        tmp = z * (c * ((x * (y / c)) - b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e+132) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -2.4e-241) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (z <= 2.7e+142) {
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a));
	} else {
		tmp = z * (c * ((x * (y / c)) - b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.3e+132:
		tmp = z * ((x * y) - (b * c))
	elif z <= -2.4e-241:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif z <= 2.7e+142:
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a))
	else:
		tmp = z * (c * ((x * (y / c)) - b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.3e+132)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -2.4e-241)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (z <= 2.7e+142)
		tmp = Float64(Float64(j * Float64(y * Float64(Float64(Float64(t * c) / y) - i))) - Float64(x * Float64(t * a)));
	else
		tmp = Float64(z * Float64(c * Float64(Float64(x * Float64(y / c)) - b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.3e+132)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -2.4e-241)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (z <= 2.7e+142)
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a));
	else
		tmp = z * (c * ((x * (y / c)) - b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.3e+132], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-241], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+142], N[(N[(j * N[(y * N[(N[(N[(t * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3000000000000002e132

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   if -2.3000000000000002e132 < z < -2.4e-241

   1. Initial program 80.9%

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

   3. Taylor expanded in b around 0 61.2%

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

   4. Taylor expanded in a around 0 57.1%

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

   if -2.4e-241 < z < 2.69999999999999983e142

   1. Initial program 79.2%

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

   3. Taylor expanded in b around 0 65.8%

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

   4. Taylor expanded in y around inf 65.9%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate-*r* 61.5%

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

      3. *-commutative 61.5%

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

      4. distribute-rgt-neg-in 61.5%

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

   7. Simplified 61.5%

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

   if 2.69999999999999983e142 < z

   1. Initial program 53.5%

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

   3. Taylor expanded in z around inf 78.2%

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

      1. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in c around inf 78.4%

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

      1. associate-/l* 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+132}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+142}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.8e+51)
     t_1
     (if (<= b 9e-59)
       (- (* x (- (* y z) (* t a))) (* i (* y j)))
       (if (<= b 3.4e+121) (+ (* j (- (* t c) (* y i))) (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.8e+51) {
		tmp = t_1;
	} else if (b <= 9e-59) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (b <= 3.4e+121) {
		tmp = (j * ((t * c) - (y * i))) + (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 = b * ((a * i) - (z * c))
    if (b <= (-1.8d+51)) then
        tmp = t_1
    else if (b <= 9d-59) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (b <= 3.4d+121) then
        tmp = (j * ((t * c) - (y * i))) + (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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.8e+51) {
		tmp = t_1;
	} else if (b <= 9e-59) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (b <= 3.4e+121) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.8e+51:
		tmp = t_1
	elif b <= 9e-59:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif b <= 3.4e+121:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.8e+51)
		tmp = t_1;
	elseif (b <= 9e-59)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (b <= 3.4e+121)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.8e+51)
		tmp = t_1;
	elseif (b <= 9e-59)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (b <= 3.4e+121)
		tmp = (j * ((t * c) - (y * i))) + (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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+51], t$95$1, If[LessEqual[b, 9e-59], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+121], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.80000000000000005e51 or 3.4000000000000001e121 < b

   1. Initial program 74.3%

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

   3. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if -1.80000000000000005e51 < b < 9.00000000000000023e-59

   1. Initial program 69.7%

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

   3. Taylor expanded in b around 0 64.3%

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

   4. Taylor expanded in c around 0 60.7%

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

      1. +-commutative 60.7%

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

      2. sub-neg 60.7%

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

      3. *-commutative 60.7%

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

      4. sub-neg 60.7%

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

      5. mul-1-neg 60.7%

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

      6. unsub-neg 60.7%

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

      7. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   if 9.00000000000000023e-59 < b < 3.4000000000000001e121

   1. Initial program 84.3%

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

   3. Taylor expanded in b around 0 77.8%

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

   4. Taylor expanded in a around 0 75.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-165}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+67}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -4.1e-80)
     t_1
     (if (<= x 3.1e-307)
       (* j (- (* t c) (* y i)))
       (if (<= x 9.6e-165)
         (* i (- (* a b) (* y j)))
         (if (<= x 9e+67) (* c (- (* t 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.1e-80) {
		tmp = t_1;
	} else if (x <= 3.1e-307) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 9.6e-165) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 9e+67) {
		tmp = c * ((t * 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 = x * ((y * z) - (t * a))
    if (x <= (-4.1d-80)) then
        tmp = t_1
    else if (x <= 3.1d-307) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 9.6d-165) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 9d+67) then
        tmp = c * ((t * 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.1e-80) {
		tmp = t_1;
	} else if (x <= 3.1e-307) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 9.6e-165) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 9e+67) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.1e-80:
		tmp = t_1
	elif x <= 3.1e-307:
		tmp = j * ((t * c) - (y * i))
	elif x <= 9.6e-165:
		tmp = i * ((a * b) - (y * j))
	elif x <= 9e+67:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.1e-80)
		tmp = t_1;
	elseif (x <= 3.1e-307)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 9.6e-165)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 9e+67)
		tmp = Float64(c * Float64(Float64(t * 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 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.1e-80)
		tmp = t_1;
	elseif (x <= 3.1e-307)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 9.6e-165)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 9e+67)
		tmp = c * ((t * 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e-80], t$95$1, If[LessEqual[x, 3.1e-307], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.6e-165], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+67], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0999999999999999e-80 or 8.9999999999999997e67 < x

   1. Initial program 74.8%

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

   3. Taylor expanded in b around 0 64.5%

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

   4. Taylor expanded in j around 0 64.8%

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

   if -4.0999999999999999e-80 < x < 3.0999999999999998e-307

   1. Initial program 78.9%

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

   3. Taylor expanded in j around inf 73.0%

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

   if 3.0999999999999998e-307 < x < 9.6000000000000009e-165

   1. Initial program 68.7%

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

   3. Taylor expanded in t around inf 67.7%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in i around -inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. associate-/l* 55.0%

