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

Percentage Accurate: 72.8% → 81.4%

Time: 23.4s

Alternatives: 25

Speedup: 0.5×

• 57.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

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

Initial Program: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

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

Alternative 1: 81.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around -inf 52.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.3%

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

Alternative 2: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-215}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-242}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+215}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= b -1.6e+190)
     t_2
     (if (<= b -2.5e+135)
       t_1
       (if (<= b -4.8e+40)
         t_2
         (if (<= b -8e-185)
           t_1
           (if (<= b -4.2e-215)
             (* z (* x y))
             (if (<= b 3.1e-242)
               t_3
               (if (<= b 2.8e-168)
                 t_1
                 (if (<= b 5.4e+106)
                   t_3
                   (if (<= b 1.9e+215) (* c (- (* a j) (* z b))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -1.6e+190) {
		tmp = t_2;
	} else if (b <= -2.5e+135) {
		tmp = t_1;
	} else if (b <= -4.8e+40) {
		tmp = t_2;
	} else if (b <= -8e-185) {
		tmp = t_1;
	} else if (b <= -4.2e-215) {
		tmp = z * (x * y);
	} else if (b <= 3.1e-242) {
		tmp = t_3;
	} else if (b <= 2.8e-168) {
		tmp = t_1;
	} else if (b <= 5.4e+106) {
		tmp = t_3;
	} else if (b <= 1.9e+215) {
		tmp = c * ((a * j) - (z * b));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = j * ((a * c) - (y * i))
    if (b <= (-1.6d+190)) then
        tmp = t_2
    else if (b <= (-2.5d+135)) then
        tmp = t_1
    else if (b <= (-4.8d+40)) then
        tmp = t_2
    else if (b <= (-8d-185)) then
        tmp = t_1
    else if (b <= (-4.2d-215)) then
        tmp = z * (x * y)
    else if (b <= 3.1d-242) then
        tmp = t_3
    else if (b <= 2.8d-168) then
        tmp = t_1
    else if (b <= 5.4d+106) then
        tmp = t_3
    else if (b <= 1.9d+215) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -1.6e+190) {
		tmp = t_2;
	} else if (b <= -2.5e+135) {
		tmp = t_1;
	} else if (b <= -4.8e+40) {
		tmp = t_2;
	} else if (b <= -8e-185) {
		tmp = t_1;
	} else if (b <= -4.2e-215) {
		tmp = z * (x * y);
	} else if (b <= 3.1e-242) {
		tmp = t_3;
	} else if (b <= 2.8e-168) {
		tmp = t_1;
	} else if (b <= 5.4e+106) {
		tmp = t_3;
	} else if (b <= 1.9e+215) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if b <= -1.6e+190:
		tmp = t_2
	elif b <= -2.5e+135:
		tmp = t_1
	elif b <= -4.8e+40:
		tmp = t_2
	elif b <= -8e-185:
		tmp = t_1
	elif b <= -4.2e-215:
		tmp = z * (x * y)
	elif b <= 3.1e-242:
		tmp = t_3
	elif b <= 2.8e-168:
		tmp = t_1
	elif b <= 5.4e+106:
		tmp = t_3
	elif b <= 1.9e+215:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -1.6e+190)
		tmp = t_2;
	elseif (b <= -2.5e+135)
		tmp = t_1;
	elseif (b <= -4.8e+40)
		tmp = t_2;
	elseif (b <= -8e-185)
		tmp = t_1;
	elseif (b <= -4.2e-215)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 3.1e-242)
		tmp = t_3;
	elseif (b <= 2.8e-168)
		tmp = t_1;
	elseif (b <= 5.4e+106)
		tmp = t_3;
	elseif (b <= 1.9e+215)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (b <= -1.6e+190)
		tmp = t_2;
	elseif (b <= -2.5e+135)
		tmp = t_1;
	elseif (b <= -4.8e+40)
		tmp = t_2;
	elseif (b <= -8e-185)
		tmp = t_1;
	elseif (b <= -4.2e-215)
		tmp = z * (x * y);
	elseif (b <= 3.1e-242)
		tmp = t_3;
	elseif (b <= 2.8e-168)
		tmp = t_1;
	elseif (b <= 5.4e+106)
		tmp = t_3;
	elseif (b <= 1.9e+215)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+190], t$95$2, If[LessEqual[b, -2.5e+135], t$95$1, If[LessEqual[b, -4.8e+40], t$95$2, If[LessEqual[b, -8e-185], t$95$1, If[LessEqual[b, -4.2e-215], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-242], t$95$3, If[LessEqual[b, 2.8e-168], t$95$1, If[LessEqual[b, 5.4e+106], t$95$3, If[LessEqual[b, 1.9e+215], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.6e190 or -2.50000000000000015e135 < b < -4.8e40 or 1.89999999999999984e215 < b

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -1.6e190 < b < -2.50000000000000015e135 or -4.8e40 < b < -7.9999999999999999e-185 or 3.10000000000000015e-242 < b < 2.8000000000000002e-168

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   if -7.9999999999999999e-185 < b < -4.2e-215

   1. Initial program 58.4%

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

   3. Taylor expanded in y around 0 85.5%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in y around inf 86.2%

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

      1. *-commutative 86.2%

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

   9. Simplified 86.2%

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

   if -4.2e-215 < b < 3.10000000000000015e-242 or 2.8000000000000002e-168 < b < 5.40000000000000012e106

   1. Initial program 75.5%

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

   3. Taylor expanded in j around inf 53.3%

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

      1. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   if 5.40000000000000012e106 < b < 1.89999999999999984e215

   1. Initial program 85.6%

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

   3. Taylor expanded in c around inf 79.2%

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

      1. *-commutative 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+190}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-215}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+215}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-214}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* z (* x y))))
   (if (<= b -1.32e+191)
     t_1
     (if (<= b -1.05e+138)
       t_2
       (if (<= b -1.05e+40)
         t_1
         (if (<= b -7.5e-185)
           t_2
           (if (<= b -6.8e-214)
             t_3
             (if (<= b 1.25e-13)
               t_2
               (if (<= b 4.6e+92)
                 (* i (- (* y j)))
                 (if (<= b 2.2e+105)
                   t_3
                   (if (<= b 4.5e+213) (* c (- (* a j) (* z b))) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = z * (x * y);
	double tmp;
	if (b <= -1.32e+191) {
		tmp = t_1;
	} else if (b <= -1.05e+138) {
		tmp = t_2;
	} else if (b <= -1.05e+40) {
		tmp = t_1;
	} else if (b <= -7.5e-185) {
		tmp = t_2;
	} else if (b <= -6.8e-214) {
		tmp = t_3;
	} else if (b <= 1.25e-13) {
		tmp = t_2;
	} else if (b <= 4.6e+92) {
		tmp = i * -(y * j);
	} else if (b <= 2.2e+105) {
		tmp = t_3;
	} else if (b <= 4.5e+213) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    t_3 = z * (x * y)
    if (b <= (-1.32d+191)) then
        tmp = t_1
    else if (b <= (-1.05d+138)) then
        tmp = t_2
    else if (b <= (-1.05d+40)) then
        tmp = t_1
    else if (b <= (-7.5d-185)) then
        tmp = t_2
    else if (b <= (-6.8d-214)) then
        tmp = t_3
    else if (b <= 1.25d-13) then
        tmp = t_2
    else if (b <= 4.6d+92) then
        tmp = i * -(y * j)
    else if (b <= 2.2d+105) then
        tmp = t_3
    else if (b <= 4.5d+213) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = z * (x * y);
	double tmp;
	if (b <= -1.32e+191) {
		tmp = t_1;
	} else if (b <= -1.05e+138) {
		tmp = t_2;
	} else if (b <= -1.05e+40) {
		tmp = t_1;
	} else if (b <= -7.5e-185) {
		tmp = t_2;
	} else if (b <= -6.8e-214) {
		tmp = t_3;
	} else if (b <= 1.25e-13) {
		tmp = t_2;
	} else if (b <= 4.6e+92) {
		tmp = i * -(y * j);
	} else if (b <= 2.2e+105) {
		tmp = t_3;
	} else if (b <= 4.5e+213) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	t_3 = z * (x * y)
	tmp = 0
	if b <= -1.32e+191:
		tmp = t_1
	elif b <= -1.05e+138:
		tmp = t_2
	elif b <= -1.05e+40:
		tmp = t_1
	elif b <= -7.5e-185:
		tmp = t_2
	elif b <= -6.8e-214:
		tmp = t_3
	elif b <= 1.25e-13:
		tmp = t_2
	elif b <= 4.6e+92:
		tmp = i * -(y * j)
	elif b <= 2.2e+105:
		tmp = t_3
	elif b <= 4.5e+213:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (b <= -1.32e+191)
		tmp = t_1;
	elseif (b <= -1.05e+138)
		tmp = t_2;
	elseif (b <= -1.05e+40)
		tmp = t_1;
	elseif (b <= -7.5e-185)
		tmp = t_2;
	elseif (b <= -6.8e-214)
		tmp = t_3;
	elseif (b <= 1.25e-13)
		tmp = t_2;
	elseif (b <= 4.6e+92)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (b <= 2.2e+105)
		tmp = t_3;
	elseif (b <= 4.5e+213)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	t_3 = z * (x * y);
	tmp = 0.0;
	if (b <= -1.32e+191)
		tmp = t_1;
	elseif (b <= -1.05e+138)
		tmp = t_2;
	elseif (b <= -1.05e+40)
		tmp = t_1;
	elseif (b <= -7.5e-185)
		tmp = t_2;
	elseif (b <= -6.8e-214)
		tmp = t_3;
	elseif (b <= 1.25e-13)
		tmp = t_2;
	elseif (b <= 4.6e+92)
		tmp = i * -(y * j);
	elseif (b <= 2.2e+105)
		tmp = t_3;
	elseif (b <= 4.5e+213)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.32e+191], t$95$1, If[LessEqual[b, -1.05e+138], t$95$2, If[LessEqual[b, -1.05e+40], t$95$1, If[LessEqual[b, -7.5e-185], t$95$2, If[LessEqual[b, -6.8e-214], t$95$3, If[LessEqual[b, 1.25e-13], t$95$2, If[LessEqual[b, 4.6e+92], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 2.2e+105], t$95$3, If[LessEqual[b, 4.5e+213], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.32e191 or -1.05000000000000003e138 < b < -1.05000000000000005e40 or 4.5000000000000002e213 < b

