Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.7% → 81.9%

Time: 27.5s

Alternatives: 25

Speedup: 0.5×

• 58.6% 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: 73.7% accurate, 1.0× speedup

Math

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

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: 81.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} 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))
	t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	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)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

Wolfram

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

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 92.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 x around inf 50.6%

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

      1. *-commutative 50.6%

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

   5. Simplified 50.6%

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

4. Final simplification 83.2%

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

Alternative 2: 42.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{-307}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-182}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-54} \lor \neg \left(b \leq 4.8 \cdot 10^{+40}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -6.8e-15)
     t_2
     (if (<= b -3.1e-126)
       t_1
       (if (<= b -1.16e-260)
         (* i (* y (- j)))
         (if (<= b 1.66e-307)
           (* (* x t) (- a))
           (if (<= b 5.1e-182)
             (* j (* t c))
             (if (<= b 8.5e-126)
               (* t (* x (- a)))
               (if (or (<= b 4.3e-54) (not (<= b 4.8e+40))) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.8e-15) {
		tmp = t_2;
	} else if (b <= -3.1e-126) {
		tmp = t_1;
	} else if (b <= -1.16e-260) {
		tmp = i * (y * -j);
	} else if (b <= 1.66e-307) {
		tmp = (x * t) * -a;
	} else if (b <= 5.1e-182) {
		tmp = j * (t * c);
	} else if (b <= 8.5e-126) {
		tmp = t * (x * -a);
	} else if ((b <= 4.3e-54) || !(b <= 4.8e+40)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-6.8d-15)) then
        tmp = t_2
    else if (b <= (-3.1d-126)) then
        tmp = t_1
    else if (b <= (-1.16d-260)) then
        tmp = i * (y * -j)
    else if (b <= 1.66d-307) then
        tmp = (x * t) * -a
    else if (b <= 5.1d-182) then
        tmp = j * (t * c)
    else if (b <= 8.5d-126) then
        tmp = t * (x * -a)
    else if ((b <= 4.3d-54) .or. (.not. (b <= 4.8d+40))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.8e-15) {
		tmp = t_2;
	} else if (b <= -3.1e-126) {
		tmp = t_1;
	} else if (b <= -1.16e-260) {
		tmp = i * (y * -j);
	} else if (b <= 1.66e-307) {
		tmp = (x * t) * -a;
	} else if (b <= 5.1e-182) {
		tmp = j * (t * c);
	} else if (b <= 8.5e-126) {
		tmp = t * (x * -a);
	} else if ((b <= 4.3e-54) || !(b <= 4.8e+40)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -6.8e-15:
		tmp = t_2
	elif b <= -3.1e-126:
		tmp = t_1
	elif b <= -1.16e-260:
		tmp = i * (y * -j)
	elif b <= 1.66e-307:
		tmp = (x * t) * -a
	elif b <= 5.1e-182:
		tmp = j * (t * c)
	elif b <= 8.5e-126:
		tmp = t * (x * -a)
	elif (b <= 4.3e-54) or not (b <= 4.8e+40):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.8e-15)
		tmp = t_2;
	elseif (b <= -3.1e-126)
		tmp = t_1;
	elseif (b <= -1.16e-260)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 1.66e-307)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 5.1e-182)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= 8.5e-126)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif ((b <= 4.3e-54) || !(b <= 4.8e+40))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.8e-15)
		tmp = t_2;
	elseif (b <= -3.1e-126)
		tmp = t_1;
	elseif (b <= -1.16e-260)
		tmp = i * (y * -j);
	elseif (b <= 1.66e-307)
		tmp = (x * t) * -a;
	elseif (b <= 5.1e-182)
		tmp = j * (t * c);
	elseif (b <= 8.5e-126)
		tmp = t * (x * -a);
	elseif ((b <= 4.3e-54) || ~((b <= 4.8e+40)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-15], t$95$2, If[LessEqual[b, -3.1e-126], t$95$1, If[LessEqual[b, -1.16e-260], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.66e-307], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 5.1e-182], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-126], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4.3e-54], N[Not[LessEqual[b, 4.8e+40]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.8000000000000001e-15 or 8.49999999999999938e-126 < b < 4.3e-54 or 4.8e40 < b

   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 b around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if -6.8000000000000001e-15 < b < -3.1000000000000001e-126 or 4.3e-54 < b < 4.8e40

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. *-commutative 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in y around inf 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

   if -3.1000000000000001e-126 < b < -1.15999999999999994e-260

   1. Initial program 62.9%

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

   3. Taylor expanded in b around 0 69.9%

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

   4. Taylor expanded in i around inf 33.5%

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

      1. associate-*r* 33.5%

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

      2. neg-mul-1 33.5%

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

   6. Simplified 33.5%

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

   if -1.15999999999999994e-260 < b < 1.66000000000000007e-307

   1. Initial program 58.4%

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

   3. Taylor expanded in t around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in j around 0 52.1%

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

      1. associate-*r* 52.1%

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

      2. neg-mul-1 52.1%

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

   8. Simplified 52.1%

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

   if 1.66000000000000007e-307 < b < 5.10000000000000017e-182

   1. Initial program 86.2%

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

   3. Taylor expanded in j around inf 69.1%

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

   4. Taylor expanded in c around inf 60.2%

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

      1. *-commutative 60.2%

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

      2. associate-*r* 64.6%

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

      3. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if 5.10000000000000017e-182 < b < 8.49999999999999938e-126

   1. Initial program 77.4%

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

   3. Taylor expanded in t around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in j around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-lft-neg-out 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

      \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{-307}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-182}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-54} \lor \neg \left(b \leq 4.8 \cdot 10^{+40}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.3 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+49}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i)))))
        (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -8.3e+65)
     t_2
     (if (<= a 6.5e-288)
       t_1
       (if (<= a 2.1e-240)
         (* z (- (* x y) (* b c)))
         (if (<= a 2.2e-16)
           t_1
           (if (<= a 1.8e+49)
             (* i (- (* a b) (* y j)))
             (if (<= a 1.42e+109) 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))) + (j * ((t * c) - (y * i)));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.3e+65) {
		tmp = t_2;
	} else if (a <= 6.5e-288) {
		tmp = t_1;
	} else if (a <= 2.1e-240) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 2.2e-16) {
		tmp = t_1;
	} else if (a <= 1.8e+49) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.42e+109) {
		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))) + (j * ((t * c) - (y * i)))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-8.3d+65)) then
        tmp = t_2
    else if (a <= 6.5d-288) then
        tmp = t_1
    else if (a <= 2.1d-240) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 2.2d-16) then
        tmp = t_1
    else if (a <= 1.8d+49) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 1.42d+109) 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))) + (j * ((t * c) - (y * i)));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.3e+65) {
		tmp = t_2;
	} else if (a <= 6.5e-288) {
		tmp = t_1;
	} else if (a <= 2.1e-240) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 2.2e-16) {
		tmp = t_1;
	} else if (a <= 1.8e+49) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.42e+109) {
		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))) + (j * ((t * c) - (y * i)))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -8.3e+65:
		tmp = t_2
	elif a <= 6.5e-288:
		tmp = t_1
	elif a <= 2.1e-240:
		tmp = z * ((x * y) - (b * c))
	elif a <= 2.2e-16:
		tmp = t_1
	elif a <= 1.8e+49:
		tmp = i * ((a * b) - (y * j))
	elif a <= 1.42e+109:
		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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.3e+65)
		tmp = t_2;
	elseif (a <= 6.5e-288)
		tmp = t_1;
	elseif (a <= 2.1e-240)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 2.2e-16)
		tmp = t_1;
	elseif (a <= 1.8e+49)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 1.42e+109)
		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))) + (j * ((t * c) - (y * i)));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -8.3e+65)
		tmp = t_2;
	elseif (a <= 6.5e-288)
		tmp = t_1;
	elseif (a <= 2.1e-240)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 2.2e-16)
		tmp = t_1;
	elseif (a <= 1.8e+49)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 1.42e+109)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.3e+65], t$95$2, If[LessEqual[a, 6.5e-288], t$95$1, If[LessEqual[a, 2.1e-240], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-16], t$95$1, If[LessEqual[a, 1.8e+49], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e+109], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.3000000000000004e65 or 1.4200000000000001e109 < a

   1. Initial program 61.0%

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

   3. Taylor expanded in a around inf 76.0%

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

      1. distribute-lft-out-- 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -8.3000000000000004e65 < a < 6.4999999999999999e-288 or 2.09999999999999994e-240 < a < 2.2e-16 or 1.79999999999999998e49 < a < 1.4200000000000001e109

   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 b around 0 74.4%

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

   if 6.4999999999999999e-288 < a < 2.09999999999999994e-240

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if 2.2e-16 < a < 1.79999999999999998e49