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

      5. *-commutative 55.0%

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

      6. associate-*r/ 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around 0 65.5%

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

   if 9.6000000000000009e-165 < x < 8.9999999999999997e67

   1. Initial program 66.7%

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

   3. Taylor expanded in c around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. *-commutative 52.1%

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

   5. Simplified 52.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-165}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+67}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-141}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.5e+120)
     t_1
     (if (<= j -3.7e-141)
       (* i (- (* a b) (* y j)))
       (if (<= j 9e-269)
         (* b (- (* a i) (* z c)))
         (if (<= j 2.5e+76) (* a (- (* b i) (* 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+120) {
		tmp = t_1;
	} else if (j <= -3.7e-141) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 9e-269) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 2.5e+76) {
		tmp = a * ((b * i) - (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 = j * ((t * c) - (y * i))
    if (j <= (-1.5d+120)) then
        tmp = t_1
    else if (j <= (-3.7d-141)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= 9d-269) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 2.5d+76) then
        tmp = a * ((b * i) - (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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+120) {
		tmp = t_1;
	} else if (j <= -3.7e-141) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 9e-269) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 2.5e+76) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.5e+120:
		tmp = t_1
	elif j <= -3.7e-141:
		tmp = i * ((a * b) - (y * j))
	elif j <= 9e-269:
		tmp = b * ((a * i) - (z * c))
	elif j <= 2.5e+76:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+120)
		tmp = t_1;
	elseif (j <= -3.7e-141)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= 9e-269)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 2.5e+76)
		tmp = Float64(a * Float64(Float64(b * i) - 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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+120)
		tmp = t_1;
	elseif (j <= -3.7e-141)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= 9e-269)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 2.5e+76)
		tmp = a * ((b * i) - (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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+120], t$95$1, If[LessEqual[j, -3.7e-141], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e-269], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+76], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.5e120 or 2.49999999999999996e76 < j

   1. Initial program 72.6%

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

   3. Taylor expanded in j around inf 73.1%

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

   if -1.5e120 < j < -3.7e-141

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 65.6%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in i around -inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. associate-/l* 52.6%

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

      5. *-commutative 52.6%

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

      6. associate-*r/ 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in t around 0 59.1%

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

   if -3.7e-141 < j < 9.0000000000000003e-269

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if 9.0000000000000003e-269 < j < 2.49999999999999996e76

   1. Initial program 76.1%

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

   3. Taylor expanded in a around inf 48.5%

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

      1. distribute-lft-out-- 48.5%

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

      2. *-commutative 48.5%

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

      3. *-commutative 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in a around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. *-commutative 48.5%

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

      3. *-commutative 48.5%

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

      4. distribute-rgt-neg-out 48.5%

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

      5. neg-mul-1 48.5%

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

      6. *-commutative 48.5%

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

      7. *-commutative 48.5%

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

      8. distribute-lft-out-- 48.5%

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

      9. sub-neg 48.5%

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

      10. mul-1-neg 48.5%

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

      11. *-commutative 48.5%

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

      12. remove-double-neg 48.5%

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

      13. *-commutative 48.5%

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

      14. +-commutative 48.5%

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

      15. *-commutative 48.5%

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

      16. mul-1-neg 48.5%

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

      17. unsub-neg 48.5%

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

      18. *-commutative 48.5%

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

   8. Simplified 48.5%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-141}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -22000000 \lor \neg \left(j \leq 1.65 \cdot 10^{-13}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -22000000.0) (not (<= j 1.65e-13)))
   (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
   (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -22000000.0) || !(j <= 1.65e-13)) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-22000000.0d0)) .or. (.not. (j <= 1.65d-13))) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -22000000.0) || !(j <= 1.65e-13)) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -22000000.0) or not (j <= 1.65e-13):
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -22000000.0) || !(j <= 1.65e-13))
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -22000000.0) || ~((j <= 1.65e-13)))
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -22000000.0], N[Not[LessEqual[j, 1.65e-13]], $MachinePrecision]], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.2e7 or 1.65e-13 < j

   1. Initial program 77.2%

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

   3. Taylor expanded in b around 0 76.1%

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

   if -2.2e7 < j < 1.65e-13

   1. Initial program 69.8%

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

   3. Taylor expanded in y around 0 64.7%

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

      1. mul-1-neg 64.7%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

      4. associate-*l* 64.7%

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

      5. distribute-rgt-neg-in 64.7%

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

      6. mul-1-neg 64.7%

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

      7. *-commutative 64.7%

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

      8. associate-*r* 62.4%

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

      9. *-commutative 62.4%

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

      10. associate-*l* 64.5%

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

      11. distribute-lft-in 65.2%

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

      12. +-commutative 65.2%

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

      13. mul-1-neg 65.2%

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

      14. unsub-neg 65.2%

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

      15. *-commutative 65.2%

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

      16. *-commutative 65.2%

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

   5. Simplified 65.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -22000000 \lor \neg \left(j \leq 1.65 \cdot 10^{-13}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) + t\_1\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -5.6e+84)
     (+ (* j (* y (- (/ (* t c) y) i))) t_1)
     (if (<= j 4.8e+47)
       (+ t_1 (* b (- (* a i) (* z c))))
       (+ (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -5.6e+84) {
		tmp = (j * (y * (((t * c) / y) - i))) + t_1;
	} else if (j <= 4.8e+47) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-5.6d+84)) then
        tmp = (j * (y * (((t * c) / y) - i))) + t_1
    else if (j <= 4.8d+47) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (j * ((t * c) - (y * i))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -5.6e+84) {
		tmp = (j * (y * (((t * c) / y) - i))) + t_1;
	} else if (j <= 4.8e+47) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -5.6e+84:
		tmp = (j * (y * (((t * c) / y) - i))) + t_1
	elif j <= 4.8e+47:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (j * ((t * c) - (y * i))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -5.6e+84)
		tmp = Float64(Float64(j * Float64(y * Float64(Float64(Float64(t * c) / y) - i))) + t_1);
	elseif (j <= 4.8e+47)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -5.6e+84)
		tmp = (j * (y * (((t * c) / y) - i))) + t_1;
	elseif (j <= 4.8e+47)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (j * ((t * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.6e+84], N[(N[(j * N[(y * N[(N[(N[(t * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 4.8e+47], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.59999999999999963e84