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -1.32e191 < b < -1.05000000000000003e138 or -1.05000000000000005e40 < b < -7.49999999999999978e-185 or -6.7999999999999998e-214 < b < 1.24999999999999997e-13

   1. Initial program 72.9%

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

   3. Taylor expanded in a around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

      5. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   if -7.49999999999999978e-185 < b < -6.7999999999999998e-214 or 4.59999999999999997e92 < b < 2.20000000000000007e105

   1. Initial program 77.5%

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

   3. Taylor expanded in y around 0 92.2%

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

   4. Taylor expanded in z around inf 85.3%

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

      1. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

   9. Simplified 77.7%

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

   if 1.24999999999999997e-13 < b < 4.59999999999999997e92

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

      4. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in x around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. distribute-rgt-neg-in 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in y around 0 43.4%

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

       1. associate-*r* 43.4%

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

       2. neg-mul-1 43.4%

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

       3. *-commutative 43.4%

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

   11. Simplified 43.4%

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

   if 2.20000000000000007e105 < b < 4.5000000000000002e213

   1. Initial program 85.6%

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

   3. Taylor expanded in c around inf 79.2%

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

      1. *-commutative 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+191}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-214}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := j \cdot t\_2 + t\_1\\ t_4 := x \cdot \left(\left(y \cdot z - t \cdot a\right) + j \cdot \frac{t\_2}{x}\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - \left(a \cdot \left(x \cdot t\right) + \left(z \cdot \left(b \cdot c - x \cdot y\right) - a \cdot \left(c \cdot j\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+158} \lor \neg \left(j \leq 2.8 \cdot 10^{+195}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (+ (* j t_2) t_1))
        (t_4 (* x (+ (- (* y z) (* t a)) (* j (/ t_2 x))))))
   (if (<= j -2.7e+135)
     t_4
     (if (<= j -1.8e+44)
       t_3
       (if (<= j -4.5e+25)
         (- t_1 (* x (- (* t a) (* y z))))
         (if (<= j 8.8e+92)
           (-
            (* b (* t i))
            (+ (* a (* x t)) (- (* z (- (* b c) (* x y))) (* a (* c j)))))
           (if (or (<= j 4.1e+158) (not (<= j 2.8e+195))) t_3 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * c) - (y * i);
	double t_3 = (j * t_2) + t_1;
	double t_4 = x * (((y * z) - (t * a)) + (j * (t_2 / x)));
	double tmp;
	if (j <= -2.7e+135) {
		tmp = t_4;
	} else if (j <= -1.8e+44) {
		tmp = t_3;
	} else if (j <= -4.5e+25) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (j <= 8.8e+92) {
		tmp = (b * (t * i)) - ((a * (x * t)) + ((z * ((b * c) - (x * y))) - (a * (c * j))));
	} else if ((j <= 4.1e+158) || !(j <= 2.8e+195)) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (a * c) - (y * i)
    t_3 = (j * t_2) + t_1
    t_4 = x * (((y * z) - (t * a)) + (j * (t_2 / x)))
    if (j <= (-2.7d+135)) then
        tmp = t_4
    else if (j <= (-1.8d+44)) then
        tmp = t_3
    else if (j <= (-4.5d+25)) then
        tmp = t_1 - (x * ((t * a) - (y * z)))
    else if (j <= 8.8d+92) then
        tmp = (b * (t * i)) - ((a * (x * t)) + ((z * ((b * c) - (x * y))) - (a * (c * j))))
    else if ((j <= 4.1d+158) .or. (.not. (j <= 2.8d+195))) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * c) - (y * i);
	double t_3 = (j * t_2) + t_1;
	double t_4 = x * (((y * z) - (t * a)) + (j * (t_2 / x)));
	double tmp;
	if (j <= -2.7e+135) {
		tmp = t_4;
	} else if (j <= -1.8e+44) {
		tmp = t_3;
	} else if (j <= -4.5e+25) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (j <= 8.8e+92) {
		tmp = (b * (t * i)) - ((a * (x * t)) + ((z * ((b * c) - (x * y))) - (a * (c * j))));
	} else if ((j <= 4.1e+158) || !(j <= 2.8e+195)) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (a * c) - (y * i)
	t_3 = (j * t_2) + t_1
	t_4 = x * (((y * z) - (t * a)) + (j * (t_2 / x)))
	tmp = 0
	if j <= -2.7e+135:
		tmp = t_4
	elif j <= -1.8e+44:
		tmp = t_3
	elif j <= -4.5e+25:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	elif j <= 8.8e+92:
		tmp = (b * (t * i)) - ((a * (x * t)) + ((z * ((b * c) - (x * y))) - (a * (c * j))))
	elif (j <= 4.1e+158) or not (j <= 2.8e+195):
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(Float64(j * t_2) + t_1)
	t_4 = Float64(x * Float64(Float64(Float64(y * z) - Float64(t * a)) + Float64(j * Float64(t_2 / x))))
	tmp = 0.0
	if (j <= -2.7e+135)
		tmp = t_4;
	elseif (j <= -1.8e+44)
		tmp = t_3;
	elseif (j <= -4.5e+25)
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (j <= 8.8e+92)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(Float64(a * Float64(x * t)) + Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) - Float64(a * Float64(c * j)))));
	elseif ((j <= 4.1e+158) || !(j <= 2.8e+195))
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (a * c) - (y * i);
	t_3 = (j * t_2) + t_1;
	t_4 = x * (((y * z) - (t * a)) + (j * (t_2 / x)));
	tmp = 0.0;
	if (j <= -2.7e+135)
		tmp = t_4;
	elseif (j <= -1.8e+44)
		tmp = t_3;
	elseif (j <= -4.5e+25)
		tmp = t_1 - (x * ((t * a) - (y * z)));
	elseif (j <= 8.8e+92)
		tmp = (b * (t * i)) - ((a * (x * t)) + ((z * ((b * c) - (x * y))) - (a * (c * j))));
	elseif ((j <= 4.1e+158) || ~((j <= 2.8e+195)))
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+135], t$95$4, If[LessEqual[j, -1.8e+44], t$95$3, If[LessEqual[j, -4.5e+25], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.8e+92], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 4.1e+158], N[Not[LessEqual[j, 2.8e+195]], $MachinePrecision]], t$95$3, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.69999999999999985e135 or 4.10000000000000004e158 < j < 2.7999999999999998e195

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 82.9%

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

   4. Taylor expanded in x around -inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. mul-1-neg 83.1%

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

      5. unsub-neg 83.1%

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

      6. mul-1-neg 83.1%

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

      7. *-commutative 83.1%

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

      8. associate-/l* 85.1%

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

      9. *-commutative 85.1%

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

      10. *-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -2.69999999999999985e135 < j < -1.8e44 or 8.79999999999999969e92 < j < 4.10000000000000004e158 or 2.7999999999999998e195 < j

   1. Initial program 69.3%

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

   3. Taylor expanded in x around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. *-commutative 80.7%

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

      3. fma-neg 86.9%

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

      4. *-rgt-identity 86.9%

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

      5. *-commutative 86.9%

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

      6. fma-neg 80.7%

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

      7. associate-*l* 80.7%

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

      8. *-rgt-identity 80.7%

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

   5. Simplified 80.7%

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

   if -1.8e44 < j < -4.5000000000000003e25

   1. Initial program 80.0%

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

   3. Taylor expanded in j around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -4.5000000000000003e25 < j < 8.79999999999999969e92

   1. Initial program 74.4%

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

   3. Taylor expanded in y around 0 79.9%

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

   4. Taylor expanded in z around 0 85.2%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in c around inf 81.7%

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

      1. *-commutative 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + j \cdot \frac{a \cdot c - y \cdot i}{x}\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - \left(a \cdot \left(x \cdot t\right) + \left(z \cdot \left(b \cdot c - x \cdot y\right) - a \cdot \left(c \cdot j\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{+158} \lor \neg \left(j \leq 2.8 \cdot 10^{+195}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + j \cdot \frac{a \cdot c - y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.3e+106)
     t_1
     (if (<= i -4.6e+17)
       (+ (* b (- (* t i) (* z c))) (* x (* y z)))
       (if (<= i 3.8e-257)
         (* a (* x (- (/ (* c j) x) t)))
         (if (<= i 1.2e+31)
           (* c (- (* a j) (* z b)))
           (if (<= i 9e+95)
             (* b (* c (- (/ (* t i) c) z)))
             (if (<= i 9e+99)
               (* j (- (* a c) (* y i)))
               (if (<= i 5.5e+157) (* y (- (* x z) (* i j))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.3e+106) {
		tmp = t_1;
	} else if (i <= -4.6e+17) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (i <= 3.8e-257) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (i <= 1.2e+31) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 9e+95) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (i <= 9e+99) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 5.5e+157) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.3d+106)) then
        tmp = t_1
    else if (i <= (-4.6d+17)) then
        tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
    else if (i <= 3.8d-257) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (i <= 1.2d+31) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 9d+95) then
        tmp = b * (c * (((t * i) / c) - z))
    else if (i <= 9d+99) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= 5.5d+157) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.3e+106) {
		tmp = t_1;
	} else if (i <= -4.6e+17) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (i <= 3.8e-257) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (i <= 1.2e+31) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 9e+95) {
		tmp = b * (c * (((t * i) / c) - z));
	} else if (i <= 9e+99) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 5.5e+157) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.3e+106:
		tmp = t_1
	elif i <= -4.6e+17:
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
	elif i <= 3.8e-257:
		tmp = a * (x * (((c * j) / x) - t))
	elif i <= 1.2e+31:
		tmp = c * ((a * j) - (z * b))
	elif i <= 9e+95:
		tmp = b * (c * (((t * i) / c) - z))
	elif i <= 9e+99:
		tmp = j * ((a * c) - (y * i))
	elif i <= 5.5e+157:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.3e+106)
		tmp = t_1;
	elseif (i <= -4.6e+17)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(y * z)));
	elseif (i <= 3.8e-257)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (i <= 1.2e+31)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 9e+95)
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)));
	elseif (i <= 9e+99)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= 5.5e+157)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * 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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.3e+106)
		tmp = t_1;
	elseif (i <= -4.6e+17)
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	elseif (i <= 3.8e-257)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (i <= 1.2e+31)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 9e+95)
		tmp = b * (c * (((t * i) / c) - z));
	elseif (i <= 9e+99)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= 5.5e+157)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.3e+106], t$95$1, If[LessEqual[i, -4.6e+17], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e-257], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e+31], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e+95], N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e+99], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+157], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -1.3000000000000001e106 or 5.5000000000000003e157 < i