   1. Initial program 66.5%

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

   3. Taylor expanded in i around inf 75.0%

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

      1. distribute-lft-out-- 75.0%

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

      2. *-commutative 75.0%

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

   5. Simplified 75.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.3 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+49}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;t\_2 - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1750000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{a \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i)))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.8e-12)
     (- t_2 (* t (- (* x a) (* c j))))
     (if (<= b 5.6e-83)
       t_1
       (if (<= b 1.4e-55)
         (* i (- (* a b) (* y j)))
         (if (<= b 1750000000000.0)
           t_1
           (if (<= b 5.2e+71)
             (* i (* y (- (/ (* a b) y) j)))
             (if (<= b 4.5e+152) 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))) + (j * ((t * c) - (y * i)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.8e-12) {
		tmp = t_2 - (t * ((x * a) - (c * j)));
	} else if (b <= 5.6e-83) {
		tmp = t_1;
	} else if (b <= 1.4e-55) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= 1750000000000.0) {
		tmp = t_1;
	} else if (b <= 5.2e+71) {
		tmp = i * (y * (((a * b) / y) - j));
	} else if (b <= 4.5e+152) {
		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))) + (j * ((t * c) - (y * i)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-3.8d-12)) then
        tmp = t_2 - (t * ((x * a) - (c * j)))
    else if (b <= 5.6d-83) then
        tmp = t_1
    else if (b <= 1.4d-55) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= 1750000000000.0d0) then
        tmp = t_1
    else if (b <= 5.2d+71) then
        tmp = i * (y * (((a * b) / y) - j))
    else if (b <= 4.5d+152) 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))) + (j * ((t * c) - (y * i)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.8e-12) {
		tmp = t_2 - (t * ((x * a) - (c * j)));
	} else if (b <= 5.6e-83) {
		tmp = t_1;
	} else if (b <= 1.4e-55) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= 1750000000000.0) {
		tmp = t_1;
	} else if (b <= 5.2e+71) {
		tmp = i * (y * (((a * b) / y) - j));
	} else if (b <= 4.5e+152) {
		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))) + (j * ((t * c) - (y * i)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.8e-12:
		tmp = t_2 - (t * ((x * a) - (c * j)))
	elif b <= 5.6e-83:
		tmp = t_1
	elif b <= 1.4e-55:
		tmp = i * ((a * b) - (y * j))
	elif b <= 1750000000000.0:
		tmp = t_1
	elif b <= 5.2e+71:
		tmp = i * (y * (((a * b) / y) - j))
	elif b <= 4.5e+152:
		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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.8e-12)
		tmp = Float64(t_2 - Float64(t * Float64(Float64(x * a) - Float64(c * j))));
	elseif (b <= 5.6e-83)
		tmp = t_1;
	elseif (b <= 1.4e-55)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= 1750000000000.0)
		tmp = t_1;
	elseif (b <= 5.2e+71)
		tmp = Float64(i * Float64(y * Float64(Float64(Float64(a * b) / y) - j)));
	elseif (b <= 4.5e+152)
		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))) + (j * ((t * c) - (y * i)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.8e-12)
		tmp = t_2 - (t * ((x * a) - (c * j)));
	elseif (b <= 5.6e-83)
		tmp = t_1;
	elseif (b <= 1.4e-55)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= 1750000000000.0)
		tmp = t_1;
	elseif (b <= 5.2e+71)
		tmp = i * (y * (((a * b) / y) - j));
	elseif (b <= 4.5e+152)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e-12], N[(t$95$2 - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e-83], t$95$1, If[LessEqual[b, 1.4e-55], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1750000000000.0], t$95$1, If[LessEqual[b, 5.2e+71], N[(i * N[(y * N[(N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+152], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.79999999999999996e-12

   1. Initial program 75.8%

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

   3. Taylor expanded in y around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. associate-*r* 71.0%

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

      3. *-commutative 71.0%

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

      4. associate-*l* 69.3%

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

      5. distribute-rgt-neg-in 69.3%

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

      6. mul-1-neg 69.3%

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

      7. *-commutative 69.3%

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

      8. *-commutative 69.3%

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

      9. associate-*r* 69.4%

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

      10. *-commutative 69.4%

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

      11. distribute-lft-in 71.1%

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

      12. +-commutative 71.1%

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

      13. mul-1-neg 71.1%

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

      14. unsub-neg 71.1%

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

      15. *-commutative 71.1%

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

      16. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   if -3.79999999999999996e-12 < b < 5.6000000000000002e-83 or 1.39999999999999992e-55 < b < 1.75e12 or 5.19999999999999983e71 < b < 4.5000000000000001e152

   1. Initial program 76.5%

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

   3. Taylor expanded in b around 0 79.1%

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

   if 5.6000000000000002e-83 < b < 1.39999999999999992e-55

   1. Initial program 63.7%

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

   3. Taylor expanded in i around inf 84.9%

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

      1. distribute-lft-out-- 84.9%

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

      2. *-commutative 84.9%

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

   5. Simplified 84.9%

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

   if 1.75e12 < b < 5.19999999999999983e71

   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 c around 0 53.6%

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

   4. Taylor expanded in y around inf 61.9%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in i around inf 77.3%

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

   if 4.5000000000000001e152 < b

   1. Initial program 55.7%

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

   3. Taylor expanded in b around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1750000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{a \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 30.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-247}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-66}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -4.2e+132)
   (* t (* c j))
   (if (<= c -3.6e-21)
     (* z (- (* b c)))
     (if (<= c -1.8e-222)
       (* t (* x (- a)))
       (if (<= c 1.25e-247)
         (* b (* a i))
         (if (<= c 1.45e-184)
           (* z (* x y))
           (if (<= c 2.6e-150)
             (* a (* b i))
             (if (<= c 5e-66)
               (* (* y i) (- j))
               (if (<= c 3.1e-41) (* x (* y z)) (* j (* t 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 (c <= -4.2e+132) {
		tmp = t * (c * j);
	} else if (c <= -3.6e-21) {
		tmp = z * -(b * c);
	} else if (c <= -1.8e-222) {
		tmp = t * (x * -a);
	} else if (c <= 1.25e-247) {
		tmp = b * (a * i);
	} else if (c <= 1.45e-184) {
		tmp = z * (x * y);
	} else if (c <= 2.6e-150) {
		tmp = a * (b * i);
	} else if (c <= 5e-66) {
		tmp = (y * i) * -j;
	} else if (c <= 3.1e-41) {
		tmp = x * (y * z);
	} else {
		tmp = j * (t * 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 (c <= (-4.2d+132)) then
        tmp = t * (c * j)
    else if (c <= (-3.6d-21)) then
        tmp = z * -(b * c)
    else if (c <= (-1.8d-222)) then
        tmp = t * (x * -a)
    else if (c <= 1.25d-247) then
        tmp = b * (a * i)
    else if (c <= 1.45d-184) then
        tmp = z * (x * y)
    else if (c <= 2.6d-150) then
        tmp = a * (b * i)
    else if (c <= 5d-66) then
        tmp = (y * i) * -j
    else if (c <= 3.1d-41) then
        tmp = x * (y * z)
    else
        tmp = j * (t * 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 (c <= -4.2e+132) {
		tmp = t * (c * j);
	} else if (c <= -3.6e-21) {
		tmp = z * -(b * c);
	} else if (c <= -1.8e-222) {
		tmp = t * (x * -a);
	} else if (c <= 1.25e-247) {
		tmp = b * (a * i);
	} else if (c <= 1.45e-184) {
		tmp = z * (x * y);
	} else if (c <= 2.6e-150) {
		tmp = a * (b * i);
	} else if (c <= 5e-66) {
		tmp = (y * i) * -j;
	} else if (c <= 3.1e-41) {
		tmp = x * (y * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -4.2e+132:
		tmp = t * (c * j)
	elif c <= -3.6e-21:
		tmp = z * -(b * c)
	elif c <= -1.8e-222:
		tmp = t * (x * -a)
	elif c <= 1.25e-247:
		tmp = b * (a * i)
	elif c <= 1.45e-184:
		tmp = z * (x * y)
	elif c <= 2.6e-150:
		tmp = a * (b * i)
	elif c <= 5e-66:
		tmp = (y * i) * -j
	elif c <= 3.1e-41:
		tmp = x * (y * z)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -4.2e+132)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= -3.6e-21)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (c <= -1.8e-222)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 1.25e-247)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 1.45e-184)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 2.6e-150)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 5e-66)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (c <= 3.1e-41)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -4.2e+132)
		tmp = t * (c * j);
	elseif (c <= -3.6e-21)
		tmp = z * -(b * c);
	elseif (c <= -1.8e-222)
		tmp = t * (x * -a);
	elseif (c <= 1.25e-247)
		tmp = b * (a * i);
	elseif (c <= 1.45e-184)
		tmp = z * (x * y);
	elseif (c <= 2.6e-150)
		tmp = a * (b * i);
	elseif (c <= 5e-66)
		tmp = (y * i) * -j;
	elseif (c <= 3.1e-41)
		tmp = x * (y * z);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -4.2e+132], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e-21], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[c, -1.8e-222], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-247], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e-184], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e-150], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e-66], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, 3.1e-41], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -4.19999999999999987e132

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in j around inf 39.2%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -4.19999999999999987e132 < c < -3.59999999999999989e-21

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around 0 38.8%

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

      1. neg-mul-1 38.8%

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

      2. *-commutative 38.8%

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

      3. distribute-rgt-neg-in 38.8%

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

   8. Simplified 38.8%

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

   if -3.59999999999999989e-21 < c < -1.79999999999999987e-222

   1. Initial program 87.2%

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

   3. Taylor expanded in t around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in j around 0 31.6%

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

      1. mul-1-neg 31.6%

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

      2. distribute-lft-neg-out 31.6%

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

      3. *-commutative 31.6%

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

   8. Simplified 31.6%

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

   if -1.79999999999999987e-222 < c < 1.24999999999999994e-247

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf 47.4%

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

      1. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in i around inf 44.7%

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

      1. *-commutative 44.7%

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

   8. Simplified 44.7%

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

   if 1.24999999999999994e-247 < c < 1.45000000000000007e-184

   1. Initial program 68.6%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around inf 47.4%

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

      1. *-commutative 47.4%

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

   8. Simplified 47.4%

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

   if 1.45000000000000007e-184 < c < 2.5999999999999998e-150

   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 44.9%

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

      1. *-commutative 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in i around inf 55.5%