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0 71.8%

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

   4. Taylor expanded in y around inf 73.9%

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

   if -5.59999999999999963e84 < j < 4.80000000000000037e47

   1. Initial program 72.8%

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

   3. Taylor expanded in j around 0 71.3%

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

   if 4.80000000000000037e47 < j

   1. Initial program 74.2%

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

   3. Taylor expanded in b around 0 84.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -7.8e+124)
     (- (* j (* y (- (/ (* t c) y) i))) (* x (* t a)))
     (if (<= j 1.45e+50)
       (+ t_1 (* b (- (* a i) (* z c))))
       (+ (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -7.8e+124) {
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a));
	} else if (j <= 1.45e+50) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-7.8d+124)) then
        tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a))
    else if (j <= 1.45d+50) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (j * ((t * c) - (y * i))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -7.8e+124) {
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a));
	} else if (j <= 1.45e+50) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -7.8e+124:
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a))
	elif j <= 1.45e+50:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (j * ((t * c) - (y * i))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -7.8e+124)
		tmp = Float64(Float64(j * Float64(y * Float64(Float64(Float64(t * c) / y) - i))) - Float64(x * Float64(t * a)));
	elseif (j <= 1.45e+50)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -7.8e+124)
		tmp = (j * (y * (((t * c) / y) - i))) - (x * (t * a));
	elseif (j <= 1.45e+50)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (j * ((t * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.8e+124], N[(N[(j * N[(y * N[(N[(N[(t * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+50], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.8000000000000001e124

   1. Initial program 71.5%

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

   3. Taylor expanded in b around 0 77.3%

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

   4. Taylor expanded in y around inf 80.2%

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

   5. Taylor expanded in y around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate-*r* 80.0%

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

      3. *-commutative 80.0%

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

      4. distribute-rgt-neg-in 80.0%

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

   7. Simplified 80.0%

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

   if -7.8000000000000001e124 < j < 1.45e50

   1. Initial program 73.5%

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

   3. Taylor expanded in j around 0 69.9%

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

   if 1.45e50 < j

   1. Initial program 74.2%

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

   3. Taylor expanded in b around 0 84.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{t \cdot c}{y} - i\right)\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.4e+129)
   (* z (- (* x y) (* b c)))
   (if (<= z 1.5e+143)
     (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
     (* z (* c (- (* x (/ y c)) b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.4e+129) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= 1.5e+143) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = z * (c * ((x * (y / c)) - b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.4d+129)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= 1.5d+143) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = z * (c * ((x * (y / c)) - b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.4e+129) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= 1.5e+143) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = z * (c * ((x * (y / c)) - b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.4e+129:
		tmp = z * ((x * y) - (b * c))
	elif z <= 1.5e+143:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = z * (c * ((x * (y / c)) - b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.4e+129)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= 1.5e+143)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(z * Float64(c * Float64(Float64(x * Float64(y / c)) - b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.4e+129)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= 1.5e+143)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = z * (c * ((x * (y / c)) - b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.4e+129], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+143], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e129

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   if -2.3999999999999999e129 < z < 1.5e143

   1. Initial program 79.9%

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

   3. Taylor expanded in b around 0 63.9%

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

   if 1.5e143 < z

   1. Initial program 53.5%

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

   3. Taylor expanded in z around inf 78.2%

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

      1. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in c around inf 78.4%

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

      1. associate-/l* 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-165}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+262}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.8e-80)
   (* z (* x y))
   (if (<= x 8.5e-165)
     (* (- y) (* i j))
     (if (<= x 1.7e+68)
       (* b (* z (- c)))
       (if (<= x 3.1e+262) (* t (* x (- a))) (* x (* y 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 (x <= -3.8e-80) {
		tmp = z * (x * y);
	} else if (x <= 8.5e-165) {
		tmp = -y * (i * j);
	} else if (x <= 1.7e+68) {
		tmp = b * (z * -c);
	} else if (x <= 3.1e+262) {
		tmp = t * (x * -a);
	} else {
		tmp = x * (y * 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 (x <= (-3.8d-80)) then
        tmp = z * (x * y)
    else if (x <= 8.5d-165) then
        tmp = -y * (i * j)
    else if (x <= 1.7d+68) then
        tmp = b * (z * -c)
    else if (x <= 3.1d+262) then
        tmp = t * (x * -a)
    else
        tmp = x * (y * 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 (x <= -3.8e-80) {
		tmp = z * (x * y);
	} else if (x <= 8.5e-165) {
		tmp = -y * (i * j);
	} else if (x <= 1.7e+68) {
		tmp = b * (z * -c);
	} else if (x <= 3.1e+262) {
		tmp = t * (x * -a);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3.8e-80:
		tmp = z * (x * y)
	elif x <= 8.5e-165:
		tmp = -y * (i * j)
	elif x <= 1.7e+68:
		tmp = b * (z * -c)
	elif x <= 3.1e+262:
		tmp = t * (x * -a)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.8e-80)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 8.5e-165)
		tmp = Float64(Float64(-y) * Float64(i * j));
	elseif (x <= 1.7e+68)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 3.1e+262)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3.8e-80)
		tmp = z * (x * y);
	elseif (x <= 8.5e-165)
		tmp = -y * (i * j);
	elseif (x <= 1.7e+68)
		tmp = b * (z * -c);
	elseif (x <= 3.1e+262)
		tmp = t * (x * -a);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.8e-80], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-165], N[((-y) * N[(i * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+68], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+262], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.79999999999999967e-80

   1. Initial program 81.2%

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

   3. Taylor expanded in z around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in x around inf 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   if -3.79999999999999967e-80 < x < 8.5e-165