   1. Initial program 61.8%

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

   3. Taylor expanded in i around inf 67.4%

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

      1. distribute-lft-out-- 67.4%

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

      2. *-commutative 67.4%

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

      3. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -1.3000000000000001e106 < i < -4.6e17

   1. Initial program 83.1%

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

   3. Taylor expanded in j around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in a around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. sub-neg 78.2%

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

      3. sub-neg 78.2%

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

      4. *-commutative 78.2%

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

      5. *-commutative 78.2%

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

   8. Simplified 78.2%

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

   if -4.6e17 < i < 3.8000000000000004e-257

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 60.8%

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

   if 3.8000000000000004e-257 < i < 1.19999999999999991e31

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if 1.19999999999999991e31 < i < 9.00000000000000033e95

   1. Initial program 63.2%

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

   3. Taylor expanded in b around inf 71.0%

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

      1. *-commutative 71.0%

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

      2. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in c around inf 77.8%

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

   if 9.00000000000000033e95 < i < 8.9999999999999999e99

   1. Initial program 100.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 8.9999999999999999e99 < i < 5.5000000000000003e157

   1. Initial program 36.1%

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

   3. Taylor expanded in y around inf 63.9%

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

      1. +-commutative 63.9%

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

      2. mul-1-neg 63.9%

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

      3. unsub-neg 63.9%

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

      4. *-commutative 63.9%

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

   5. Simplified 63.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* c (- (/ (* t i) c) z)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -4.8e+104)
     t_2
     (if (<= i -2.6e+18)
       t_1
       (if (<= i 4.9e-258)
         (* a (* x (- (/ (* c j) x) t)))
         (if (<= i 6e+32)
           (* c (- (* a j) (* z b)))
           (if (<= i 6.5e+95)
             t_1
             (if (<= i 4.1e+102)
               (* j (- (* a c) (* y i)))
               (if (<= i 5.5e+157) (* y (- (* x z) (* i j))) 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 = b * (c * (((t * i) / c) - z));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.8e+104) {
		tmp = t_2;
	} else if (i <= -2.6e+18) {
		tmp = t_1;
	} else if (i <= 4.9e-258) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (i <= 6e+32) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 6.5e+95) {
		tmp = t_1;
	} else if (i <= 4.1e+102) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 5.5e+157) {
		tmp = y * ((x * z) - (i * j));
	} 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 = b * (c * (((t * i) / c) - z))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-4.8d+104)) then
        tmp = t_2
    else if (i <= (-2.6d+18)) then
        tmp = t_1
    else if (i <= 4.9d-258) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (i <= 6d+32) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 6.5d+95) then
        tmp = t_1
    else if (i <= 4.1d+102) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= 5.5d+157) then
        tmp = y * ((x * z) - (i * j))
    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 = b * (c * (((t * i) / c) - z));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.8e+104) {
		tmp = t_2;
	} else if (i <= -2.6e+18) {
		tmp = t_1;
	} else if (i <= 4.9e-258) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (i <= 6e+32) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 6.5e+95) {
		tmp = t_1;
	} else if (i <= 4.1e+102) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 5.5e+157) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (c * (((t * i) / c) - z))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.8e+104:
		tmp = t_2
	elif i <= -2.6e+18:
		tmp = t_1
	elif i <= 4.9e-258:
		tmp = a * (x * (((c * j) / x) - t))
	elif i <= 6e+32:
		tmp = c * ((a * j) - (z * b))
	elif i <= 6.5e+95:
		tmp = t_1
	elif i <= 4.1e+102:
		tmp = j * ((a * c) - (y * i))
	elif i <= 5.5e+157:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.8e+104)
		tmp = t_2;
	elseif (i <= -2.6e+18)
		tmp = t_1;
	elseif (i <= 4.9e-258)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (i <= 6e+32)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 6.5e+95)
		tmp = t_1;
	elseif (i <= 4.1e+102)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= 5.5e+157)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (c * (((t * i) / c) - z));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.8e+104)
		tmp = t_2;
	elseif (i <= -2.6e+18)
		tmp = t_1;
	elseif (i <= 4.9e-258)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (i <= 6e+32)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 6.5e+95)
		tmp = t_1;
	elseif (i <= 4.1e+102)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= 5.5e+157)
		tmp = y * ((x * z) - (i * j));
	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[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+104], t$95$2, If[LessEqual[i, -2.6e+18], t$95$1, If[LessEqual[i, 4.9e-258], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e+32], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.5e+95], t$95$1, If[LessEqual[i, 4.1e+102], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+157], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.8e104 or 5.5000000000000003e157 < i

   1. Initial program 61.8%

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

   3. Taylor expanded in i around inf 67.4%

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

      1. distribute-lft-out-- 67.4%

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

      2. *-commutative 67.4%

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

      3. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -4.8e104 < i < -2.6e18 or 6e32 < i < 6.5e95

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in c around inf 73.0%

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

   if -2.6e18 < i < 4.9000000000000001e-258

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 60.8%

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

   if 4.9000000000000001e-258 < i < 6e32

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if 6.5e95 < i < 4.1e102

   1. Initial program 100.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 4.1e102 < i < 5.5000000000000003e157

   1. Initial program 36.1%

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

   3. Taylor expanded in y around inf 63.9%

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

      1. +-commutative 63.9%

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

      2. mul-1-neg 63.9%

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

      3. unsub-neg 63.9%

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

      4. *-commutative 63.9%

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

   5. Simplified 63.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := j \cdot t\_2\\ t_4 := x \cdot \left(\left(y \cdot z + \frac{t\_3}{x}\right) - t \cdot a\right)\\ t_5 := y \cdot z - t \cdot a\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+78}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \left(t\_5 + \frac{t\_1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_5 + j \cdot \frac{t\_2}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (* j t_2))
        (t_4 (* x (- (+ (* y z) (/ t_3 x)) (* t a))))
        (t_5 (- (* y z) (* t a))))
   (if (<= x -2.3e-45)
     t_4
     (if (<= x 1.55e-106)
       (+ t_3 t_1)
       (if (<= x 2.95e+78)
         t_4
         (if (<= x 4e+286)
           (* x (+ t_5 (/ t_1 x)))
           (* x (+ t_5 (* j (/ t_2 x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * c) - (y * i);
	double t_3 = j * t_2;
	double t_4 = x * (((y * z) + (t_3 / x)) - (t * a));
	double t_5 = (y * z) - (t * a);
	double tmp;
	if (x <= -2.3e-45) {
		tmp = t_4;
	} else if (x <= 1.55e-106) {
		tmp = t_3 + t_1;
	} else if (x <= 2.95e+78) {
		tmp = t_4;
	} else if (x <= 4e+286) {
		tmp = x * (t_5 + (t_1 / x));
	} else {
		tmp = x * (t_5 + (j * (t_2 / x)));
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (a * c) - (y * i)
    t_3 = j * t_2
    t_4 = x * (((y * z) + (t_3 / x)) - (t * a))
    t_5 = (y * z) - (t * a)
    if (x <= (-2.3d-45)) then
        tmp = t_4
    else if (x <= 1.55d-106) then
        tmp = t_3 + t_1
    else if (x <= 2.95d+78) then
        tmp = t_4
    else if (x <= 4d+286) then
        tmp = x * (t_5 + (t_1 / x))
    else
        tmp = x * (t_5 + (j * (t_2 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * c) - (y * i);
	double t_3 = j * t_2;
	double t_4 = x * (((y * z) + (t_3 / x)) - (t * a));
	double t_5 = (y * z) - (t * a);
	double tmp;
	if (x <= -2.3e-45) {
		tmp = t_4;
	} else if (x <= 1.55e-106) {
		tmp = t_3 + t_1;
	} else if (x <= 2.95e+78) {
		tmp = t_4;
	} else if (x <= 4e+286) {
		tmp = x * (t_5 + (t_1 / x));
	} else {
		tmp = x * (t_5 + (j * (t_2 / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (a * c) - (y * i)
	t_3 = j * t_2
	t_4 = x * (((y * z) + (t_3 / x)) - (t * a))
	t_5 = (y * z) - (t * a)
	tmp = 0
	if x <= -2.3e-45:
		tmp = t_4
	elif x <= 1.55e-106:
		tmp = t_3 + t_1
	elif x <= 2.95e+78:
		tmp = t_4
	elif x <= 4e+286:
		tmp = x * (t_5 + (t_1 / x))
	else:
		tmp = x * (t_5 + (j * (t_2 / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(j * t_2)
	t_4 = Float64(x * Float64(Float64(Float64(y * z) + Float64(t_3 / x)) - Float64(t * a)))
	t_5 = Float64(Float64(y * z) - Float64(t * a))
	tmp = 0.0
	if (x <= -2.3e-45)
		tmp = t_4;
	elseif (x <= 1.55e-106)
		tmp = Float64(t_3 + t_1);
	elseif (x <= 2.95e+78)
		tmp = t_4;
	elseif (x <= 4e+286)
		tmp = Float64(x * Float64(t_5 + Float64(t_1 / x)));
	else
		tmp = Float64(x * Float64(t_5 + Float64(j * Float64(t_2 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (a * c) - (y * i);
	t_3 = j * t_2;
	t_4 = x * (((y * z) + (t_3 / x)) - (t * a));
	t_5 = (y * z) - (t * a);
	tmp = 0.0;
	if (x <= -2.3e-45)
		tmp = t_4;
	elseif (x <= 1.55e-106)
		tmp = t_3 + t_1;
	elseif (x <= 2.95e+78)
		tmp = t_4;
	elseif (x <= 4e+286)
		tmp = x * (t_5 + (t_1 / x));
	else
		tmp = x * (t_5 + (j * (t_2 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * z), $MachinePrecision] + N[(t$95$3 / x), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e-45], t$95$4, If[LessEqual[x, 1.55e-106], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[x, 2.95e+78], t$95$4, If[LessEqual[x, 4e+286], N[(x * N[(t$95$5 + N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$5 + N[(j * N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.29999999999999992e-45 or 1.54999999999999993e-106 < x < 2.95e78