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

      1. *-commutative 55.5%

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

   8. Simplified 55.5%

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

   if 2.5999999999999998e-150 < c < 4.99999999999999962e-66

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 58.0%

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

   4. Taylor expanded in c around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-lft-neg-out 58.4%

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

      3. *-commutative 58.4%

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

   6. Simplified 58.4%

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

   if 4.99999999999999962e-66 < c < 3.10000000000000001e-41

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around inf 59.3%

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

   if 3.10000000000000001e-41 < c

   1. Initial program 69.6%

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

   3. Taylor expanded in j around inf 57.0%

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

   4. Taylor expanded in c around inf 39.9%

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

      1. *-commutative 39.9%

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

      2. associate-*r* 44.6%

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

      3. *-commutative 44.6%

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

   6. Simplified 44.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-247}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-66}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+49}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+109}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* x (* y z))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -2.5e+16)
     t_3
     (if (<= a 6.5e-288)
       t_2
       (if (<= a 4.5e-240)
         (* z (- (* x y) (* b c)))
         (if (<= a 8.5e-22)
           t_2
           (if (<= a 4.7e+49)
             (* i (- (* a b) (* y j)))
             (if (<= a 1.35e+109) (- t_1 (* a (* x t))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.5e+16) {
		tmp = t_3;
	} else if (a <= 6.5e-288) {
		tmp = t_2;
	} else if (a <= 4.5e-240) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 8.5e-22) {
		tmp = t_2;
	} else if (a <= 4.7e+49) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.35e+109) {
		tmp = t_1 - (a * (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (x * (y * z))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-2.5d+16)) then
        tmp = t_3
    else if (a <= 6.5d-288) then
        tmp = t_2
    else if (a <= 4.5d-240) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 8.5d-22) then
        tmp = t_2
    else if (a <= 4.7d+49) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 1.35d+109) then
        tmp = t_1 - (a * (x * t))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.5e+16) {
		tmp = t_3;
	} else if (a <= 6.5e-288) {
		tmp = t_2;
	} else if (a <= 4.5e-240) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 8.5e-22) {
		tmp = t_2;
	} else if (a <= 4.7e+49) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.35e+109) {
		tmp = t_1 - (a * (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (x * (y * z))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.5e+16:
		tmp = t_3
	elif a <= 6.5e-288:
		tmp = t_2
	elif a <= 4.5e-240:
		tmp = z * ((x * y) - (b * c))
	elif a <= 8.5e-22:
		tmp = t_2
	elif a <= 4.7e+49:
		tmp = i * ((a * b) - (y * j))
	elif a <= 1.35e+109:
		tmp = t_1 - (a * (x * t))
	else:
		tmp = t_3
	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)))
	t_2 = Float64(t_1 + Float64(x * Float64(y * z)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.5e+16)
		tmp = t_3;
	elseif (a <= 6.5e-288)
		tmp = t_2;
	elseif (a <= 4.5e-240)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 8.5e-22)
		tmp = t_2;
	elseif (a <= 4.7e+49)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 1.35e+109)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 + (x * (y * z));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2.5e+16)
		tmp = t_3;
	elseif (a <= 6.5e-288)
		tmp = t_2;
	elseif (a <= 4.5e-240)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 8.5e-22)
		tmp = t_2;
	elseif (a <= 4.7e+49)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 1.35e+109)
		tmp = t_1 - (a * (x * t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+16], t$95$3, If[LessEqual[a, 6.5e-288], t$95$2, If[LessEqual[a, 4.5e-240], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-22], t$95$2, If[LessEqual[a, 4.7e+49], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+109], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5e16 or 1.35000000000000001e109 < a

   1. Initial program 61.9%

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

   3. Taylor expanded in a around inf 74.6%

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

      1. distribute-lft-out-- 74.6%

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

      2. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   if -2.5e16 < a < 6.4999999999999999e-288 or 4.5000000000000001e-240 < a < 8.5000000000000001e-22

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0 74.6%

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

   4. Taylor expanded in a around 0 66.5%

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

   if 6.4999999999999999e-288 < a < 4.5000000000000001e-240

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if 8.5000000000000001e-22 < a < 4.6999999999999997e49

   1. Initial program 66.5%

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

   3. Taylor expanded in i around inf 75.0%

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

      1. distribute-lft-out-- 75.0%

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

      2. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if 4.6999999999999997e49 < a < 1.35000000000000001e109

   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 b around 0 66.4%

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

   4. Taylor expanded in z around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. *-commutative 60.1%

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

      4. mul-1-neg 60.1%

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

      5. unsub-neg 60.1%

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

      6. *-commutative 60.1%

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

      7. *-commutative 60.1%

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

   6. Simplified 60.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+49}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+109}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+63} \lor \neg \left(b \leq 4.3 \cdot 10^{+145}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -1.55e+18)
     t_3
     (if (<= b -1.2e-232)
       t_2
       (if (<= b 2.8e-295)
         t_1
         (if (<= b 2.95e-64)
           t_2
           (if (<= b 4.8e+40)
             (* y (- (* x z) (* i j)))
             (if (or (<= b 3.1e+63) (not (<= b 4.3e+145))) t_3 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e+18) {
		tmp = t_3;
	} else if (b <= -1.2e-232) {
		tmp = t_2;
	} else if (b <= 2.8e-295) {
		tmp = t_1;
	} else if (b <= 2.95e-64) {
		tmp = t_2;
	} else if (b <= 4.8e+40) {
		tmp = y * ((x * z) - (i * j));
	} else if ((b <= 3.1e+63) || !(b <= 4.3e+145)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-1.55d+18)) then
        tmp = t_3
    else if (b <= (-1.2d-232)) then
        tmp = t_2
    else if (b <= 2.8d-295) then
        tmp = t_1
    else if (b <= 2.95d-64) then
        tmp = t_2
    else if (b <= 4.8d+40) then
        tmp = y * ((x * z) - (i * j))
    else if ((b <= 3.1d+63) .or. (.not. (b <= 4.3d+145))) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.55e+18) {
		tmp = t_3;
	} else if (b <= -1.2e-232) {
		tmp = t_2;
	} else if (b <= 2.8e-295) {
		tmp = t_1;
	} else if (b <= 2.95e-64) {
		tmp = t_2;
	} else if (b <= 4.8e+40) {
		tmp = y * ((x * z) - (i * j));
	} else if ((b <= 3.1e+63) || !(b <= 4.3e+145)) {
		tmp = t_3;
	} 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))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.55e+18:
		tmp = t_3
	elif b <= -1.2e-232:
		tmp = t_2
	elif b <= 2.8e-295:
		tmp = t_1
	elif b <= 2.95e-64:
		tmp = t_2
	elif b <= 4.8e+40:
		tmp = y * ((x * z) - (i * j))
	elif (b <= 3.1e+63) or not (b <= 4.3e+145):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.55e+18)
		tmp = t_3;
	elseif (b <= -1.2e-232)
		tmp = t_2;
	elseif (b <= 2.8e-295)
		tmp = t_1;
	elseif (b <= 2.95e-64)
		tmp = t_2;
	elseif (b <= 4.8e+40)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif ((b <= 3.1e+63) || !(b <= 4.3e+145))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.55e+18)
		tmp = t_3;
	elseif (b <= -1.2e-232)
		tmp = t_2;
	elseif (b <= 2.8e-295)
		tmp = t_1;
	elseif (b <= 2.95e-64)
		tmp = t_2;
	elseif (b <= 4.8e+40)
		tmp = y * ((x * z) - (i * j));
	elseif ((b <= 3.1e+63) || ~((b <= 4.3e+145)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+18], t$95$3, If[LessEqual[b, -1.2e-232], t$95$2, If[LessEqual[b, 2.8e-295], t$95$1, If[LessEqual[b, 2.95e-64], t$95$2, If[LessEqual[b, 4.8e+40], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3.1e+63], N[Not[LessEqual[b, 4.3e+145]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55e18 or 4.8e40 < b < 3.1000000000000001e63 or 4.29999999999999998e145 < b

   1. Initial program 67.2%

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

   3. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if -1.55e18 < b < -1.19999999999999999e-232 or 2.7999999999999999e-295 < b < 2.94999999999999997e-64

   1. Initial program 75.5%

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

   3. Taylor expanded in t around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   if -1.19999999999999999e-232 < b < 2.7999999999999999e-295 or 3.1000000000000001e63 < b < 4.29999999999999998e145

   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 j around inf 66.0%

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

   if 2.94999999999999997e-64 < b < 4.8e40

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

      5. *-commutative 57.4%

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

   5. Simplified 57.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+63} \lor \neg \left(b \leq 4.3 \cdot 10^{+145}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -1.05e+16)
     t_3
     (if (<= b -2.8e-232)
       t_2
       (if (<= b 4.9e-293)
         t_1
         (if (<= b 7.8e-68)
           t_2
           (if (<= b 2.1e+25)
             t_1
             (if (<= b 5.5e+71)
               (* a (* b i))
               (if (<= b 3.3e+146) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.05e+16) {
		tmp = t_3;
	} else if (b <= -2.8e-232) {
		tmp = t_2;
	} else if (b <= 4.9e-293) {
		tmp = t_1;
	} else if (b <= 7.8e-68) {
		tmp = t_2;
	} else if (b <= 2.1e+25) {
		tmp = t_1;
	} else if (b <= 5.5e+71) {
		tmp = a * (b * i);
	} else if (b <= 3.3e+146) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-1.05d+16)) then
        tmp = t_3
    else if (b <= (-2.8d-232)) then
        tmp = t_2
    else if (b <= 4.9d-293) then
        tmp = t_1
    else if (b <= 7.8d-68) then
        tmp = t_2
    else if (b <= 2.1d+25) then
        tmp = t_1
    else if (b <= 5.5d+71) then
        tmp = a * (b * i)
    else if (b <= 3.3d+146) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.05e+16) {
		tmp = t_3;
	} else if (b <= -2.8e-232) {
		tmp = t_2;
	} else if (b <= 4.9e-293) {
		tmp = t_1;
	} else if (b <= 7.8e-68) {
		tmp = t_2;
	} else if (b <= 2.1e+25) {
		tmp = t_1;
	} else if (b <= 5.5e+71) {
		tmp = a * (b * i);
	} else if (b <= 3.3e+146) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.05e+16:
		tmp = t_3
	elif b <= -2.8e-232:
		tmp = t_2
	elif b <= 4.9e-293:
		tmp = t_1
	elif b <= 7.8e-68:
		tmp = t_2
	elif b <= 2.1e+25:
		tmp = t_1
	elif b <= 5.5e+71:
		tmp = a * (b * i)
	elif b <= 3.3e+146:
		tmp = t_1
	else:
		tmp = t_3
	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)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.05e+16)
		tmp = t_3;
	elseif (b <= -2.8e-232)
		tmp = t_2;
	elseif (b <= 4.9e-293)
		tmp = t_1;
	elseif (b <= 7.8e-68)
		tmp = t_2;
	elseif (b <= 2.1e+25)
		tmp = t_1;
	elseif (b <= 5.5e+71)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 3.3e+146)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.05e+16)
		tmp = t_3;
	elseif (b <= -2.8e-232)
		tmp = t_2;
	elseif (b <= 4.9e-293)
		tmp = t_1;
	elseif (b <= 7.8e-68)
		tmp = t_2;
	elseif (b <= 2.1e+25)
		tmp = t_1;
	elseif (b <= 5.5e+71)
		tmp = a * (b * i);
	elseif (b <= 3.3e+146)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+16], t$95$3, If[LessEqual[b, -2.8e-232], t$95$2, If[LessEqual[b, 4.9e-293], t$95$1, If[LessEqual[b, 7.8e-68], t$95$2, If[LessEqual[b, 2.1e+25], t$95$1, If[LessEqual[b, 5.5e+71], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+146], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.05e16 or 3.30000000000000016e146 < b