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in x around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. distribute-lft-neg-out 43.6%

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

      3. *-commutative 43.6%

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

   8. Simplified 43.6%

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

   if 8.5e-165 < x < 1.70000000000000008e68

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 42.8%

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

      1. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in a around 0 32.8%

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

      1. mul-1-neg 32.8%

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

      2. distribute-rgt-neg-in 32.8%

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

      3. *-commutative 32.8%

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

      4. distribute-rgt-neg-in 32.8%

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

   8. Simplified 32.8%

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

   if 1.70000000000000008e68 < x < 3.09999999999999991e262

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

      2. *-commutative 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in x around inf 56.0%

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

      1. associate-*r* 56.0%

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

      2. neg-mul-1 56.0%

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

      3. *-commutative 56.0%

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

   8. Simplified 56.0%

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

      1. distribute-lft-neg-out 56.0%

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

      2. add-sqr-sqrt 16.7%

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

      3. sqrt-unprod 36.2%

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

      4. sqr-neg 36.2%

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

      5. sqrt-unprod 16.8%

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

      6. add-sqr-sqrt 16.8%

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

      7. associate-*r* 10.8%

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

      8. add-sqr-sqrt 10.7%

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

      9. sqrt-unprod 33.3%

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

      10. sqr-neg 33.3%

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

      11. sqrt-unprod 19.6%

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

      12. add-sqr-sqrt 58.9%

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

   10. Applied egg-rr 58.9%

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

   if 3.09999999999999991e262 < x

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in x around inf 70.0%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-165}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+262}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+262}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2.5e-79)
   (* z (* x y))
   (if (<= x 8.2e-165)
     (* j (* y (- i)))
     (if (<= x 1.1e+68)
       (* b (* z (- c)))
       (if (<= x 1.9e+262) (* t (* x (- a))) (* x (* y 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 (x <= -2.5e-79) {
		tmp = z * (x * y);
	} else if (x <= 8.2e-165) {
		tmp = j * (y * -i);
	} else if (x <= 1.1e+68) {
		tmp = b * (z * -c);
	} else if (x <= 1.9e+262) {
		tmp = t * (x * -a);
	} else {
		tmp = x * (y * 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 (x <= (-2.5d-79)) then
        tmp = z * (x * y)
    else if (x <= 8.2d-165) then
        tmp = j * (y * -i)
    else if (x <= 1.1d+68) then
        tmp = b * (z * -c)
    else if (x <= 1.9d+262) then
        tmp = t * (x * -a)
    else
        tmp = x * (y * 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 (x <= -2.5e-79) {
		tmp = z * (x * y);
	} else if (x <= 8.2e-165) {
		tmp = j * (y * -i);
	} else if (x <= 1.1e+68) {
		tmp = b * (z * -c);
	} else if (x <= 1.9e+262) {
		tmp = t * (x * -a);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2.5e-79:
		tmp = z * (x * y)
	elif x <= 8.2e-165:
		tmp = j * (y * -i)
	elif x <= 1.1e+68:
		tmp = b * (z * -c)
	elif x <= 1.9e+262:
		tmp = t * (x * -a)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2.5e-79)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 8.2e-165)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (x <= 1.1e+68)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 1.9e+262)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2.5e-79)
		tmp = z * (x * y);
	elseif (x <= 8.2e-165)
		tmp = j * (y * -i);
	elseif (x <= 1.1e+68)
		tmp = b * (z * -c);
	elseif (x <= 1.9e+262)
		tmp = t * (x * -a);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2.5e-79], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-165], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+68], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+262], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.5e-79

   1. Initial program 81.2%

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

   3. Taylor expanded in z around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in x around inf 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   if -2.5e-79 < x < 8.2000000000000004e-165

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in x around 0 41.0%

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

      1. mul-1-neg 41.0%

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

      2. *-commutative 41.0%

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

      3. distribute-rgt-neg-in 41.0%

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

   8. Simplified 41.0%

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

   9. Taylor expanded in j around 0 41.0%

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

       1. *-commutative 41.0%

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

       2. neg-mul-1 41.0%

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

       3. distribute-rgt-neg-in 41.0%

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

       4. associate-*r* 42.3%

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

       5. distribute-rgt-neg-out 42.3%

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

   11. Simplified 42.3%

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

   if 8.2000000000000004e-165 < x < 1.09999999999999994e68

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 42.8%

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

      1. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in a around 0 32.8%

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

      1. mul-1-neg 32.8%

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

      2. distribute-rgt-neg-in 32.8%

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

      3. *-commutative 32.8%

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

      4. distribute-rgt-neg-in 32.8%

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

   8. Simplified 32.8%

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

   if 1.09999999999999994e68 < x < 1.90000000000000017e262

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

      2. *-commutative 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in x around inf 56.0%