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 71.9%

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

   4. Taylor expanded in x around inf 72.9%

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

   if -2.29999999999999992e-45 < x < 1.54999999999999993e-106

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. fma-neg 82.8%

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

      4. *-rgt-identity 82.8%

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

      5. *-commutative 82.8%

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

      6. fma-neg 78.8%

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

      7. associate-*l* 78.8%

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

      8. *-rgt-identity 78.8%

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

   5. Simplified 78.8%

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

   if 2.95e78 < x < 4.00000000000000013e286

   1. Initial program 72.8%

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

   3. Taylor expanded in j around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x around inf 77.8%

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

      1. associate--l+ 77.8%

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

   8. Simplified 77.8%

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

   if 4.00000000000000013e286 < x

   1. Initial program 82.8%

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

   3. Taylor expanded in b around 0 82.8%

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

   4. Taylor expanded in x around -inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. *-commutative 82.8%

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

      3. distribute-rgt-neg-in 82.8%

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

      4. mul-1-neg 82.8%

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

      5. unsub-neg 82.8%

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

      6. mul-1-neg 82.8%

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

      7. *-commutative 82.8%

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

      8. associate-/l* 99.5%

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

      9. *-commutative 99.5%

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

      10. *-commutative 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{b \cdot \left(t \cdot i - z \cdot c\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + j \cdot \frac{a \cdot c - y \cdot i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(\left(y \cdot z + \frac{t\_2}{x}\right) - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{t\_1}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* x (- (+ (* y z) (/ t_2 x)) (* t a)))))
   (if (<= x -2.35e-43)
     t_3
     (if (<= x 1.55e-106)
       (+ t_2 t_1)
       (if (<= x 2.95e+78)
         t_3
         (if (<= x 7e+286)
           (* x (+ (- (* y z) (* t a)) (/ t_1 x)))
           (* 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 t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * (((y * z) + (t_2 / x)) - (t * a));
	double tmp;
	if (x <= -2.35e-43) {
		tmp = t_3;
	} else if (x <= 1.55e-106) {
		tmp = t_2 + t_1;
	} else if (x <= 2.95e+78) {
		tmp = t_3;
	} else if (x <= 7e+286) {
		tmp = x * (((y * z) - (t * a)) + (t_1 / x));
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * (((y * z) + (t_2 / x)) - (t * a))
    if (x <= (-2.35d-43)) then
        tmp = t_3
    else if (x <= 1.55d-106) then
        tmp = t_2 + t_1
    else if (x <= 2.95d+78) then
        tmp = t_3
    else if (x <= 7d+286) then
        tmp = x * (((y * z) - (t * a)) + (t_1 / x))
    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 t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * (((y * z) + (t_2 / x)) - (t * a));
	double tmp;
	if (x <= -2.35e-43) {
		tmp = t_3;
	} else if (x <= 1.55e-106) {
		tmp = t_2 + t_1;
	} else if (x <= 2.95e+78) {
		tmp = t_3;
	} else if (x <= 7e+286) {
		tmp = x * (((y * z) - (t * a)) + (t_1 / x));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = x * (((y * z) + (t_2 / x)) - (t * a))
	tmp = 0
	if x <= -2.35e-43:
		tmp = t_3
	elif x <= 1.55e-106:
		tmp = t_2 + t_1
	elif x <= 2.95e+78:
		tmp = t_3
	elif x <= 7e+286:
		tmp = x * (((y * z) - (t * a)) + (t_1 / x))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(Float64(y * z) + Float64(t_2 / x)) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.35e-43)
		tmp = t_3;
	elseif (x <= 1.55e-106)
		tmp = Float64(t_2 + t_1);
	elseif (x <= 2.95e+78)
		tmp = t_3;
	elseif (x <= 7e+286)
		tmp = Float64(x * Float64(Float64(Float64(y * z) - Float64(t * a)) + Float64(t_1 / x)));
	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)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = x * (((y * z) + (t_2 / x)) - (t * a));
	tmp = 0.0;
	if (x <= -2.35e-43)
		tmp = t_3;
	elseif (x <= 1.55e-106)
		tmp = t_2 + t_1;
	elseif (x <= 2.95e+78)
		tmp = t_3;
	elseif (x <= 7e+286)
		tmp = x * (((y * z) - (t * a)) + (t_1 / x));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * z), $MachinePrecision] + N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.35e-43], t$95$3, If[LessEqual[x, 1.55e-106], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[x, 2.95e+78], t$95$3, If[LessEqual[x, 7e+286], N[(x * N[(N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.35e-43 or 1.54999999999999993e-106 < x < 2.95e78

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 71.9%

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

   4. Taylor expanded in x around inf 72.9%

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

   if -2.35e-43 < x < 1.54999999999999993e-106

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. fma-neg 82.8%

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

      4. *-rgt-identity 82.8%

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

      5. *-commutative 82.8%

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

      6. fma-neg 78.8%

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

      7. associate-*l* 78.8%

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

      8. *-rgt-identity 78.8%

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

   5. Simplified 78.8%

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

   if 2.95e78 < x < 7.00000000000000002e286

   1. Initial program 72.8%

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

   3. Taylor expanded in j around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x around inf 77.8%

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

      1. associate--l+ 77.8%

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

   8. Simplified 77.8%

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

   if 7.00000000000000002e286 < x

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 18.0%

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

   4. Taylor expanded in z around inf 84.4%

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

      1. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   9. Simplified 84.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{b \cdot \left(t \cdot i - z \cdot c\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.00032:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -4.2e+152)
     t_2
     (if (<= a -2.75e+50)
       t_1
       (if (<= a -0.00032)
         t_2
         (if (<= a -1.02e-109)
           (* y (- (* x z) (* i j)))
           (if (<= a -3.3e-292)
             t_1
             (if (<= a 1.2e+51) (* z (- (* x y) (* b c))) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+152) {
		tmp = t_2;
	} else if (a <= -2.75e+50) {
		tmp = t_1;
	} else if (a <= -0.00032) {
		tmp = t_2;
	} else if (a <= -1.02e-109) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= -3.3e-292) {
		tmp = t_1;
	} else if (a <= 1.2e+51) {
		tmp = z * ((x * y) - (b * c));
	} 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 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-4.2d+152)) then
        tmp = t_2
    else if (a <= (-2.75d+50)) then
        tmp = t_1
    else if (a <= (-0.00032d0)) then
        tmp = t_2
    else if (a <= (-1.02d-109)) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= (-3.3d-292)) then
        tmp = t_1
    else if (a <= 1.2d+51) then
        tmp = z * ((x * y) - (b * c))
    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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+152) {
		tmp = t_2;
	} else if (a <= -2.75e+50) {
		tmp = t_1;
	} else if (a <= -0.00032) {
		tmp = t_2;
	} else if (a <= -1.02e-109) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= -3.3e-292) {
		tmp = t_1;
	} else if (a <= 1.2e+51) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.2e+152:
		tmp = t_2
	elif a <= -2.75e+50:
		tmp = t_1
	elif a <= -0.00032:
		tmp = t_2
	elif a <= -1.02e-109:
		tmp = y * ((x * z) - (i * j))
	elif a <= -3.3e-292:
		tmp = t_1
	elif a <= 1.2e+51:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.2e+152)
		tmp = t_2;
	elseif (a <= -2.75e+50)
		tmp = t_1;
	elseif (a <= -0.00032)
		tmp = t_2;
	elseif (a <= -1.02e-109)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= -3.3e-292)
		tmp = t_1;
	elseif (a <= 1.2e+51)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.2e+152)
		tmp = t_2;
	elseif (a <= -2.75e+50)
		tmp = t_1;
	elseif (a <= -0.00032)
		tmp = t_2;
	elseif (a <= -1.02e-109)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= -3.3e-292)
		tmp = t_1;
	elseif (a <= 1.2e+51)
		tmp = z * ((x * y) - (b * c));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+152], t$95$2, If[LessEqual[a, -2.75e+50], t$95$1, If[LessEqual[a, -0.00032], t$95$2, If[LessEqual[a, -1.02e-109], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.3e-292], t$95$1, If[LessEqual[a, 1.2e+51], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2000000000000003e152 or -2.7499999999999999e50 < a < -3.20000000000000026e-4 or 1.1999999999999999e51 < a

   1. Initial program 69.7%

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

   3. Taylor expanded in a around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. *-commutative 75.3%

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

      5. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -4.2000000000000003e152 < a < -2.7499999999999999e50 or -1.02e-109 < a < -3.29999999999999995e-292

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   if -3.20000000000000026e-4 < a < -1.02e-109

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   if -3.29999999999999995e-292 < a < 1.1999999999999999e51