   1. Initial program 67.2%

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

   3. Taylor expanded in b around inf 65.9%

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

      1. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   if -1.05e16 < b < -2.79999999999999993e-232 or 4.9e-293 < b < 7.80000000000000064e-68

   1. Initial program 75.2%

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

   3. Taylor expanded in t around inf 57.5%

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

      1. +-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

      4. *-commutative 57.5%

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

   5. Simplified 57.5%

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

   if -2.79999999999999993e-232 < b < 4.9e-293 or 7.80000000000000064e-68 < b < 2.0999999999999999e25 or 5.5e71 < b < 3.30000000000000016e146

   1. Initial program 77.3%

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

   3. Taylor expanded in j around inf 61.9%

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

   if 2.0999999999999999e25 < b < 5.5e71

   1. Initial program 49.7%

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

   3. Taylor expanded in b around inf 58.5%

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

      1. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in i around inf 58.8%

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

      1. *-commutative 58.8%

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

   8. Simplified 58.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-232}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-293}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+146}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;c \leq -9.2 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -8.3 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= c -9.2e+127)
     (* t (- (* c j) (* x a)))
     (if (<= c -4.2e-21)
       (* z (- (* x y) (* b c)))
       (if (<= c -8.3e-252)
         (* a (- (* b i) (* x t)))
         (if (<= c -1.7e-301)
           (* y (- (* x z) (* i j)))
           (if (<= c 3.4e-206)
             t_1
             (if (<= c 4e-66)
               (* i (- (* a b) (* y j)))
               (if (<= c 3.9e-29) t_1 (* c (- (* t j) (* z b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -9.2e+127) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -4.2e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -8.3e-252) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -1.7e-301) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.4e-206) {
		tmp = t_1;
	} else if (c <= 4e-66) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 3.9e-29) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (c <= (-9.2d+127)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-4.2d-21)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-8.3d-252)) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= (-1.7d-301)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 3.4d-206) then
        tmp = t_1
    else if (c <= 4d-66) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 3.9d-29) then
        tmp = t_1
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -9.2e+127) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -4.2e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -8.3e-252) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -1.7e-301) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.4e-206) {
		tmp = t_1;
	} else if (c <= 4e-66) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 3.9e-29) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if c <= -9.2e+127:
		tmp = t * ((c * j) - (x * a))
	elif c <= -4.2e-21:
		tmp = z * ((x * y) - (b * c))
	elif c <= -8.3e-252:
		tmp = a * ((b * i) - (x * t))
	elif c <= -1.7e-301:
		tmp = y * ((x * z) - (i * j))
	elif c <= 3.4e-206:
		tmp = t_1
	elif c <= 4e-66:
		tmp = i * ((a * b) - (y * j))
	elif c <= 3.9e-29:
		tmp = t_1
	else:
		tmp = c * ((t * j) - (z * b))
	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 (c <= -9.2e+127)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -4.2e-21)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -8.3e-252)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= -1.7e-301)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 3.4e-206)
		tmp = t_1;
	elseif (c <= 4e-66)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 3.9e-29)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (c <= -9.2e+127)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -4.2e-21)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -8.3e-252)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= -1.7e-301)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 3.4e-206)
		tmp = t_1;
	elseif (c <= 4e-66)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 3.9e-29)
		tmp = t_1;
	else
		tmp = c * ((t * j) - (z * b));
	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[c, -9.2e+127], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.2e-21], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.3e-252], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-301], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e-206], t$95$1, If[LessEqual[c, 4e-66], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e-29], t$95$1, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -9.2000000000000007e127

   1. Initial program 55.2%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

      4. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   if -9.2000000000000007e127 < c < -4.20000000000000025e-21

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -4.20000000000000025e-21 < c < -8.29999999999999968e-252

   1. Initial program 87.8%

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

   3. Taylor expanded in a around inf 58.0%

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

      1. distribute-lft-out-- 58.0%

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

      2. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   if -8.29999999999999968e-252 < c < -1.7000000000000001e-301

   1. Initial program 38.9%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -1.7000000000000001e-301 < c < 3.39999999999999985e-206 or 3.9999999999999999e-66 < c < 3.8999999999999998e-29

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 64.5%

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

      1. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   if 3.39999999999999985e-206 < c < 3.9999999999999999e-66

   1. Initial program 67.2%

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

   3. Taylor expanded in i around inf 78.0%

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

      1. distribute-lft-out-- 78.0%

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

      2. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   if 3.8999999999999998e-29 < c

   1. Initial program 69.2%

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

   3. Taylor expanded in c around inf 60.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -8.3 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{elif}\;a \leq 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - a \cdot \left(x \cdot t\right)\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1)))
   (if (<= a -1.7e+66)
     (* a (- (* b i) (* x t)))
     (if (<= a 6.5e-288)
       t_2
       (if (<= a 1.95e-235)
         (- (* b (- (* a i) (* z c))) (* t (- (* x a) (* c j))))
         (if (<= a 1e-34) t_2 (+ (- t_1 (* a (* x t))) (* a (* b i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double tmp;
	if (a <= -1.7e+66) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= 6.5e-288) {
		tmp = t_2;
	} else if (a <= 1.95e-235) {
		tmp = (b * ((a * i) - (z * c))) - (t * ((x * a) - (c * j)));
	} else if (a <= 1e-34) {
		tmp = t_2;
	} else {
		tmp = (t_1 - (a * (x * t))) + (a * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    if (a <= (-1.7d+66)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= 6.5d-288) then
        tmp = t_2
    else if (a <= 1.95d-235) then
        tmp = (b * ((a * i) - (z * c))) - (t * ((x * a) - (c * j)))
    else if (a <= 1d-34) then
        tmp = t_2
    else
        tmp = (t_1 - (a * (x * t))) + (a * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double tmp;
	if (a <= -1.7e+66) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= 6.5e-288) {
		tmp = t_2;
	} else if (a <= 1.95e-235) {
		tmp = (b * ((a * i) - (z * c))) - (t * ((x * a) - (c * j)));
	} else if (a <= 1e-34) {
		tmp = t_2;
	} else {
		tmp = (t_1 - (a * (x * t))) + (a * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = (x * ((y * z) - (t * a))) + t_1
	tmp = 0
	if a <= -1.7e+66:
		tmp = a * ((b * i) - (x * t))
	elif a <= 6.5e-288:
		tmp = t_2
	elif a <= 1.95e-235:
		tmp = (b * ((a * i) - (z * c))) - (t * ((x * a) - (c * j)))
	elif a <= 1e-34:
		tmp = t_2
	else:
		tmp = (t_1 - (a * (x * t))) + (a * (b * i))
	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)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	tmp = 0.0
	if (a <= -1.7e+66)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= 6.5e-288)
		tmp = t_2;
	elseif (a <= 1.95e-235)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(t * Float64(Float64(x * a) - Float64(c * j))));
	elseif (a <= 1e-34)
		tmp = t_2;
	else
		tmp = Float64(Float64(t_1 - Float64(a * Float64(x * t))) + Float64(a * Float64(b * i)));
	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));
	t_2 = (x * ((y * z) - (t * a))) + t_1;
	tmp = 0.0;
	if (a <= -1.7e+66)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= 6.5e-288)
		tmp = t_2;
	elseif (a <= 1.95e-235)
		tmp = (b * ((a * i) - (z * c))) - (t * ((x * a) - (c * j)));
	elseif (a <= 1e-34)
		tmp = t_2;
	else
		tmp = (t_1 - (a * (x * t))) + (a * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[a, -1.7e+66], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-288], t$95$2, If[LessEqual[a, 1.95e-235], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-34], t$95$2, N[(N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.70000000000000015e66

   1. Initial program 59.3%

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

   3. Taylor expanded in a around inf 81.8%

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

      1. distribute-lft-out-- 81.8%

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

      2. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   if -1.70000000000000015e66 < a < 6.4999999999999999e-288 or 1.94999999999999985e-235 < a < 9.99999999999999928e-35

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0 75.4%

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

   if 6.4999999999999999e-288 < a < 1.94999999999999985e-235

   1. Initial program 67.2%

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

   3. Taylor expanded in y around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. associate-*r* 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*l* 74.3%