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

      1. associate-*r* 56.0%

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

      2. neg-mul-1 56.0%

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

      3. *-commutative 56.0%

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

   8. Simplified 56.0%

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

      1. distribute-lft-neg-out 56.0%

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

      2. add-sqr-sqrt 16.7%

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

      3. sqrt-unprod 36.2%

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

      4. sqr-neg 36.2%

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

      5. sqrt-unprod 16.8%

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

      6. add-sqr-sqrt 16.8%

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

      7. associate-*r* 10.8%

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

      8. add-sqr-sqrt 10.7%

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

      9. sqrt-unprod 33.3%

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

      10. sqr-neg 33.3%

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

      11. sqrt-unprod 19.6%

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

      12. add-sqr-sqrt 58.9%

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

   10. Applied egg-rr 58.9%

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

   if 1.90000000000000017e262 < x

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in x around inf 70.0%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+262}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+262}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -4.5e-173)
   (* z (* x y))
   (if (<= x 4.3e-162)
     (* i (* a b))
     (if (<= x 4.5e+68)
       (* b (* z (- c)))
       (if (<= x 2.9e+262) (* t (* x (- a))) (* x (* y 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 (x <= -4.5e-173) {
		tmp = z * (x * y);
	} else if (x <= 4.3e-162) {
		tmp = i * (a * b);
	} else if (x <= 4.5e+68) {
		tmp = b * (z * -c);
	} else if (x <= 2.9e+262) {
		tmp = t * (x * -a);
	} else {
		tmp = x * (y * 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 (x <= (-4.5d-173)) then
        tmp = z * (x * y)
    else if (x <= 4.3d-162) then
        tmp = i * (a * b)
    else if (x <= 4.5d+68) then
        tmp = b * (z * -c)
    else if (x <= 2.9d+262) then
        tmp = t * (x * -a)
    else
        tmp = x * (y * 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 (x <= -4.5e-173) {
		tmp = z * (x * y);
	} else if (x <= 4.3e-162) {
		tmp = i * (a * b);
	} else if (x <= 4.5e+68) {
		tmp = b * (z * -c);
	} else if (x <= 2.9e+262) {
		tmp = t * (x * -a);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -4.5e-173:
		tmp = z * (x * y)
	elif x <= 4.3e-162:
		tmp = i * (a * b)
	elif x <= 4.5e+68:
		tmp = b * (z * -c)
	elif x <= 2.9e+262:
		tmp = t * (x * -a)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -4.5e-173)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 4.3e-162)
		tmp = Float64(i * Float64(a * b));
	elseif (x <= 4.5e+68)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (x <= 2.9e+262)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -4.5e-173)
		tmp = z * (x * y);
	elseif (x <= 4.3e-162)
		tmp = i * (a * b);
	elseif (x <= 4.5e+68)
		tmp = b * (z * -c);
	elseif (x <= 2.9e+262)
		tmp = t * (x * -a);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -4.5e-173], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e-162], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+68], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+262], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.50000000000000018e-173

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 52.6%

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

      1. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in x around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if -4.50000000000000018e-173 < x < 4.29999999999999996e-162

   1. Initial program 76.3%

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

   3. Taylor expanded in b around inf 43.7%

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

      1. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in a around inf 30.1%

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

      1. *-commutative 30.1%

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

   8. Simplified 30.1%

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

   9. Taylor expanded in a around 0 30.1%

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

       1. associate-*r* 31.7%

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

   11. Simplified 31.7%

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

   if 4.29999999999999996e-162 < x < 4.5000000000000003e68

   1. Initial program 65.3%

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

   3. Taylor expanded in b around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in a around 0 34.0%

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

      1. mul-1-neg 34.0%

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

      2. distribute-rgt-neg-in 34.0%

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

      3. *-commutative 34.0%

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

      4. distribute-rgt-neg-in 34.0%

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

   8. Simplified 34.0%

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

   if 4.5000000000000003e68 < x < 2.8999999999999998e262

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

      2. *-commutative 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in x around inf 56.0%

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

      1. associate-*r* 56.0%

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

      2. neg-mul-1 56.0%

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

      3. *-commutative 56.0%

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

   8. Simplified 56.0%

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

      1. distribute-lft-neg-out 56.0%

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

      2. add-sqr-sqrt 16.7%

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

      3. sqrt-unprod 36.2%

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

      4. sqr-neg 36.2%

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

      5. sqrt-unprod 16.8%

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

      6. add-sqr-sqrt 16.8%

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

      7. associate-*r* 10.8%

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

      8. add-sqr-sqrt 10.7%

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

      9. sqrt-unprod 33.3%

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

      10. sqr-neg 33.3%

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

      11. sqrt-unprod 19.6%

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

      12. add-sqr-sqrt 58.9%

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

   10. Applied egg-rr 58.9%

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

   if 2.8999999999999998e262 < x

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in x around inf 70.0%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+262}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+160} \lor \neg \left(b \leq 3.8 \cdot 10^{+121}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -5e+160) (not (<= b 3.8e+121)))
   (* b (- (* a i) (* z c)))
   (+ (* j (- (* t c) (* y i))) (* x (* y 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 ((b <= -5e+160) || !(b <= 3.8e+121)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * 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 ((b <= (-5d+160)) .or. (.not. (b <= 3.8d+121))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (j * ((t * c) - (y * i))) + (x * (y * 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 ((b <= -5e+160) || !(b <= 3.8e+121)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -5e+160) or not (b <= 3.8e+121):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -5e+160) || !(b <= 3.8e+121))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -5e+160) || ~((b <= 3.8e+121)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -5e+160], N[Not[LessEqual[b, 3.8e+121]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.0000000000000002e160 or 3.8e121 < b

   1. Initial program 72.2%

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

   3. Taylor expanded in b around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -5.0000000000000002e160 < b < 3.8e121

   1. Initial program 73.7%

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

   3. Taylor expanded in b around 0 66.9%

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

   4. Taylor expanded in a around 0 59.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+160} \lor \neg \left(b \leq 3.8 \cdot 10^{+121}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.5 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.46 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -6.5e-45)
     t_1
     (if (<= i 2e-196)
       (* c (- (* t j) (* z b)))
       (if (<= i 1.46e+54) (* a (- (* b i) (* 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 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -6.5e-45) {
		tmp = t_1;
	} else if (i <= 2e-196) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 1.46e+54) {
		tmp = a * ((b * i) - (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 = i * ((a * b) - (y * j))
    if (i <= (-6.5d-45)) then
        tmp = t_1
    else if (i <= 2d-196) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 1.46d+54) then
        tmp = a * ((b * i) - (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 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -6.5e-45) {
		tmp = t_1;
	} else if (i <= 2e-196) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 1.46e+54) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -6.5e-45:
		tmp = t_1
	elif i <= 2e-196:
		tmp = c * ((t * j) - (z * b))
	elif i <= 1.46e+54:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -6.5e-45)
		tmp = t_1;
	elseif (i <= 2e-196)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 1.46e+54)
		tmp = Float64(a * Float64(Float64(b * i) - 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 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -6.5e-45)
		tmp = t_1;
	elseif (i <= 2e-196)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 1.46e+54)
		tmp = a * ((b * i) - (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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.5e-45], t$95$1, If[LessEqual[i, 2e-196], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.46e+54], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.4999999999999995e-45 or 1.46000000000000003e54 < i