   1. Initial program 75.7%

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

   3. Taylor expanded in z around inf 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -0.00032:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{-298}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.7e-25)
     t_2
     (if (<= a -7e-78)
       t_1
       (if (<= a -5.4e-100)
         t_2
         (if (<= a -3e-224)
           (* b (* z (- c)))
           (if (<= a 1.68e-298)
             (* b (* t i))
             (if (<= a 1.22e-80) 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 = z * (x * y);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.7e-25) {
		tmp = t_2;
	} else if (a <= -7e-78) {
		tmp = t_1;
	} else if (a <= -5.4e-100) {
		tmp = t_2;
	} else if (a <= -3e-224) {
		tmp = b * (z * -c);
	} else if (a <= 1.68e-298) {
		tmp = b * (t * i);
	} else if (a <= 1.22e-80) {
		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 = z * (x * y)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.7d-25)) then
        tmp = t_2
    else if (a <= (-7d-78)) then
        tmp = t_1
    else if (a <= (-5.4d-100)) then
        tmp = t_2
    else if (a <= (-3d-224)) then
        tmp = b * (z * -c)
    else if (a <= 1.68d-298) then
        tmp = b * (t * i)
    else if (a <= 1.22d-80) 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 = z * (x * y);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.7e-25) {
		tmp = t_2;
	} else if (a <= -7e-78) {
		tmp = t_1;
	} else if (a <= -5.4e-100) {
		tmp = t_2;
	} else if (a <= -3e-224) {
		tmp = b * (z * -c);
	} else if (a <= 1.68e-298) {
		tmp = b * (t * i);
	} else if (a <= 1.22e-80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.7e-25:
		tmp = t_2
	elif a <= -7e-78:
		tmp = t_1
	elif a <= -5.4e-100:
		tmp = t_2
	elif a <= -3e-224:
		tmp = b * (z * -c)
	elif a <= 1.68e-298:
		tmp = b * (t * i)
	elif a <= 1.22e-80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.7e-25)
		tmp = t_2;
	elseif (a <= -7e-78)
		tmp = t_1;
	elseif (a <= -5.4e-100)
		tmp = t_2;
	elseif (a <= -3e-224)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 1.68e-298)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.22e-80)
		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 = z * (x * y);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.7e-25)
		tmp = t_2;
	elseif (a <= -7e-78)
		tmp = t_1;
	elseif (a <= -5.4e-100)
		tmp = t_2;
	elseif (a <= -3e-224)
		tmp = b * (z * -c);
	elseif (a <= 1.68e-298)
		tmp = b * (t * i);
	elseif (a <= 1.22e-80)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-25], t$95$2, If[LessEqual[a, -7e-78], t$95$1, If[LessEqual[a, -5.4e-100], t$95$2, If[LessEqual[a, -3e-224], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.68e-298], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-80], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.70000000000000016e-25 or -6.9999999999999999e-78 < a < -5.40000000000000031e-100 or 1.22e-80 < a

   1. Initial program 72.1%

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

   3. Taylor expanded in a around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if -2.70000000000000016e-25 < a < -6.9999999999999999e-78 or 1.68000000000000008e-298 < a < 1.22e-80

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0 70.7%

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

   4. Taylor expanded in z around inf 60.0%

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

      1. *-commutative 60.0%

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

   6. Simplified 60.0%

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

   7. Taylor expanded in y around inf 46.1%

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

      1. *-commutative 46.1%

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

   9. Simplified 46.1%

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

   if -5.40000000000000031e-100 < a < -2.99999999999999982e-224

   1. Initial program 83.4%

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

   3. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

      2. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in t around 0 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   8. Simplified 44.8%

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

   if -2.99999999999999982e-224 < a < 1.68000000000000008e-298

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

   8. Simplified 49.5%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{-298}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+106} \lor \neg \left(x \leq 1.6 \cdot 10^{+145}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (- t_1 (* x (- (* t a) (* y z))))))
   (if (<= x -4.7e-45)
     t_2
     (if (<= x 1.55e-106)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (or (<= x 2.8e+106) (not (<= x 1.6e+145)))
         t_2
         (* c (- (* a j) (* z b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (x <= -4.7e-45) {
		tmp = t_2;
	} else if (x <= 1.55e-106) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if ((x <= 2.8e+106) || !(x <= 1.6e+145)) {
		tmp = t_2;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 - (x * ((t * a) - (y * z)))
    if (x <= (-4.7d-45)) then
        tmp = t_2
    else if (x <= 1.55d-106) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if ((x <= 2.8d+106) .or. (.not. (x <= 1.6d+145))) then
        tmp = t_2
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (x <= -4.7e-45) {
		tmp = t_2;
	} else if (x <= 1.55e-106) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if ((x <= 2.8e+106) || !(x <= 1.6e+145)) {
		tmp = t_2;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 - (x * ((t * a) - (y * z)))
	tmp = 0
	if x <= -4.7e-45:
		tmp = t_2
	elif x <= 1.55e-106:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif (x <= 2.8e+106) or not (x <= 1.6e+145):
		tmp = t_2
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (x <= -4.7e-45)
		tmp = t_2;
	elseif (x <= 1.55e-106)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif ((x <= 2.8e+106) || !(x <= 1.6e+145))
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (x <= -4.7e-45)
		tmp = t_2;
	elseif (x <= 1.55e-106)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif ((x <= 2.8e+106) || ~((x <= 1.6e+145)))
		tmp = t_2;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.7e-45], t$95$2, If[LessEqual[x, 1.55e-106], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.8e+106], N[Not[LessEqual[x, 1.6e+145]], $MachinePrecision]], t$95$2, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6999999999999998e-45 or 1.54999999999999993e-106 < x < 2.79999999999999993e106 or 1.60000000000000004e145 < x

   1. Initial program 75.9%

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

   3. Taylor expanded in b around 0 73.2%

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

   if -4.6999999999999998e-45 < x < 1.54999999999999993e-106

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. fma-neg 82.8%

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

      4. *-rgt-identity 82.8%

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

      5. *-commutative 82.8%

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

      6. fma-neg 78.8%

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

      7. associate-*l* 78.8%

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

      8. *-rgt-identity 78.8%

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

   5. Simplified 78.8%

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

   if 2.79999999999999993e106 < x < 1.60000000000000004e145

   1. Initial program 55.3%

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

   3. Taylor expanded in c around inf 82.6%

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

      1. *-commutative 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+106} \lor \neg \left(x \leq 1.6 \cdot 10^{+145}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;t\_2 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+214}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -9.2e+197)
     (+ t_2 (* x (* y z)))
     (if (<= b -3.5e+131)
       t_1
       (if (<= b -2.65e+72)
         t_2
         (if (<= b 1.1e+128)
           t_1
           (if (<= b 1.85e+214) (* c (- (* a j) (* z b))) 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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.2e+197) {
		tmp = t_2 + (x * (y * z));
	} else if (b <= -3.5e+131) {
		tmp = t_1;
	} else if (b <= -2.65e+72) {
		tmp = t_2;
	} else if (b <= 1.1e+128) {
		tmp = t_1;
	} else if (b <= 1.85e+214) {
		tmp = c * ((a * j) - (z * b));
	} 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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-9.2d+197)) then
        tmp = t_2 + (x * (y * z))
    else if (b <= (-3.5d+131)) then
        tmp = t_1
    else if (b <= (-2.65d+72)) then
        tmp = t_2
    else if (b <= 1.1d+128) then
        tmp = t_1
    else if (b <= 1.85d+214) then
        tmp = c * ((a * j) - (z * b))
    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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -9.2e+197) {
		tmp = t_2 + (x * (y * z));
	} else if (b <= -3.5e+131) {
		tmp = t_1;
	} else if (b <= -2.65e+72) {
		tmp = t_2;
	} else if (b <= 1.1e+128) {
		tmp = t_1;
	} else if (b <= 1.85e+214) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -9.2e+197:
		tmp = t_2 + (x * (y * z))
	elif b <= -3.5e+131:
		tmp = t_1
	elif b <= -2.65e+72:
		tmp = t_2
	elif b <= 1.1e+128:
		tmp = t_1
	elif b <= 1.85e+214:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.2e+197)
		tmp = Float64(t_2 + Float64(x * Float64(y * z)));
	elseif (b <= -3.5e+131)
		tmp = t_1;
	elseif (b <= -2.65e+72)
		tmp = t_2;
	elseif (b <= 1.1e+128)
		tmp = t_1;
	elseif (b <= 1.85e+214)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.2e+197)
		tmp = t_2 + (x * (y * z));
	elseif (b <= -3.5e+131)
		tmp = t_1;
	elseif (b <= -2.65e+72)
		tmp = t_2;
	elseif (b <= 1.1e+128)
		tmp = t_1;
	elseif (b <= 1.85e+214)
		tmp = c * ((a * j) - (z * b));
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+197], N[(t$95$2 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e+131], t$95$1, If[LessEqual[b, -2.65e+72], t$95$2, If[LessEqual[b, 1.1e+128], t$95$1, If[LessEqual[b, 1.85e+214], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.2000000000000002e197

   1. Initial program 71.2%

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

   3. Taylor expanded in j around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in a around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. sub-neg 91.0%

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

      3. sub-neg 91.0%

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

      4. *-commutative 91.0%

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

      5. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   if -9.2000000000000002e197 < b < -3.4999999999999999e131 or -2.6500000000000001e72 < b < 1.10000000000000008e128

   1. Initial program 75.6%

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

   3. Taylor expanded in b around 0 75.3%

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

   if -3.4999999999999999e131 < b < -2.6500000000000001e72 or 1.8499999999999999e214 < b

   1. Initial program 59.6%

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

   3. Taylor expanded in b around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if 1.10000000000000008e128 < b < 1.8499999999999999e214