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

      5. distribute-rgt-neg-in 74.3%

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

      6. mul-1-neg 74.3%

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

      7. *-commutative 74.3%

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

      8. *-commutative 74.3%

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

      9. associate-*r* 74.3%

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

      10. *-commutative 74.3%

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

      11. distribute-lft-in 74.3%

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

      12. +-commutative 74.3%

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

      13. mul-1-neg 74.3%

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

      14. unsub-neg 74.3%

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

      15. *-commutative 74.3%

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

      16. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if 9.99999999999999928e-35 < a

   1. Initial program 63.9%

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

   3. Taylor expanded in z around 0 68.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-288}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{elif}\;a \leq 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -4e+16)
     t_3
     (if (<= a 5.6e-288)
       t_2
       (if (<= a 1.15e-240)
         t_1
         (if (<= a 7.6e-25)
           t_2
           (if (<= a 5.4e+76)
             (* i (- (* a b) (* y j)))
             (if (<= a 3.3e+103) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4e+16) {
		tmp = t_3;
	} else if (a <= 5.6e-288) {
		tmp = t_2;
	} else if (a <= 1.15e-240) {
		tmp = t_1;
	} else if (a <= 7.6e-25) {
		tmp = t_2;
	} else if (a <= 5.4e+76) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 3.3e+103) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-4d+16)) then
        tmp = t_3
    else if (a <= 5.6d-288) then
        tmp = t_2
    else if (a <= 1.15d-240) then
        tmp = t_1
    else if (a <= 7.6d-25) then
        tmp = t_2
    else if (a <= 5.4d+76) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 3.3d+103) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4e+16) {
		tmp = t_3;
	} else if (a <= 5.6e-288) {
		tmp = t_2;
	} else if (a <= 1.15e-240) {
		tmp = t_1;
	} else if (a <= 7.6e-25) {
		tmp = t_2;
	} else if (a <= 5.4e+76) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 3.3e+103) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4e+16:
		tmp = t_3
	elif a <= 5.6e-288:
		tmp = t_2
	elif a <= 1.15e-240:
		tmp = t_1
	elif a <= 7.6e-25:
		tmp = t_2
	elif a <= 5.4e+76:
		tmp = i * ((a * b) - (y * j))
	elif a <= 3.3e+103:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4e+16)
		tmp = t_3;
	elseif (a <= 5.6e-288)
		tmp = t_2;
	elseif (a <= 1.15e-240)
		tmp = t_1;
	elseif (a <= 7.6e-25)
		tmp = t_2;
	elseif (a <= 5.4e+76)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 3.3e+103)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4e+16)
		tmp = t_3;
	elseif (a <= 5.6e-288)
		tmp = t_2;
	elseif (a <= 1.15e-240)
		tmp = t_1;
	elseif (a <= 7.6e-25)
		tmp = t_2;
	elseif (a <= 5.4e+76)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 3.3e+103)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+16], t$95$3, If[LessEqual[a, 5.6e-288], t$95$2, If[LessEqual[a, 1.15e-240], t$95$1, If[LessEqual[a, 7.6e-25], t$95$2, If[LessEqual[a, 5.4e+76], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+103], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4e16 or 3.30000000000000009e103 < a

   1. Initial program 62.8%

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

   3. Taylor expanded in a around inf 74.1%

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

      1. distribute-lft-out-- 74.1%

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

      2. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   if -4e16 < a < 5.5999999999999999e-288 or 1.14999999999999996e-240 < a < 7.5999999999999996e-25

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0 74.6%

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

   4. Taylor expanded in a around 0 66.5%

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

   if 5.5999999999999999e-288 < a < 1.14999999999999996e-240 or 5.3999999999999998e76 < a < 3.30000000000000009e103

   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 70.2%

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

      1. *-commutative 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if 7.5999999999999996e-25 < a < 5.3999999999999998e76

   1. Initial program 62.2%

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

   3. Taylor expanded in i around inf 69.1%

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

      1. distribute-lft-out-- 69.1%

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

      2. *-commutative 69.1%

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

   5. Simplified 69.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-288}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+135}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-141}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1950000000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= x -1.22e+135)
     (* z (* x y))
     (if (<= x -4e-78)
       (* (* y i) (- j))
       (if (<= x 1.42e-238)
         t_1
         (if (<= x 3.9e-141)
           (* c (* t j))
           (if (<= x 1950000000000.0)
             (* a (* b i))
             (if (<= x 3.25e+94) t_1 (* 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 t_1 = c * (z * -b);
	double tmp;
	if (x <= -1.22e+135) {
		tmp = z * (x * y);
	} else if (x <= -4e-78) {
		tmp = (y * i) * -j;
	} else if (x <= 1.42e-238) {
		tmp = t_1;
	} else if (x <= 3.9e-141) {
		tmp = c * (t * j);
	} else if (x <= 1950000000000.0) {
		tmp = a * (b * i);
	} else if (x <= 3.25e+94) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (x <= (-1.22d+135)) then
        tmp = z * (x * y)
    else if (x <= (-4d-78)) then
        tmp = (y * i) * -j
    else if (x <= 1.42d-238) then
        tmp = t_1
    else if (x <= 3.9d-141) then
        tmp = c * (t * j)
    else if (x <= 1950000000000.0d0) then
        tmp = a * (b * i)
    else if (x <= 3.25d+94) then
        tmp = t_1
    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 t_1 = c * (z * -b);
	double tmp;
	if (x <= -1.22e+135) {
		tmp = z * (x * y);
	} else if (x <= -4e-78) {
		tmp = (y * i) * -j;
	} else if (x <= 1.42e-238) {
		tmp = t_1;
	} else if (x <= 3.9e-141) {
		tmp = c * (t * j);
	} else if (x <= 1950000000000.0) {
		tmp = a * (b * i);
	} else if (x <= 3.25e+94) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if x <= -1.22e+135:
		tmp = z * (x * y)
	elif x <= -4e-78:
		tmp = (y * i) * -j
	elif x <= 1.42e-238:
		tmp = t_1
	elif x <= 3.9e-141:
		tmp = c * (t * j)
	elif x <= 1950000000000.0:
		tmp = a * (b * i)
	elif x <= 3.25e+94:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (x <= -1.22e+135)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= -4e-78)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (x <= 1.42e-238)
		tmp = t_1;
	elseif (x <= 3.9e-141)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 1950000000000.0)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 3.25e+94)
		tmp = t_1;
	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)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (x <= -1.22e+135)
		tmp = z * (x * y);
	elseif (x <= -4e-78)
		tmp = (y * i) * -j;
	elseif (x <= 1.42e-238)
		tmp = t_1;
	elseif (x <= 3.9e-141)
		tmp = c * (t * j);
	elseif (x <= 1950000000000.0)
		tmp = a * (b * i);
	elseif (x <= 3.25e+94)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e+135], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-78], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[x, 1.42e-238], t$95$1, If[LessEqual[x, 3.9e-141], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1950000000000.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.25e+94], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.21999999999999996e135

   1. Initial program 58.5%

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

   3. Taylor expanded in z around inf 38.8%

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

      1. *-commutative 38.8%

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

      2. *-commutative 38.8%

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

   5. Simplified 38.8%

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

   6. Taylor expanded in y around inf 30.8%

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

      1. *-commutative 30.8%

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

   8. Simplified 30.8%

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

   if -1.21999999999999996e135 < x < -4e-78

   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 j around inf 50.3%

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

   4. Taylor expanded in c around 0 31.1%

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

      1. mul-1-neg 31.1%

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

      2. distribute-lft-neg-out 31.1%

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

      3. *-commutative 31.1%

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

   6. Simplified 31.1%

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

   if -4e-78 < x < 1.4199999999999999e-238 or 1.95e12 < x < 3.24999999999999988e94

   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 c around inf 53.7%

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

   4. Taylor expanded in j around 0 36.8%

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

      1. neg-mul-1 36.8%

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

      2. distribute-lft-neg-in 36.8%

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

      3. *-commutative 36.8%

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

   6. Simplified 36.8%

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

   if 1.4199999999999999e-238 < x < 3.8999999999999997e-141

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in j around inf 59.3%

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

   if 3.8999999999999997e-141 < x < 1.95e12

   1. Initial program 73.6%

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

   3. Taylor expanded in b around inf 41.2%

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

      1. *-commutative 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in i around inf 37.7%