   1. Initial program 62.0%

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

   3. Taylor expanded in t around inf 61.3%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in i around -inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. associate-/l* 51.2%

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

      5. *-commutative 51.2%

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

      6. associate-*r/ 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in t around 0 60.3%

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

   if -6.4999999999999995e-45 < i < 2.0000000000000001e-196

   1. Initial program 84.9%

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

   3. Taylor expanded in c around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   if 2.0000000000000001e-196 < i < 1.46000000000000003e54

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 46.9%

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

      1. distribute-lft-out-- 46.9%

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

      2. *-commutative 46.9%

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

      3. *-commutative 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in a around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. *-commutative 46.9%

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

      3. *-commutative 46.9%

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

      4. distribute-rgt-neg-out 46.9%

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

      5. neg-mul-1 46.9%

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

      6. *-commutative 46.9%

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

      7. *-commutative 46.9%

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

      8. distribute-lft-out-- 46.9%

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

      9. sub-neg 46.9%

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

      10. mul-1-neg 46.9%

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

      11. *-commutative 46.9%

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

      12. remove-double-neg 46.9%

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

      13. *-commutative 46.9%

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

      14. +-commutative 46.9%

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

      15. *-commutative 46.9%

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

      16. mul-1-neg 46.9%

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

      17. unsub-neg 46.9%

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

      18. *-commutative 46.9%

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

   8. Simplified 46.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.46 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -360000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -360000000.0)
     t_1
     (if (<= c -2.5e-110)
       (* x (* y z))
       (if (<= c 1.5e-11) (* a (- (* b i) (* 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -360000000.0) {
		tmp = t_1;
	} else if (c <= -2.5e-110) {
		tmp = x * (y * z);
	} else if (c <= 1.5e-11) {
		tmp = a * ((b * i) - (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 = c * ((t * j) - (z * b))
    if (c <= (-360000000.0d0)) then
        tmp = t_1
    else if (c <= (-2.5d-110)) then
        tmp = x * (y * z)
    else if (c <= 1.5d-11) then
        tmp = a * ((b * i) - (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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -360000000.0) {
		tmp = t_1;
	} else if (c <= -2.5e-110) {
		tmp = x * (y * z);
	} else if (c <= 1.5e-11) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -360000000.0:
		tmp = t_1
	elif c <= -2.5e-110:
		tmp = x * (y * z)
	elif c <= 1.5e-11:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -360000000.0)
		tmp = t_1;
	elseif (c <= -2.5e-110)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1.5e-11)
		tmp = Float64(a * Float64(Float64(b * i) - 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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -360000000.0)
		tmp = t_1;
	elseif (c <= -2.5e-110)
		tmp = x * (y * z);
	elseif (c <= 1.5e-11)
		tmp = a * ((b * i) - (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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -360000000.0], t$95$1, If[LessEqual[c, -2.5e-110], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e-11], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.6e8 or 1.5e-11 < c

   1. Initial program 60.5%

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

   3. Taylor expanded in c around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if -3.6e8 < c < -2.5e-110

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in x around inf 52.8%

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

   if -2.5e-110 < c < 1.5e-11

   1. Initial program 83.9%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. distribute-lft-out-- 47.4%

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

      2. *-commutative 47.4%

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

      3. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in a around 0 47.4%

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

      1. mul-1-neg 47.4%

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

      2. *-commutative 47.4%

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

      3. *-commutative 47.4%

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

      4. distribute-rgt-neg-out 47.4%

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

      5. neg-mul-1 47.4%

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

      6. *-commutative 47.4%

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

      7. *-commutative 47.4%

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

      8. distribute-lft-out-- 47.4%

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

      9. sub-neg 47.4%

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

      10. mul-1-neg 47.4%

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

      11. *-commutative 47.4%

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

      12. remove-double-neg 47.4%

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

      13. *-commutative 47.4%

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

      14. +-commutative 47.4%

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

      15. *-commutative 47.4%

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

      16. mul-1-neg 47.4%

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

      17. unsub-neg 47.4%

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

      18. *-commutative 47.4%

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

   8. Simplified 47.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -360000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+262}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.3e+146)
   (* z (* x y))
   (if (<= x 1.2e+68)
     (* b (- (* a i) (* z c)))
     (if (<= x 2.1e+262) (* a (- (* b i) (* x t))) (* x (* y 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 (x <= -1.3e+146) {
		tmp = z * (x * y);
	} else if (x <= 1.2e+68) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 2.1e+262) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = x * (y * 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 (x <= (-1.3d+146)) then
        tmp = z * (x * y)
    else if (x <= 1.2d+68) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 2.1d+262) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = x * (y * 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 (x <= -1.3e+146) {
		tmp = z * (x * y);
	} else if (x <= 1.2e+68) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 2.1e+262) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.3e+146:
		tmp = z * (x * y)
	elif x <= 1.2e+68:
		tmp = b * ((a * i) - (z * c))
	elif x <= 2.1e+262:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.3e+146)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 1.2e+68)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 2.1e+262)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.3e+146)
		tmp = z * (x * y);
	elseif (x <= 1.2e+68)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 2.1e+262)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.3e+146], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+68], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+262], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.30000000000000007e146

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -1.30000000000000007e146 < x < 1.20000000000000004e68

   1. Initial program 75.9%

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

   3. Taylor expanded in b around inf 40.3%

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

      1. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   if 1.20000000000000004e68 < x < 2.09999999999999989e262

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. distribute-lft-out-- 59.1%

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

      2. *-commutative 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in a around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. *-commutative 59.1%