   1. Initial program 83.2%

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

   3. Taylor expanded in c around inf 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+128}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+214}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -z \cdot \left(b \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-239}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z (* b c)))) (t_2 (* c (* a j))))
   (if (<= z -6.6e+89)
     t_1
     (if (<= z -6.7e-239)
       (* i (- (* y j)))
       (if (<= z 2.3e-112)
         t_2
         (if (<= z 7e-83)
           (* y (* j (- i)))
           (if (<= z 4.3e-26) t_2 (if (<= z 9.5e+173) t_1 (* 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 t_1 = -(z * (b * c));
	double t_2 = c * (a * j);
	double tmp;
	if (z <= -6.6e+89) {
		tmp = t_1;
	} else if (z <= -6.7e-239) {
		tmp = i * -(y * j);
	} else if (z <= 2.3e-112) {
		tmp = t_2;
	} else if (z <= 7e-83) {
		tmp = y * (j * -i);
	} else if (z <= 4.3e-26) {
		tmp = t_2;
	} else if (z <= 9.5e+173) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -(z * (b * c))
    t_2 = c * (a * j)
    if (z <= (-6.6d+89)) then
        tmp = t_1
    else if (z <= (-6.7d-239)) then
        tmp = i * -(y * j)
    else if (z <= 2.3d-112) then
        tmp = t_2
    else if (z <= 7d-83) then
        tmp = y * (j * -i)
    else if (z <= 4.3d-26) then
        tmp = t_2
    else if (z <= 9.5d+173) then
        tmp = t_1
    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 t_1 = -(z * (b * c));
	double t_2 = c * (a * j);
	double tmp;
	if (z <= -6.6e+89) {
		tmp = t_1;
	} else if (z <= -6.7e-239) {
		tmp = i * -(y * j);
	} else if (z <= 2.3e-112) {
		tmp = t_2;
	} else if (z <= 7e-83) {
		tmp = y * (j * -i);
	} else if (z <= 4.3e-26) {
		tmp = t_2;
	} else if (z <= 9.5e+173) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -(z * (b * c))
	t_2 = c * (a * j)
	tmp = 0
	if z <= -6.6e+89:
		tmp = t_1
	elif z <= -6.7e-239:
		tmp = i * -(y * j)
	elif z <= 2.3e-112:
		tmp = t_2
	elif z <= 7e-83:
		tmp = y * (j * -i)
	elif z <= 4.3e-26:
		tmp = t_2
	elif z <= 9.5e+173:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(-Float64(z * Float64(b * c)))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (z <= -6.6e+89)
		tmp = t_1;
	elseif (z <= -6.7e-239)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (z <= 2.3e-112)
		tmp = t_2;
	elseif (z <= 7e-83)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (z <= 4.3e-26)
		tmp = t_2;
	elseif (z <= 9.5e+173)
		tmp = t_1;
	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)
	t_1 = -(z * (b * c));
	t_2 = c * (a * j);
	tmp = 0.0;
	if (z <= -6.6e+89)
		tmp = t_1;
	elseif (z <= -6.7e-239)
		tmp = i * -(y * j);
	elseif (z <= 2.3e-112)
		tmp = t_2;
	elseif (z <= 7e-83)
		tmp = y * (j * -i);
	elseif (z <= 4.3e-26)
		tmp = t_2;
	elseif (z <= 9.5e+173)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = (-N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+89], t$95$1, If[LessEqual[z, -6.7e-239], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.3e-112], t$95$2, If[LessEqual[z, 7e-83], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-26], t$95$2, If[LessEqual[z, 9.5e+173], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.59999999999999948e89 or 4.29999999999999988e-26 < z < 9.5000000000000005e173

   1. Initial program 68.1%

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

   3. Taylor expanded in y around 0 70.3%

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

   4. Taylor expanded in z around inf 62.9%

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

      1. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in y around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-lft-neg-out 44.3%

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

      3. *-commutative 44.3%

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

   9. Simplified 44.3%

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

   if -6.59999999999999948e89 < z < -6.70000000000000038e-239

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in x around 0 32.2%

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

      1. mul-1-neg 32.2%

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

      2. distribute-rgt-neg-in 32.2%

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

   8. Simplified 32.2%

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

   9. Taylor expanded in y around 0 37.0%

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

       1. associate-*r* 37.0%

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

       2. neg-mul-1 37.0%

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

       3. *-commutative 37.0%

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

   11. Simplified 37.0%

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

   if -6.70000000000000038e-239 < z < 2.29999999999999991e-112 or 7.00000000000000061e-83 < z < 4.29999999999999988e-26

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in j around inf 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   9. Taylor expanded in a around 0 39.7%

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

       1. *-commutative 39.7%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

   11. Simplified 46.1%

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

   if 2.29999999999999991e-112 < z < 7.00000000000000061e-83

   1. Initial program 85.5%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. +-commutative 85.6%

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

      2. mul-1-neg 85.6%

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

      3. unsub-neg 85.6%

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

      4. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in x around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. distribute-rgt-neg-in 72.1%

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

   8. Simplified 72.1%

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

   if 9.5000000000000005e173 < z

   1. Initial program 56.0%

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

   3. Taylor expanded in y around 0 66.0%

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

   4. Taylor expanded in z around inf 72.6%

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

      1. *-commutative 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in y around inf 55.4%

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

      1. *-commutative 55.4%

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

   9. Simplified 55.4%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+89}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-239}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-112}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+173}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{t\_1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (- t_2 (* x (- (* t a) (* y z))))))
   (if (<= x -1.15e-43)
     t_3
     (if (<= x 1.55e-106)
       (+ t_2 t_1)
       (if (<= x 2.95e+78) t_3 (* x (+ (- (* y z) (* t a)) (/ t_1 x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (x <= -1.15e-43) {
		tmp = t_3;
	} else if (x <= 1.55e-106) {
		tmp = t_2 + t_1;
	} else if (x <= 2.95e+78) {
		tmp = t_3;
	} else {
		tmp = x * (((y * z) - (t * a)) + (t_1 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 - (x * ((t * a) - (y * z)))
    if (x <= (-1.15d-43)) then
        tmp = t_3
    else if (x <= 1.55d-106) then
        tmp = t_2 + t_1
    else if (x <= 2.95d+78) then
        tmp = t_3
    else
        tmp = x * (((y * z) - (t * a)) + (t_1 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (x <= -1.15e-43) {
		tmp = t_3;
	} else if (x <= 1.55e-106) {
		tmp = t_2 + t_1;
	} else if (x <= 2.95e+78) {
		tmp = t_3;
	} else {
		tmp = x * (((y * z) - (t * a)) + (t_1 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 - (x * ((t * a) - (y * z)))
	tmp = 0
	if x <= -1.15e-43:
		tmp = t_3
	elif x <= 1.55e-106:
		tmp = t_2 + t_1
	elif x <= 2.95e+78:
		tmp = t_3
	else:
		tmp = x * (((y * z) - (t * a)) + (t_1 / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (x <= -1.15e-43)
		tmp = t_3;
	elseif (x <= 1.55e-106)
		tmp = Float64(t_2 + t_1);
	elseif (x <= 2.95e+78)
		tmp = t_3;
	else
		tmp = Float64(x * Float64(Float64(Float64(y * z) - Float64(t * a)) + Float64(t_1 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (x <= -1.15e-43)
		tmp = t_3;
	elseif (x <= 1.55e-106)
		tmp = t_2 + t_1;
	elseif (x <= 2.95e+78)
		tmp = t_3;
	else
		tmp = x * (((y * z) - (t * a)) + (t_1 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e-43], t$95$3, If[LessEqual[x, 1.55e-106], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[x, 2.95e+78], t$95$3, N[(x * N[(N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1499999999999999e-43 or 1.54999999999999993e-106 < x < 2.95e78

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 71.9%

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

   if -1.1499999999999999e-43 < x < 1.54999999999999993e-106

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. fma-neg 82.8%

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

      4. *-rgt-identity 82.8%

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

      5. *-commutative 82.8%

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

      6. fma-neg 78.8%

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

      7. associate-*l* 78.8%

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

      8. *-rgt-identity 78.8%

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

   5. Simplified 78.8%

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

   if 2.95e78 < x

   1. Initial program 74.0%

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

   3. Taylor expanded in j around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf 76.4%

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

      1. associate--l+ 76.4%

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

   8. Simplified 76.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-43}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{b \cdot \left(t \cdot i - z \cdot c\right)}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+22}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* a j))))
   (if (<= a -4.8e-33)
     t_2
     (if (<= a -2.6e-224)
       (* b (* z (- c)))
       (if (<= a 6.2e-305)
         (* b (* t i))
         (if (<= a 1.35e-42)
           t_1
           (if (<= a 3.1e+22)
             (- (* z (* b c)))
             (if (<= a 7.5e+134) 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 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -4.8e-33) {
		tmp = t_2;
	} else if (a <= -2.6e-224) {
		tmp = b * (z * -c);
	} else if (a <= 6.2e-305) {
		tmp = b * (t * i);
	} else if (a <= 1.35e-42) {
		tmp = t_1;
	} else if (a <= 3.1e+22) {
		tmp = -(z * (b * c));
	} else if (a <= 7.5e+134) {
		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 = z * (x * y)
    t_2 = c * (a * j)
    if (a <= (-4.8d-33)) then
        tmp = t_2
    else if (a <= (-2.6d-224)) then
        tmp = b * (z * -c)
    else if (a <= 6.2d-305) then
        tmp = b * (t * i)
    else if (a <= 1.35d-42) then
        tmp = t_1
    else if (a <= 3.1d+22) then
        tmp = -(z * (b * c))
    else if (a <= 7.5d+134) 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 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -4.8e-33) {
		tmp = t_2;
	} else if (a <= -2.6e-224) {
		tmp = b * (z * -c);
	} else if (a <= 6.2e-305) {
		tmp = b * (t * i);
	} else if (a <= 1.35e-42) {
		tmp = t_1;
	} else if (a <= 3.1e+22) {
		tmp = -(z * (b * c));
	} else if (a <= 7.5e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (a * j)
	tmp = 0
	if a <= -4.8e-33:
		tmp = t_2
	elif a <= -2.6e-224:
		tmp = b * (z * -c)
	elif a <= 6.2e-305:
		tmp = b * (t * i)
	elif a <= 1.35e-42:
		tmp = t_1
	elif a <= 3.1e+22:
		tmp = -(z * (b * c))
	elif a <= 7.5e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -4.8e-33)
		tmp = t_2;
	elseif (a <= -2.6e-224)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 6.2e-305)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.35e-42)
		tmp = t_1;
	elseif (a <= 3.1e+22)
		tmp = Float64(-Float64(z * Float64(b * c)));
	elseif (a <= 7.5e+134)
		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 = z * (x * y);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (a <= -4.8e-33)
		tmp = t_2;
	elseif (a <= -2.6e-224)
		tmp = b * (z * -c);
	elseif (a <= 6.2e-305)
		tmp = b * (t * i);
	elseif (a <= 1.35e-42)
		tmp = t_1;
	elseif (a <= 3.1e+22)
		tmp = -(z * (b * c));
	elseif (a <= 7.5e+134)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e-33], t$95$2, If[LessEqual[a, -2.6e-224], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-305], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-42], t$95$1, If[LessEqual[a, 3.1e+22], (-N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), If[LessEqual[a, 7.5e+134], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.8e-33 or 7.5000000000000001e134 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in j around inf 40.3%