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

      1. *-commutative 37.7%

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

   8. Simplified 37.7%

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

   if 3.24999999999999988e94 < x

   1. Initial program 62.8%

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

   3. Taylor expanded in z around inf 45.2%

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

      1. *-commutative 45.2%

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

      2. *-commutative 45.2%

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

   5. Simplified 45.2%

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

   6. Taylor expanded in y around inf 45.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+135}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-238}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-141}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1950000000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 280000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= x -8e+73)
     (* t (* x (- a)))
     (if (<= x -3.1e-78)
       (* (* y i) (- j))
       (if (<= x 8.5e-239)
         t_1
         (if (<= x 1.08e-134)
           (* c (* t j))
           (if (<= x 280000000.0)
             (* a (* b i))
             (if (<= x 9.2e+94) t_1 (* 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 t_1 = c * (z * -b);
	double tmp;
	if (x <= -8e+73) {
		tmp = t * (x * -a);
	} else if (x <= -3.1e-78) {
		tmp = (y * i) * -j;
	} else if (x <= 8.5e-239) {
		tmp = t_1;
	} else if (x <= 1.08e-134) {
		tmp = c * (t * j);
	} else if (x <= 280000000.0) {
		tmp = a * (b * i);
	} else if (x <= 9.2e+94) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (x <= (-8d+73)) then
        tmp = t * (x * -a)
    else if (x <= (-3.1d-78)) then
        tmp = (y * i) * -j
    else if (x <= 8.5d-239) then
        tmp = t_1
    else if (x <= 1.08d-134) then
        tmp = c * (t * j)
    else if (x <= 280000000.0d0) then
        tmp = a * (b * i)
    else if (x <= 9.2d+94) then
        tmp = t_1
    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 t_1 = c * (z * -b);
	double tmp;
	if (x <= -8e+73) {
		tmp = t * (x * -a);
	} else if (x <= -3.1e-78) {
		tmp = (y * i) * -j;
	} else if (x <= 8.5e-239) {
		tmp = t_1;
	} else if (x <= 1.08e-134) {
		tmp = c * (t * j);
	} else if (x <= 280000000.0) {
		tmp = a * (b * i);
	} else if (x <= 9.2e+94) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if x <= -8e+73:
		tmp = t * (x * -a)
	elif x <= -3.1e-78:
		tmp = (y * i) * -j
	elif x <= 8.5e-239:
		tmp = t_1
	elif x <= 1.08e-134:
		tmp = c * (t * j)
	elif x <= 280000000.0:
		tmp = a * (b * i)
	elif x <= 9.2e+94:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (x <= -8e+73)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= -3.1e-78)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (x <= 8.5e-239)
		tmp = t_1;
	elseif (x <= 1.08e-134)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 280000000.0)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 9.2e+94)
		tmp = t_1;
	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)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (x <= -8e+73)
		tmp = t * (x * -a);
	elseif (x <= -3.1e-78)
		tmp = (y * i) * -j;
	elseif (x <= 8.5e-239)
		tmp = t_1;
	elseif (x <= 1.08e-134)
		tmp = c * (t * j);
	elseif (x <= 280000000.0)
		tmp = a * (b * i);
	elseif (x <= 9.2e+94)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+73], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-78], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[x, 8.5e-239], t$95$1, If[LessEqual[x, 1.08e-134], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 280000000.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+94], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.99999999999999986e73

   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 t around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in j around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. distribute-lft-neg-out 43.2%

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

      3. *-commutative 43.2%

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

   8. Simplified 43.2%

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

   if -7.99999999999999986e73 < x < -3.10000000000000018e-78

   1. Initial program 71.4%

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

   3. Taylor expanded in j around inf 58.2%

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

   4. Taylor expanded in c around 0 34.9%

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

      1. mul-1-neg 34.9%

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

      2. distribute-lft-neg-out 34.9%

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

      3. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   if -3.10000000000000018e-78 < x < 8.49999999999999958e-239 or 2.8e8 < x < 9.1999999999999999e94

   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 c around inf 53.7%

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

   4. Taylor expanded in j around 0 36.8%

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

      1. neg-mul-1 36.8%

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

      2. distribute-lft-neg-in 36.8%

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

      3. *-commutative 36.8%

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

   6. Simplified 36.8%

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

   if 8.49999999999999958e-239 < x < 1.07999999999999999e-134

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in j around inf 59.3%

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

   if 1.07999999999999999e-134 < x < 2.8e8

   1. Initial program 73.6%

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

   3. Taylor expanded in b around inf 41.2%

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

      1. *-commutative 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in i around inf 37.7%

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

      1. *-commutative 37.7%

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

   8. Simplified 37.7%

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

   if 9.1999999999999999e94 < x

   1. Initial program 62.8%

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

   3. Taylor expanded in z around inf 45.2%

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

      1. *-commutative 45.2%

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

      2. *-commutative 45.2%

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

   5. Simplified 45.2%

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

   6. Taylor expanded in y around inf 45.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 280000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.15 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-231}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-66}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -4.2e+132)
   (* t (* c j))
   (if (<= c -3.15e-21)
     (* z (- (* b c)))
     (if (<= c -3e-231)
       (* (* x t) (- a))
       (if (<= c 1.95e-153)
         (* b (* a i))
         (if (<= c 3.9e-66)
           (* (* y i) (- j))
           (if (<= c 3.6e-39) (* x (* y z)) (* j (* t 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 (c <= -4.2e+132) {
		tmp = t * (c * j);
	} else if (c <= -3.15e-21) {
		tmp = z * -(b * c);
	} else if (c <= -3e-231) {
		tmp = (x * t) * -a;
	} else if (c <= 1.95e-153) {
		tmp = b * (a * i);
	} else if (c <= 3.9e-66) {
		tmp = (y * i) * -j;
	} else if (c <= 3.6e-39) {
		tmp = x * (y * z);
	} else {
		tmp = j * (t * 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 (c <= (-4.2d+132)) then
        tmp = t * (c * j)
    else if (c <= (-3.15d-21)) then
        tmp = z * -(b * c)
    else if (c <= (-3d-231)) then
        tmp = (x * t) * -a
    else if (c <= 1.95d-153) then
        tmp = b * (a * i)
    else if (c <= 3.9d-66) then
        tmp = (y * i) * -j
    else if (c <= 3.6d-39) then
        tmp = x * (y * z)
    else
        tmp = j * (t * 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 (c <= -4.2e+132) {
		tmp = t * (c * j);
	} else if (c <= -3.15e-21) {
		tmp = z * -(b * c);
	} else if (c <= -3e-231) {
		tmp = (x * t) * -a;
	} else if (c <= 1.95e-153) {
		tmp = b * (a * i);
	} else if (c <= 3.9e-66) {
		tmp = (y * i) * -j;
	} else if (c <= 3.6e-39) {
		tmp = x * (y * z);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -4.2e+132:
		tmp = t * (c * j)
	elif c <= -3.15e-21:
		tmp = z * -(b * c)
	elif c <= -3e-231:
		tmp = (x * t) * -a
	elif c <= 1.95e-153:
		tmp = b * (a * i)
	elif c <= 3.9e-66:
		tmp = (y * i) * -j
	elif c <= 3.6e-39:
		tmp = x * (y * z)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -4.2e+132)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= -3.15e-21)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (c <= -3e-231)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (c <= 1.95e-153)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 3.9e-66)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (c <= 3.6e-39)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -4.2e+132)
		tmp = t * (c * j);
	elseif (c <= -3.15e-21)
		tmp = z * -(b * c);
	elseif (c <= -3e-231)
		tmp = (x * t) * -a;
	elseif (c <= 1.95e-153)
		tmp = b * (a * i);
	elseif (c <= 3.9e-66)
		tmp = (y * i) * -j;
	elseif (c <= 3.6e-39)
		tmp = x * (y * z);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -4.2e+132], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.15e-21], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[c, -3e-231], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[c, 1.95e-153], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e-66], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, 3.6e-39], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -4.19999999999999987e132

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in j around inf 39.2%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -4.19999999999999987e132 < c < -3.15e-21

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in y around 0 38.8%

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

      1. neg-mul-1 38.8%

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

      2. *-commutative 38.8%

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

      3. distribute-rgt-neg-in 38.8%

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

   8. Simplified 38.8%

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

   if -3.15e-21 < c < -3.0000000000000003e-231

   1. Initial program 88.7%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in j around 0 34.8%

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

      1. associate-*r* 34.8%

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

      2. neg-mul-1 34.8%

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

   8. Simplified 34.8%

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

   if -3.0000000000000003e-231 < c < 1.9500000000000001e-153

   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 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%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in i around inf 36.3%

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

      1. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   if 1.9500000000000001e-153 < c < 3.89999999999999983e-66

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 58.0%

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

   4. Taylor expanded in c around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-lft-neg-out 58.4%

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

      3. *-commutative 58.4%

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

   6. Simplified 58.4%

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

   if 3.89999999999999983e-66 < c < 3.6000000000000001e-39

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around inf 59.3%

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

   if 3.6000000000000001e-39 < c

   1. Initial program 69.6%

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

   3. Taylor expanded in j around inf 57.0%

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

   4. Taylor expanded in c around inf 39.9%

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

      1. *-commutative 39.9%

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

      2. associate-*r* 44.6%

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

      3. *-commutative 44.6%

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

   6. Simplified 44.6%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.15 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-231}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-66}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.8e+23)
     t_2
     (if (<= b -7.5e-231)
       t_1
       (if (<= b 1.1e-297)
         (* j (- (* t c) (* y i)))
         (if (<= b 7.2e-39)
           t_1
           (if (<= b 5.2e+40) (* x (- (* y z) (* t a))) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.8e+23) {
		tmp = t_2;
	} else if (b <= -7.5e-231) {
		tmp = t_1;
	} else if (b <= 1.1e-297) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 7.2e-39) {
		tmp = t_1;
	} else if (b <= 5.2e+40) {
		tmp = x * ((y * z) - (t * a));
	} 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 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.8d+23)) then
        tmp = t_2
    else if (b <= (-7.5d-231)) then
        tmp = t_1
    else if (b <= 1.1d-297) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 7.2d-39) then
        tmp = t_1
    else if (b <= 5.2d+40) then
        tmp = x * ((y * z) - (t * a))
    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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.8e+23) {
		tmp = t_2;
	} else if (b <= -7.5e-231) {
		tmp = t_1;
	} else if (b <= 1.1e-297) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 7.2e-39) {
		tmp = t_1;
	} else if (b <= 5.2e+40) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.8e+23:
		tmp = t_2
	elif b <= -7.5e-231:
		tmp = t_1
	elif b <= 1.1e-297:
		tmp = j * ((t * c) - (y * i))
	elif b <= 7.2e-39:
		tmp = t_1
	elif b <= 5.2e+40:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.8e+23)
		tmp = t_2;
	elseif (b <= -7.5e-231)
		tmp = t_1;
	elseif (b <= 1.1e-297)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 7.2e-39)
		tmp = t_1;
	elseif (b <= 5.2e+40)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.8e+23)
		tmp = t_2;
	elseif (b <= -7.5e-231)
		tmp = t_1;
	elseif (b <= 1.1e-297)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 7.2e-39)
		tmp = t_1;
	elseif (b <= 5.2e+40)
		tmp = x * ((y * z) - (t * a));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+23], t$95$2, If[LessEqual[b, -7.5e-231], t$95$1, If[LessEqual[b, 1.1e-297], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-39], t$95$1, If[LessEqual[b, 5.2e+40], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.7999999999999999e23 or 5.2000000000000001e40 < b