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

      4. distribute-rgt-neg-out 59.1%

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

      5. neg-mul-1 59.1%

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

      6. *-commutative 59.1%

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

      7. *-commutative 59.1%

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

      8. distribute-lft-out-- 59.1%

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

      9. sub-neg 59.1%

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

      10. mul-1-neg 59.1%

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

      11. *-commutative 59.1%

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

      12. remove-double-neg 59.1%

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

      13. *-commutative 59.1%

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

      14. +-commutative 59.1%

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

      15. *-commutative 59.1%

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

      16. mul-1-neg 59.1%

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

      17. unsub-neg 59.1%

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

      18. *-commutative 59.1%

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

   8. Simplified 59.1%

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

   if 2.09999999999999989e262 < x

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in x around inf 70.0%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+262}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+111}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2e-26)
   (* x (* y z))
   (if (<= z 2.5e-68)
     (* a (- (* b i) (* x t)))
     (if (<= z 1.3e+111) (* (- y) (* i j)) (* 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 (z <= -2e-26) {
		tmp = x * (y * z);
	} else if (z <= 2.5e-68) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.3e+111) {
		tmp = -y * (i * j);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2d-26)) then
        tmp = x * (y * z)
    else if (z <= 2.5d-68) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.3d+111) then
        tmp = -y * (i * j)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2e-26) {
		tmp = x * (y * z);
	} else if (z <= 2.5e-68) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.3e+111) {
		tmp = -y * (i * j);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2e-26:
		tmp = x * (y * z)
	elif z <= 2.5e-68:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.3e+111:
		tmp = -y * (i * j)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2e-26)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 2.5e-68)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.3e+111)
		tmp = Float64(Float64(-y) * Float64(i * j));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2e-26)
		tmp = x * (y * z);
	elseif (z <= 2.5e-68)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.3e+111)
		tmp = -y * (i * j);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2e-26], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-68], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+111], N[((-y) * N[(i * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0000000000000001e-26

   1. Initial program 67.6%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around inf 45.4%

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

   if -2.0000000000000001e-26 < z < 2.49999999999999986e-68

   1. Initial program 80.7%

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

   3. Taylor expanded in a around inf 49.1%

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

      1. distribute-lft-out-- 49.1%

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

      2. *-commutative 49.1%

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

      3. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in a around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. *-commutative 49.1%

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

      3. *-commutative 49.1%

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

      4. distribute-rgt-neg-out 49.1%

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

      5. neg-mul-1 49.1%

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

      6. *-commutative 49.1%

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

      7. *-commutative 49.1%

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

      8. distribute-lft-out-- 49.1%

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

      9. sub-neg 49.1%

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

      10. mul-1-neg 49.1%

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

      11. *-commutative 49.1%

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

      12. remove-double-neg 49.1%

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

      13. *-commutative 49.1%

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

      14. +-commutative 49.1%

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

      15. *-commutative 49.1%

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

      16. mul-1-neg 49.1%

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

      17. unsub-neg 49.1%

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

      18. *-commutative 49.1%

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

   8. Simplified 49.1%

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

   if 2.49999999999999986e-68 < z < 1.2999999999999999e111

   1. Initial program 78.1%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in x around 0 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-lft-neg-out 42.3%

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

      3. *-commutative 42.3%

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

   8. Simplified 42.3%

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

   if 1.2999999999999999e111 < z

   1. Initial program 59.7%

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

   3. Taylor expanded in b around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in a around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. distribute-rgt-neg-in 44.5%

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

      3. *-commutative 44.5%

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

      4. distribute-rgt-neg-in 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+111}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-57} \lor \neg \left(z \leq 1.7 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -3.9e-57) (not (<= z 1.7e-58))) (* x (* y z)) (* b (* a 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 ((z <= -3.9e-57) || !(z <= 1.7e-58)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * 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 ((z <= (-3.9d-57)) .or. (.not. (z <= 1.7d-58))) then
        tmp = x * (y * z)
    else
        tmp = b * (a * 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 ((z <= -3.9e-57) || !(z <= 1.7e-58)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -3.9e-57) or not (z <= 1.7e-58):
		tmp = x * (y * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -3.9e-57) || !(z <= 1.7e-58))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -3.9e-57) || ~((z <= 1.7e-58)))
		tmp = x * (y * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -3.9e-57], N[Not[LessEqual[z, 1.7e-58]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.90000000000000006e-57 or 1.69999999999999987e-58 < z

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x around inf 36.9%

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

   if -3.90000000000000006e-57 < z < 1.69999999999999987e-58

   1. Initial program 78.3%

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

   3. Taylor expanded in b around inf 37.8%

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

      1. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in a around inf 31.3%

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

      1. *-commutative 31.3%

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

   8. Simplified 31.3%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-57} \lor \neg \left(z \leq 1.7 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.9e-56)
   (* x (* y z))
   (if (<= z 3e-70) (* i (* a b)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.9e-56) {
		tmp = x * (y * z);
	} else if (z <= 3e-70) {
		tmp = i * (a * b);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.9d-56)) then
        tmp = x * (y * z)
    else if (z <= 3d-70) then
        tmp = i * (a * b)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.9e-56) {
		tmp = x * (y * z);
	} else if (z <= 3e-70) {
		tmp = i * (a * b);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.9e-56:
		tmp = x * (y * z)
	elif z <= 3e-70:
		tmp = i * (a * b)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.9e-56)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 3e-70)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.9e-56)
		tmp = x * (y * z);
	elseif (z <= 3e-70)
		tmp = i * (a * b);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.9e-56], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-70], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999991e-56