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

      1. *-commutative 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in a around 0 40.3%

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

       1. *-commutative 40.3%

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

       2. associate-*r* 45.3%

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

       3. *-commutative 45.3%

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

   11. Simplified 45.3%

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

   if -4.8e-33 < a < -2.6000000000000002e-224

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in t around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. *-commutative 38.4%

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

      3. distribute-rgt-neg-in 38.4%

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

   8. Simplified 38.4%

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

   if -2.6000000000000002e-224 < a < 6.1999999999999997e-305

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

   8. Simplified 49.5%

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

   if 6.1999999999999997e-305 < a < 1.35e-42 or 3.1000000000000002e22 < a < 7.5000000000000001e134

   1. Initial program 76.1%

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

   3. Taylor expanded in y around 0 77.5%

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

   4. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

   6. Simplified 51.5%

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

   7. Taylor expanded in y around inf 42.5%

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

      1. *-commutative 42.5%

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

   9. Simplified 42.5%

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

   if 1.35e-42 < a < 3.1000000000000002e22

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 67.3%

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

   4. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in y around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-lft-neg-out 51.3%

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

      3. *-commutative 51.3%

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

   9. Simplified 51.3%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+22}:\\ \;\;\;\;-z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.18 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -3.3e+104)
     t_1
     (if (<= i -3.6e+17)
       (+ (* b (- (* t i) (* z c))) (* x (* y z)))
       (if (<= i -6.4e-35)
         (* a (- (* c j) (* x t)))
         (if (<= i -1.18e-238)
           (- (* x (- (* y z) (* t a))) (* b (* z c)))
           (if (<= i 2.85e+32) (* c (- (* a j) (* z b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.3e+104) {
		tmp = t_1;
	} else if (i <= -3.6e+17) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (i <= -6.4e-35) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -1.18e-238) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (i <= 2.85e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-3.3d+104)) then
        tmp = t_1
    else if (i <= (-3.6d+17)) then
        tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
    else if (i <= (-6.4d-35)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= (-1.18d-238)) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (i <= 2.85d+32) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.3e+104) {
		tmp = t_1;
	} else if (i <= -3.6e+17) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (i <= -6.4e-35) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -1.18e-238) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (i <= 2.85e+32) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.3e+104:
		tmp = t_1
	elif i <= -3.6e+17:
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
	elif i <= -6.4e-35:
		tmp = a * ((c * j) - (x * t))
	elif i <= -1.18e-238:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif i <= 2.85e+32:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.3e+104)
		tmp = t_1;
	elseif (i <= -3.6e+17)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(y * z)));
	elseif (i <= -6.4e-35)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= -1.18e-238)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (i <= 2.85e+32)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.3e+104)
		tmp = t_1;
	elseif (i <= -3.6e+17)
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	elseif (i <= -6.4e-35)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= -1.18e-238)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (i <= 2.85e+32)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.3e+104], t$95$1, If[LessEqual[i, -3.6e+17], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.4e-35], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.18e-238], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.85e+32], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.29999999999999985e104 or 2.85e32 < i

   1. Initial program 59.9%

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

   3. Taylor expanded in i around inf 64.3%

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

      1. distribute-lft-out-- 64.3%

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

      2. *-commutative 64.3%

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

      3. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -3.29999999999999985e104 < i < -3.6e17

   1. Initial program 83.1%

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

   3. Taylor expanded in j around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in a around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. sub-neg 78.2%

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

      3. sub-neg 78.2%

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

      4. *-commutative 78.2%

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

      5. *-commutative 78.2%

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

   8. Simplified 78.2%

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

   if -3.6e17 < i < -6.3999999999999996e-35

   1. Initial program 69.8%

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

   3. Taylor expanded in a around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. *-commutative 90.0%

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

      5. *-commutative 90.0%

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

   5. Simplified 90.0%

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

   if -6.3999999999999996e-35 < i < -1.18e-238

   1. Initial program 82.7%

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

   3. Taylor expanded in j around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in z around inf 64.6%

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

      1. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if -1.18e-238 < i < 2.85e32

   1. Initial program 83.9%

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

   3. Taylor expanded in c around inf 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.18 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+194} \lor \neg \left(b \leq -1.45 \cdot 10^{+138} \lor \neg \left(b \leq -2 \cdot 10^{+40}\right) \land b \leq 4.6 \cdot 10^{+136}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.6e+194)
         (not
          (or (<= b -1.45e+138) (and (not (<= b -2e+40)) (<= b 4.6e+136)))))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.6e+194) || !((b <= -1.45e+138) || (!(b <= -2e+40) && (b <= 4.6e+136)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.6d+194)) .or. (.not. (b <= (-1.45d+138)) .or. (.not. (b <= (-2d+40))) .and. (b <= 4.6d+136))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.6e+194) || !((b <= -1.45e+138) || (!(b <= -2e+40) && (b <= 4.6e+136)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.6e+194) or not ((b <= -1.45e+138) or (not (b <= -2e+40) and (b <= 4.6e+136))):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.6e+194) || !((b <= -1.45e+138) || (!(b <= -2e+40) && (b <= 4.6e+136))))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.6e+194) || ~(((b <= -1.45e+138) || (~((b <= -2e+40)) && (b <= 4.6e+136)))))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.6e+194], N[Not[Or[LessEqual[b, -1.45e+138], And[N[Not[LessEqual[b, -2e+40]], $MachinePrecision], LessEqual[b, 4.6e+136]]]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.60000000000000011e194 or -1.45000000000000005e138 < b < -2.00000000000000006e40 or 4.6e136 < b

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   if -1.60000000000000011e194 < b < -1.45000000000000005e138 or -2.00000000000000006e40 < b < 4.6e136

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. *-commutative 49.8%

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

      5. *-commutative 49.8%

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

   5. Simplified 49.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+194} \lor \neg \left(b \leq -1.45 \cdot 10^{+138} \lor \neg \left(b \leq -2 \cdot 10^{+40}\right) \land b \leq 4.6 \cdot 10^{+136}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-302}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= a -3.1e-33)
     t_1
     (if (<= a -1.5e-226)
       (* b (* z (- c)))
       (if (<= a 2.7e-302)
         (* b (* t i))
         (if (<= a 1.8e+133) (* z (* x y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (a <= -3.1e-33) {
		tmp = t_1;
	} else if (a <= -1.5e-226) {
		tmp = b * (z * -c);
	} else if (a <= 2.7e-302) {
		tmp = b * (t * i);
	} else if (a <= 1.8e+133) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (a * j)
    if (a <= (-3.1d-33)) then
        tmp = t_1
    else if (a <= (-1.5d-226)) then
        tmp = b * (z * -c)
    else if (a <= 2.7d-302) then
        tmp = b * (t * i)
    else if (a <= 1.8d+133) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (a <= -3.1e-33) {
		tmp = t_1;
	} else if (a <= -1.5e-226) {
		tmp = b * (z * -c);
	} else if (a <= 2.7e-302) {
		tmp = b * (t * i);
	} else if (a <= 1.8e+133) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if a <= -3.1e-33:
		tmp = t_1
	elif a <= -1.5e-226:
		tmp = b * (z * -c)
	elif a <= 2.7e-302:
		tmp = b * (t * i)
	elif a <= 1.8e+133:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -3.1e-33)
		tmp = t_1;
	elseif (a <= -1.5e-226)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 2.7e-302)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.8e+133)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	tmp = 0.0;
	if (a <= -3.1e-33)
		tmp = t_1;
	elseif (a <= -1.5e-226)
		tmp = b * (z * -c);
	elseif (a <= 2.7e-302)
		tmp = b * (t * i);
	elseif (a <= 1.8e+133)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e-33], t$95$1, If[LessEqual[a, -1.5e-226], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-302], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+133], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.09999999999999997e-33 or 1.79999999999999989e133 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in j around inf 40.3%

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

      1. *-commutative 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in a around 0 40.3%

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

       1. *-commutative 40.3%

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

       2. associate-*r* 45.3%

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

       3. *-commutative 45.3%

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

   11. Simplified 45.3%

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

   if -3.09999999999999997e-33 < a < -1.49999999999999998e-226

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in t around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. *-commutative 38.4%

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

      3. distribute-rgt-neg-in 38.4%

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

   8. Simplified 38.4%

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

   if -1.49999999999999998e-226 < a < 2.70000000000000006e-302

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

   8. Simplified 49.5%

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

   if 2.70000000000000006e-302 < a < 1.79999999999999989e133

   1. Initial program 77.6%

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

   3. Taylor expanded in y around 0 76.3%

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

   4. Taylor expanded in z around inf 51.6%

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

      1. *-commutative 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in y around inf 37.9%