   1. Initial program 68.5%

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

   3. Taylor expanded in b around inf 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -1.7999999999999999e23 < b < -7.5000000000000001e-231 or 1.0999999999999999e-297 < b < 7.2000000000000001e-39

   1. Initial program 74.6%

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

   3. Taylor expanded in t around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if -7.5000000000000001e-231 < b < 1.0999999999999999e-297

   1. Initial program 65.5%

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

   3. Taylor expanded in j around inf 66.2%

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

   if 7.2000000000000001e-39 < b < 5.2000000000000001e40

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-66}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.4e-55)
     t_1
     (if (<= c 2e-152)
       (* b (- (* a i) (* z c)))
       (if (<= c 4.5e-66)
         (* (* y i) (- j))
         (if (<= c 1.3e-38) (* 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.4e-55) {
		tmp = t_1;
	} else if (c <= 2e-152) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 4.5e-66) {
		tmp = (y * i) * -j;
	} else if (c <= 1.3e-38) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-1.4d-55)) then
        tmp = t_1
    else if (c <= 2d-152) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 4.5d-66) then
        tmp = (y * i) * -j
    else if (c <= 1.3d-38) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.4e-55) {
		tmp = t_1;
	} else if (c <= 2e-152) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 4.5e-66) {
		tmp = (y * i) * -j;
	} else if (c <= 1.3e-38) {
		tmp = x * (y * z);
	} 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 <= -1.4e-55:
		tmp = t_1
	elif c <= 2e-152:
		tmp = b * ((a * i) - (z * c))
	elif c <= 4.5e-66:
		tmp = (y * i) * -j
	elif c <= 1.3e-38:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.4e-55)
		tmp = t_1;
	elseif (c <= 2e-152)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 4.5e-66)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (c <= 1.3e-38)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.4e-55)
		tmp = t_1;
	elseif (c <= 2e-152)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 4.5e-66)
		tmp = (y * i) * -j;
	elseif (c <= 1.3e-38)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.4e-55], t$95$1, If[LessEqual[c, 2e-152], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e-66], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, 1.3e-38], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.39999999999999992e-55 or 1.30000000000000005e-38 < c

   1. Initial program 65.9%

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

   3. Taylor expanded in c around inf 55.2%

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

   if -1.39999999999999992e-55 < c < 2.00000000000000013e-152

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf 37.1%

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

      1. *-commutative 37.1%

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

   5. Simplified 37.1%

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

   if 2.00000000000000013e-152 < c < 4.4999999999999998e-66

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 58.0%

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

   4. Taylor expanded in c around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-lft-neg-out 58.4%

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

      3. *-commutative 58.4%

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

   6. Simplified 58.4%

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

   if 4.4999999999999998e-66 < c < 1.30000000000000005e-38

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around inf 59.3%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-66}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.1e-11)
     t_2
     (if (<= b 2.9e+25)
       t_1
       (if (<= b 5.2e+71) (* a (* b i)) (if (<= b 4.8e+145) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.1e-11) {
		tmp = t_2;
	} else if (b <= 2.9e+25) {
		tmp = t_1;
	} else if (b <= 5.2e+71) {
		tmp = a * (b * i);
	} else if (b <= 4.8e+145) {
		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 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.1d-11)) then
        tmp = t_2
    else if (b <= 2.9d+25) then
        tmp = t_1
    else if (b <= 5.2d+71) then
        tmp = a * (b * i)
    else if (b <= 4.8d+145) 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 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.1e-11) {
		tmp = t_2;
	} else if (b <= 2.9e+25) {
		tmp = t_1;
	} else if (b <= 5.2e+71) {
		tmp = a * (b * i);
	} else if (b <= 4.8e+145) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.1e-11:
		tmp = t_2
	elif b <= 2.9e+25:
		tmp = t_1
	elif b <= 5.2e+71:
		tmp = a * (b * i)
	elif b <= 4.8e+145:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.1e-11)
		tmp = t_2;
	elseif (b <= 2.9e+25)
		tmp = t_1;
	elseif (b <= 5.2e+71)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 4.8e+145)
		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 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.1e-11)
		tmp = t_2;
	elseif (b <= 2.9e+25)
		tmp = t_1;
	elseif (b <= 5.2e+71)
		tmp = a * (b * i);
	elseif (b <= 4.8e+145)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e-11], t$95$2, If[LessEqual[b, 2.9e+25], t$95$1, If[LessEqual[b, 5.2e+71], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+145], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.0999999999999999e-11 or 4.79999999999999984e145 < b

   1. Initial program 68.5%

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

   3. Taylor expanded in b around inf 63.2%

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

      1. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   if -2.0999999999999999e-11 < b < 2.8999999999999999e25 or 5.19999999999999983e71 < b < 4.79999999999999984e145

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 50.8%

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

   if 2.8999999999999999e25 < b < 5.19999999999999983e71

   1. Initial program 49.7%

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

   3. Taylor expanded in b around inf 58.5%

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

      1. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in i around inf 58.8%

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

      1. *-commutative 58.8%

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

   8. Simplified 58.8%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+145}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.76 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-209}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -1.76e+21)
     t_1
     (if (<= y 9.2e-209)
       (* j (* t c))
       (if (<= y 1.5e-9)
         (* b (* a i))
         (if (<= y 3.4e+79) (* c (* t j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.76e+21) {
		tmp = t_1;
	} else if (y <= 9.2e-209) {
		tmp = j * (t * c);
	} else if (y <= 1.5e-9) {
		tmp = b * (a * i);
	} else if (y <= 3.4e+79) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-1.76d+21)) then
        tmp = t_1
    else if (y <= 9.2d-209) then
        tmp = j * (t * c)
    else if (y <= 1.5d-9) then
        tmp = b * (a * i)
    else if (y <= 3.4d+79) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.76e+21) {
		tmp = t_1;
	} else if (y <= 9.2e-209) {
		tmp = j * (t * c);
	} else if (y <= 1.5e-9) {
		tmp = b * (a * i);
	} else if (y <= 3.4e+79) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -1.76e+21:
		tmp = t_1
	elif y <= 9.2e-209:
		tmp = j * (t * c)
	elif y <= 1.5e-9:
		tmp = b * (a * i)
	elif y <= 3.4e+79:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.76e+21)
		tmp = t_1;
	elseif (y <= 9.2e-209)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 1.5e-9)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 3.4e+79)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.76e+21)
		tmp = t_1;
	elseif (y <= 9.2e-209)
		tmp = j * (t * c);
	elseif (y <= 1.5e-9)
		tmp = b * (a * i);
	elseif (y <= 3.4e+79)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.76e+21], t$95$1, If[LessEqual[y, 9.2e-209], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-9], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+79], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.76e21 or 3.40000000000000032e79 < y

   1. Initial program 61.5%

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

   3. Taylor expanded in z around inf 44.1%

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

      1. *-commutative 44.1%

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

      2. *-commutative 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in y around inf 36.6%

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

   if -1.76e21 < y < 9.1999999999999999e-209

   1. Initial program 77.6%

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

   3. Taylor expanded in j around inf 42.3%

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

   4. Taylor expanded in c around inf 32.0%

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

      1. *-commutative 32.0%

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

      2. associate-*r* 34.9%

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

      3. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   if 9.1999999999999999e-209 < y < 1.49999999999999999e-9

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 33.7%

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

      1. *-commutative 33.7%

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

   8. Simplified 33.7%

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

   if 1.49999999999999999e-9 < y < 3.40000000000000032e79

   1. Initial program 86.8%

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

   3. Taylor expanded in t around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in j around inf 36.3%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-209}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.85e+19)
   (* x (* y z))
   (if (<= y 1.1e-204)
     (* j (* t c))
     (if (<= y 1.15e-10)
       (* b (* a i))
       (if (<= y 3.4e+79) (* c (* t j)) (* 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 (y <= -2.85e+19) {
		tmp = x * (y * z);
	} else if (y <= 1.1e-204) {
		tmp = j * (t * c);
	} else if (y <= 1.15e-10) {
		tmp = b * (a * i);
	} else if (y <= 3.4e+79) {
		tmp = c * (t * j);
	} 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 (y <= (-2.85d+19)) then
        tmp = x * (y * z)
    else if (y <= 1.1d-204) then
        tmp = j * (t * c)
    else if (y <= 1.15d-10) then
        tmp = b * (a * i)
    else if (y <= 3.4d+79) then
        tmp = c * (t * j)
    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 (y <= -2.85e+19) {
		tmp = x * (y * z);
	} else if (y <= 1.1e-204) {
		tmp = j * (t * c);
	} else if (y <= 1.15e-10) {
		tmp = b * (a * i);
	} else if (y <= 3.4e+79) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.85e+19:
		tmp = x * (y * z)
	elif y <= 1.1e-204:
		tmp = j * (t * c)
	elif y <= 1.15e-10:
		tmp = b * (a * i)
	elif y <= 3.4e+79:
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.85e+19)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 1.1e-204)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 1.15e-10)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 3.4e+79)
		tmp = Float64(c * Float64(t * j));
	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 (y <= -2.85e+19)
		tmp = x * (y * z);
	elseif (y <= 1.1e-204)
		tmp = j * (t * c);
	elseif (y <= 1.15e-10)
		tmp = b * (a * i);
	elseif (y <= 3.4e+79)
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.85e+19], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-204], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-10], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+79], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.85e19