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around inf 43.1%

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

   if -2.89999999999999991e-56 < z < 3.0000000000000001e-70

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 36.9%

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

      1. *-commutative 36.9%

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

   5. Simplified 36.9%

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

   6. Taylor expanded in a around inf 30.6%

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

      1. *-commutative 30.6%

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

   8. Simplified 30.6%

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

   9. Taylor expanded in a around 0 30.6%

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

       1. associate-*r* 31.6%

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

   11. Simplified 31.6%

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

   if 3.0000000000000001e-70 < z

   1. Initial program 67.4%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in x around inf 31.6%

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

      1. *-commutative 31.6%

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

   8. Simplified 31.6%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-64}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.7e-54)
   (* x (* y z))
   (if (<= z 4.8e-64) (* b (* a i)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.7e-54) {
		tmp = x * (y * z);
	} else if (z <= 4.8e-64) {
		tmp = b * (a * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.7d-54)) then
        tmp = x * (y * z)
    else if (z <= 4.8d-64) then
        tmp = b * (a * i)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.7e-54) {
		tmp = x * (y * z);
	} else if (z <= 4.8e-64) {
		tmp = b * (a * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.7e-54:
		tmp = x * (y * z)
	elif z <= 4.8e-64:
		tmp = b * (a * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.7e-54)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 4.8e-64)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.7e-54)
		tmp = x * (y * z);
	elseif (z <= 4.8e-64)
		tmp = b * (a * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.7e-54], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-64], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999994e-54

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around inf 43.1%

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

   if -1.69999999999999994e-54 < z < 4.79999999999999997e-64

   1. Initial program 79.8%

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

   3. Taylor expanded in b around inf 37.5%

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

      1. *-commutative 37.5%

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

   5. Simplified 37.5%

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

   6. Taylor expanded in a around inf 30.9%

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

      1. *-commutative 30.9%

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

   8. Simplified 30.9%

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

   if 4.79999999999999997e-64 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around inf 32.0%

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

      1. *-commutative 32.0%

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

   8. Simplified 32.0%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-64}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -7e-57)
   (* x (* y z))
   (if (<= z 2.7e-59) (* b (* a 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 (z <= -7e-57) {
		tmp = x * (y * z);
	} else if (z <= 2.7e-59) {
		tmp = b * (a * 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 (z <= (-7d-57)) then
        tmp = x * (y * z)
    else if (z <= 2.7d-59) then
        tmp = b * (a * 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 (z <= -7e-57) {
		tmp = x * (y * z);
	} else if (z <= 2.7e-59) {
		tmp = b * (a * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -7e-57:
		tmp = x * (y * z)
	elif z <= 2.7e-59:
		tmp = b * (a * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -7e-57)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 2.7e-59)
		tmp = Float64(b * Float64(a * 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 (z <= -7e-57)
		tmp = x * (y * z);
	elseif (z <= 2.7e-59)
		tmp = b * (a * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -7e-57], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-59], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999983e-57

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around inf 43.1%

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

   if -6.99999999999999983e-57 < z < 2.6999999999999999e-59

   1. Initial program 78.3%

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

   3. Taylor expanded in b around inf 37.8%

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

      1. *-commutative 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in a around inf 31.3%

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

      1. *-commutative 31.3%

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

   8. Simplified 31.3%

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

   if 2.6999999999999999e-59 < z

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in x around inf 30.3%

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

      1. *-commutative 30.3%

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

   8. Simplified 30.3%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.86 \cdot 10^{+205}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z 1.86e+205) (* a (* b i)) (* a (* x t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 1.86e+205) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= 1.86d+205) then
        tmp = a * (b * i)
    else
        tmp = a * (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 1.86e+205) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= 1.86e+205:
		tmp = a * (b * i)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= 1.86e+205)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= 1.86e+205)
		tmp = a * (b * i);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, 1.86e+205], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.8600000000000001e205

   1. Initial program 74.4%

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

   3. Taylor expanded in b around inf 34.5%

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

      1. *-commutative 34.5%

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

   5. Simplified 34.5%

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

   6. Taylor expanded in a around inf 19.7%

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

      1. *-commutative 19.7%

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

   8. Simplified 19.7%

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

   if 1.8600000000000001e205 < z

   1. Initial program 60.5%

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

   3. Taylor expanded in a around inf 11.6%

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

      1. distribute-lft-out-- 11.6%

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

      2. *-commutative 11.6%

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

      3. *-commutative 11.6%

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

   5. Simplified 11.6%

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

   6. Taylor expanded in x around inf 11.5%

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

      1. associate-*r* 11.5%

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

      2. neg-mul-1 11.5%

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

      3. *-commutative 11.5%

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

   8. Simplified 11.5%

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

      1. neg-sub0 11.5%

         \[\leadsto \color{blue}{\left(0 - a\right)} \cdot \left(x \cdot t\right) \]

      2. sub-neg 11.5%

         \[\leadsto \color{blue}{\left(0 + \left(-a\right)\right)} \cdot \left(x \cdot t\right) \]

      3. add-sqr-sqrt 1.3%

         \[\leadsto \left(0 + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}}\right) \cdot \left(x \cdot t\right) \]

      4. sqrt-unprod 6.7%

         \[\leadsto \left(0 + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}}\right) \cdot \left(x \cdot t\right) \]

      5. sqr-neg 6.7%

         \[\leadsto \left(0 + \sqrt{\color{blue}{a \cdot a}}\right) \cdot \left(x \cdot t\right) \]

      6. sqrt-unprod 1.1%

         \[\leadsto \left(0 + \color{blue}{\sqrt{a} \cdot \sqrt{a}}\right) \cdot \left(x \cdot t\right) \]

      7. add-sqr-sqrt 21.8%

         \[\leadsto \left(0 + \color{blue}{a}\right) \cdot \left(x \cdot t\right) \]

   10. Applied egg-rr 21.8%

       \[\leadsto \color{blue}{\left(0 + a\right)} \cdot \left(x \cdot t\right) \]
   11. Step-by-step derivation

       1. +-lft-identity 21.8%

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

   12. Simplified 21.8%

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

4. Final simplification 19.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.86 \cdot 10^{+205}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.3%

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

3. Taylor expanded in b around inf 35.0%

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

   1. *-commutative 35.0%

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

5. Simplified 35.0%

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

6. Taylor expanded in a around inf 18.3%

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

   1. *-commutative 18.3%

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

8. Simplified 18.3%

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

9. Final simplification 18.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Developer Target 1: 68.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

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