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

      1. *-commutative 37.9%

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

   9. Simplified 37.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-302}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* a j))))
   (if (<= a -2.45e-33)
     t_2
     (if (<= a -1.4e-223)
       t_1
       (if (<= a 4.8e-300) (* b (* t i)) (if (<= a 1.5e+133) 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 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -2.45e-33) {
		tmp = t_2;
	} else if (a <= -1.4e-223) {
		tmp = t_1;
	} else if (a <= 4.8e-300) {
		tmp = b * (t * i);
	} else if (a <= 1.5e+133) {
		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 = z * (x * y)
    t_2 = c * (a * j)
    if (a <= (-2.45d-33)) then
        tmp = t_2
    else if (a <= (-1.4d-223)) then
        tmp = t_1
    else if (a <= 4.8d-300) then
        tmp = b * (t * i)
    else if (a <= 1.5d+133) 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 = z * (x * y);
	double t_2 = c * (a * j);
	double tmp;
	if (a <= -2.45e-33) {
		tmp = t_2;
	} else if (a <= -1.4e-223) {
		tmp = t_1;
	} else if (a <= 4.8e-300) {
		tmp = b * (t * i);
	} else if (a <= 1.5e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (a * j)
	tmp = 0
	if a <= -2.45e-33:
		tmp = t_2
	elif a <= -1.4e-223:
		tmp = t_1
	elif a <= 4.8e-300:
		tmp = b * (t * i)
	elif a <= 1.5e+133:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -2.45e-33)
		tmp = t_2;
	elseif (a <= -1.4e-223)
		tmp = t_1;
	elseif (a <= 4.8e-300)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.5e+133)
		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 = z * (x * y);
	t_2 = c * (a * j);
	tmp = 0.0;
	if (a <= -2.45e-33)
		tmp = t_2;
	elseif (a <= -1.4e-223)
		tmp = t_1;
	elseif (a <= 4.8e-300)
		tmp = b * (t * i);
	elseif (a <= 1.5e+133)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.45e-33], t$95$2, If[LessEqual[a, -1.4e-223], t$95$1, If[LessEqual[a, 4.8e-300], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+133], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4499999999999999e-33 or 1.50000000000000003e133 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in j around inf 40.3%

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

      1. *-commutative 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in a around 0 40.3%

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

       1. *-commutative 40.3%

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

       2. associate-*r* 45.3%

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

       3. *-commutative 45.3%

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

   11. Simplified 45.3%

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

   if -2.4499999999999999e-33 < a < -1.40000000000000007e-223 or 4.79999999999999999e-300 < a < 1.50000000000000003e133

   1. Initial program 76.9%

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

   3. Taylor expanded in y around 0 75.2%

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

   4. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in y around inf 34.5%

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

      1. *-commutative 34.5%

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

   9. Simplified 34.5%

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

   if -1.40000000000000007e-223 < a < 4.79999999999999999e-300

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 63.3%

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

      1. *-commutative 63.3%

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

      2. *-commutative 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in t around inf 47.0%

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

      1. *-commutative 47.0%

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

   8. Simplified 47.0%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -31.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -31.5)
     t_1
     (if (<= c 1.08e-179)
       (* y (- (* x z) (* i j)))
       (if (<= c 6.8e-33) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -31.5) {
		tmp = t_1;
	} else if (c <= 1.08e-179) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 6.8e-33) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-31.5d0)) then
        tmp = t_1
    else if (c <= 1.08d-179) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 6.8d-33) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -31.5) {
		tmp = t_1;
	} else if (c <= 1.08e-179) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 6.8e-33) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -31.5:
		tmp = t_1
	elif c <= 1.08e-179:
		tmp = y * ((x * z) - (i * j))
	elif c <= 6.8e-33:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -31.5)
		tmp = t_1;
	elseif (c <= 1.08e-179)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 6.8e-33)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -31.5)
		tmp = t_1;
	elseif (c <= 1.08e-179)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 6.8e-33)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -31.5], t$95$1, If[LessEqual[c, 1.08e-179], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-33], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -31.5 or 6.8000000000000001e-33 < c

   1. Initial program 71.5%

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

   3. Taylor expanded in c around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -31.5 < c < 1.08000000000000006e-179

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   if 1.08000000000000006e-179 < c < 6.8000000000000001e-33

   1. Initial program 73.0%

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

   3. Taylor expanded in a around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. *-commutative 47.9%

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

      5. *-commutative 47.9%

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

   5. Simplified 47.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -31.5:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30} \lor \neg \left(z \leq 8.4 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -4.4e-30) (not (<= z 8.4e+46))) (* x (* y z)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.4e-30) || !(z <= 8.4e+46)) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-4.4d-30)) .or. (.not. (z <= 8.4d+46))) then
        tmp = x * (y * z)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -4.4e-30) || !(z <= 8.4e+46)) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -4.4e-30) or not (z <= 8.4e+46):
		tmp = x * (y * z)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -4.4e-30) || !(z <= 8.4e+46))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -4.4e-30) || ~((z <= 8.4e+46)))
		tmp = x * (y * z);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -4.4e-30], N[Not[LessEqual[z, 8.4e+46]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999967e-30 or 8.4e46 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in y around 0 65.3%

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

   4. Taylor expanded in z around inf 64.8%

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

      1. *-commutative 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in y around inf 36.6%

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

      1. *-commutative 36.6%

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

   9. Simplified 36.6%

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

   if -4.39999999999999967e-30 < z < 8.4e46

   1. Initial program 79.9%

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

   3. Taylor expanded in a around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

      5. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in j around inf 31.3%

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

      1. *-commutative 31.3%

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

   8. Simplified 31.3%

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

   9. Taylor expanded in a around 0 31.3%

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

       1. *-commutative 31.3%

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

       2. associate-*r* 36.0%

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

       3. *-commutative 36.0%

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

   11. Simplified 36.0%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30} \lor \neg \left(z \leq 8.4 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -330000 \lor \neg \left(c \leq 1.95 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -330000.0) (not (<= c 1.95e-50))) (* a (* c j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -330000.0) || !(c <= 1.95e-50)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-330000.0d0)) .or. (.not. (c <= 1.95d-50))) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -330000.0) || !(c <= 1.95e-50)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -330000.0) or not (c <= 1.95e-50):
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -330000.0) || !(c <= 1.95e-50))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -330000.0) || ~((c <= 1.95e-50)))
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -330000.0], N[Not[LessEqual[c, 1.95e-50]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.3e5 or 1.9500000000000001e-50 < c

   1. Initial program 71.6%

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

   3. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

      5. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in j around inf 39.6%

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

      1. *-commutative 39.6%

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

   8. Simplified 39.6%

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

   if -3.3e5 < c < 1.9500000000000001e-50

   1. Initial program 76.0%

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

   3. Taylor expanded in b around inf 34.7%

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

      1. *-commutative 34.7%

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

      2. *-commutative 34.7%

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

   5. Simplified 34.7%

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

   6. Taylor expanded in t around inf 28.8%

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

      1. *-commutative 28.8%

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

   8. Simplified 28.8%

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

   9. Taylor expanded in b around 0 28.8%

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

       1. associate-*r* 26.9%

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

       2. *-commutative 26.9%

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

       3. associate-*r* 29.5%

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

   11. Simplified 29.5%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -330000 \lor \neg \left(c \leq 1.95 \cdot 10^{-50}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -620000000000 \lor \neg \left(c \leq 2.5 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -620000000000.0) (not (<= c 2.5e-51)))
   (* a (* c j))
   (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -620000000000.0) || !(c <= 2.5e-51)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-620000000000.0d0)) .or. (.not. (c <= 2.5d-51))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -620000000000.0) || !(c <= 2.5e-51)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -620000000000.0) or not (c <= 2.5e-51):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -620000000000.0) || !(c <= 2.5e-51))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -620000000000.0) || ~((c <= 2.5e-51)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -620000000000.0], N[Not[LessEqual[c, 2.5e-51]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.2e11 or 2.50000000000000002e-51 < c

   1. Initial program 71.6%

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

   3. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

      5. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in j around inf 39.6%

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

      1. *-commutative 39.6%

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

   8. Simplified 39.6%

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

   if -6.2e11 < c < 2.50000000000000002e-51

   1. Initial program 76.0%

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

   3. Taylor expanded in b around inf 34.7%

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

      1. *-commutative 34.7%

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

      2. *-commutative 34.7%

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

   5. Simplified 34.7%

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

   6. Taylor expanded in t around inf 28.8%

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

      1. *-commutative 28.8%

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

   8. Simplified 28.8%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -620000000000 \lor \neg \left(c \leq 2.5 \cdot 10^{-51}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.05e+110)
   (* y (* x z))
   (if (<= z 2e+46) (* c (* a j)) (* x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.05e+110) {
		tmp = y * (x * z);
	} else if (z <= 2e+46) {
		tmp = c * (a * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.05d+110)) then
        tmp = y * (x * z)
    else if (z <= 2d+46) then
        tmp = c * (a * j)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.05e+110) {
		tmp = y * (x * z);
	} else if (z <= 2e+46) {
		tmp = c * (a * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.05e+110:
		tmp = y * (x * z)
	elif z <= 2e+46:
		tmp = c * (a * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.05e+110)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 2e+46)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.05e+110)
		tmp = y * (x * z);
	elseif (z <= 2e+46)
		tmp = c * (a * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.05e+110], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+46], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000007e110

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. *-commutative 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in x around inf 41.6%

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

   if -1.05000000000000007e110 < z < 2e46

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

      5. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in j around inf 31.0%

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

      1. *-commutative 31.0%

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

   8. Simplified 31.0%

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

   9. Taylor expanded in a around 0 31.0%

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

       1. *-commutative 31.0%

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

       2. associate-*r* 33.9%

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

       3. *-commutative 33.9%

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

   11. Simplified 33.9%

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

   if 2e46 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0 72.3%

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

   4. Taylor expanded in z around inf 68.6%

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

      1. *-commutative 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in y around inf 43.1%

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

      1. *-commutative 43.1%

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

   9. Simplified 43.1%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.7%

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

3. Taylor expanded in a around inf 41.9%

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

   1. +-commutative 41.9%

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

   2. mul-1-neg 41.9%

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

   3. unsub-neg 41.9%

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

   4. *-commutative 41.9%

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

   5. *-commutative 41.9%

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

5. Simplified 41.9%

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

6. Taylor expanded in j around inf 25.2%

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

   1. *-commutative 25.2%

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

8. Simplified 25.2%

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

9. Final simplification 25.2%

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

Developer target: 59.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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