   1. Initial program 58.0%

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

   3. Taylor expanded in z around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in y around inf 38.0%

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

   if -2.85e19 < y < 1.0999999999999999e-204

   1. Initial program 77.6%

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

   3. Taylor expanded in j around inf 42.3%

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

   4. Taylor expanded in c around inf 32.0%

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

      1. *-commutative 32.0%

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

      2. associate-*r* 34.9%

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

      3. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   if 1.0999999999999999e-204 < y < 1.15000000000000004e-10

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 33.7%

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

      1. *-commutative 33.7%

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

   8. Simplified 33.7%

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

   if 1.15000000000000004e-10 < y < 3.40000000000000032e79

   1. Initial program 86.8%

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

   3. Taylor expanded in t around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in j around inf 36.3%

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

   if 3.40000000000000032e79 < y

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. *-commutative 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-206}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -8.4e+26)
   (* x (* y z))
   (if (<= y 7.8e-206)
     (* j (* t c))
     (if (<= y 2.1e-8)
       (* b (* a i))
       (if (<= y 3.5e+79) (* t (* c j)) (* 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 (y <= -8.4e+26) {
		tmp = x * (y * z);
	} else if (y <= 7.8e-206) {
		tmp = j * (t * c);
	} else if (y <= 2.1e-8) {
		tmp = b * (a * i);
	} else if (y <= 3.5e+79) {
		tmp = t * (c * j);
	} 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 (y <= (-8.4d+26)) then
        tmp = x * (y * z)
    else if (y <= 7.8d-206) then
        tmp = j * (t * c)
    else if (y <= 2.1d-8) then
        tmp = b * (a * i)
    else if (y <= 3.5d+79) then
        tmp = t * (c * j)
    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 (y <= -8.4e+26) {
		tmp = x * (y * z);
	} else if (y <= 7.8e-206) {
		tmp = j * (t * c);
	} else if (y <= 2.1e-8) {
		tmp = b * (a * i);
	} else if (y <= 3.5e+79) {
		tmp = t * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -8.4e+26:
		tmp = x * (y * z)
	elif y <= 7.8e-206:
		tmp = j * (t * c)
	elif y <= 2.1e-8:
		tmp = b * (a * i)
	elif y <= 3.5e+79:
		tmp = t * (c * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -8.4e+26)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 7.8e-206)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 2.1e-8)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 3.5e+79)
		tmp = Float64(t * Float64(c * j));
	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 (y <= -8.4e+26)
		tmp = x * (y * z);
	elseif (y <= 7.8e-206)
		tmp = j * (t * c);
	elseif (y <= 2.1e-8)
		tmp = b * (a * i);
	elseif (y <= 3.5e+79)
		tmp = t * (c * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -8.4e+26], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-206], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-8], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+79], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.4000000000000003e26

   1. Initial program 58.0%

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

   3. Taylor expanded in z around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in y around inf 38.0%

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

   if -8.4000000000000003e26 < y < 7.80000000000000014e-206

   1. Initial program 77.6%

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

   3. Taylor expanded in j around inf 42.3%

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

   4. Taylor expanded in c around inf 32.0%

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

      1. *-commutative 32.0%

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

      2. associate-*r* 34.9%

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

      3. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   if 7.80000000000000014e-206 < y < 2.09999999999999994e-8

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 33.7%

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

      1. *-commutative 33.7%

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

   8. Simplified 33.7%

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

   if 2.09999999999999994e-8 < y < 3.4999999999999998e79

   1. Initial program 86.8%

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

   3. Taylor expanded in t around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in j around inf 36.3%

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

      1. associate-*r* 36.3%

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

      2. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   if 3.4999999999999998e79 < y

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. *-commutative 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-206}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.2e+28)
   (* x (* y z))
   (if (<= y 3.9e-210)
     (* j (* t c))
     (if (<= y 7.5e-63)
       (* c (* z (- b)))
       (if (<= y 4.2e+79) (* c (* t j)) (* 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 (y <= -3.2e+28) {
		tmp = x * (y * z);
	} else if (y <= 3.9e-210) {
		tmp = j * (t * c);
	} else if (y <= 7.5e-63) {
		tmp = c * (z * -b);
	} else if (y <= 4.2e+79) {
		tmp = c * (t * j);
	} 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 (y <= (-3.2d+28)) then
        tmp = x * (y * z)
    else if (y <= 3.9d-210) then
        tmp = j * (t * c)
    else if (y <= 7.5d-63) then
        tmp = c * (z * -b)
    else if (y <= 4.2d+79) then
        tmp = c * (t * j)
    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 (y <= -3.2e+28) {
		tmp = x * (y * z);
	} else if (y <= 3.9e-210) {
		tmp = j * (t * c);
	} else if (y <= 7.5e-63) {
		tmp = c * (z * -b);
	} else if (y <= 4.2e+79) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.2e+28:
		tmp = x * (y * z)
	elif y <= 3.9e-210:
		tmp = j * (t * c)
	elif y <= 7.5e-63:
		tmp = c * (z * -b)
	elif y <= 4.2e+79:
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.2e+28)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 3.9e-210)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 7.5e-63)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (y <= 4.2e+79)
		tmp = Float64(c * Float64(t * j));
	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 (y <= -3.2e+28)
		tmp = x * (y * z);
	elseif (y <= 3.9e-210)
		tmp = j * (t * c);
	elseif (y <= 7.5e-63)
		tmp = c * (z * -b);
	elseif (y <= 4.2e+79)
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.2e+28], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-210], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-63], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+79], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.2e28

   1. Initial program 58.0%

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

   3. Taylor expanded in z around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in y around inf 38.0%

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

   if -3.2e28 < y < 3.8999999999999998e-210

   1. Initial program 77.3%

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

   3. Taylor expanded in j around inf 41.7%

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

   4. Taylor expanded in c around inf 31.2%

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

      1. *-commutative 31.2%

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

      2. associate-*r* 34.2%

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

      3. *-commutative 34.2%

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

   6. Simplified 34.2%

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

   if 3.8999999999999998e-210 < y < 7.5000000000000003e-63

   1. Initial program 87.3%

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

   3. Taylor expanded in c around inf 39.0%

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

   4. Taylor expanded in j around 0 34.9%

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

      1. neg-mul-1 34.9%

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

      2. distribute-lft-neg-in 34.9%

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

      3. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   if 7.5000000000000003e-63 < y < 4.20000000000000016e79

   1. Initial program 76.6%

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

   3. Taylor expanded in t around inf 45.3%

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

      1. +-commutative 45.3%

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

      2. mul-1-neg 45.3%

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

      3. unsub-neg 45.3%

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

      4. *-commutative 45.3%

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

   5. Simplified 45.3%

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

   6. Taylor expanded in j around inf 39.7%

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

   if 4.20000000000000016e79 < y

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around inf 37.1%

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

      1. *-commutative 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+16} \lor \neg \left(a \leq 2.4 \cdot 10^{-60}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -4.5e+16) (not (<= a 2.4e-60))) (* b (* a i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.5e+16) || !(a <= 2.4e-60)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-4.5d+16)) .or. (.not. (a <= 2.4d-60))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.5e+16) || !(a <= 2.4e-60)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -4.5e+16) or not (a <= 2.4e-60):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -4.5e+16) || !(a <= 2.4e-60))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -4.5e+16) || ~((a <= 2.4e-60)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -4.5e+16], N[Not[LessEqual[a, 2.4e-60]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5e16 or 2.40000000000000009e-60 < a

   1. Initial program 63.8%

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

   3. Taylor expanded in b around inf 46.5%

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

      1. *-commutative 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in i around inf 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   if -4.5e16 < a < 2.40000000000000009e-60

   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 t around inf 38.6%

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

      1. +-commutative 38.6%

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

      2. mul-1-neg 38.6%

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

      3. unsub-neg 38.6%

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

      4. *-commutative 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in j around inf 30.4%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+16} \lor \neg \left(a \leq 2.4 \cdot 10^{-60}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+16} \lor \neg \left(a \leq 1.18 \cdot 10^{-11}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.1e+16) (not (<= a 1.18e-11))) (* b (* a i)) (* j (* t c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.1e+16) || !(a <= 1.18e-11)) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-2.1d+16)) .or. (.not. (a <= 1.18d-11))) then
        tmp = b * (a * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.1e+16) || !(a <= 1.18e-11)) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.1e+16) or not (a <= 1.18e-11):
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.1e+16) || !(a <= 1.18e-11))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.1e+16) || ~((a <= 1.18e-11)))
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.1e+16], N[Not[LessEqual[a, 1.18e-11]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1e16 or 1.18e-11 < a

   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 b around inf 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in i around inf 40.9%

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

      1. *-commutative 40.9%

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

   8. Simplified 40.9%

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

   if -2.1e16 < a < 1.18e-11

   1. Initial program 78.4%

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

   3. Taylor expanded in j around inf 46.8%

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

   4. Taylor expanded in c around inf 29.9%

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

      1. *-commutative 29.9%

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

      2. associate-*r* 30.6%

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

      3. *-commutative 30.6%

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

   6. Simplified 30.6%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+16} \lor \neg \left(a \leq 1.18 \cdot 10^{-11}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 23.2% 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 71.7%

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

3. Taylor expanded in b around inf 35.8%

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

   1. *-commutative 35.8%

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

5. Simplified 35.8%

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

6. Taylor expanded in i around inf 21.2%

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

   1. *-commutative 21.2%

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

8. Simplified 21.2%

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

9. Final simplification 21.2%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Alternative 25: 23.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.7%

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

3. Taylor expanded in b around inf 35.8%

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

   1. *-commutative 35.8%

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

5. Simplified 35.8%

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

6. Taylor expanded in i around inf 21.3%

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

   1. *-commutative 21.3%

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

8. Simplified 21.3%

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

9. Final simplification 21.3%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
10. Add Preprocessing

Developer target: 68.9% 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 2024067 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* 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)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* 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)))) (- (* 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)))))