Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.0% → 81.7%

Time: 24.7s

Alternatives: 23

Speedup: 0.5×

• 57.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. *-commutative 51.8%

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

   5. Simplified 51.8%

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

4. Final simplification 86.2%

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

Alternative 2: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-109}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 0.00032:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (* z (- (* a (/ i z)) c)))))
   (if (<= b -8.5e+83)
     t_3
     (if (<= b -1.15e-95)
       t_1
       (if (<= b -3.8e-109)
         (* z (- (* x y) (* b c)))
         (if (<= b -2.4e-111)
           t_2
           (if (<= b -2.6e-282)
             t_1
             (if (<= b 3e-242)
               (* x (* a (- (* y (/ z a)) t)))
               (if (<= b 4.1e-228)
                 (* y (- (* x z) (* i j)))
                 (if (<= b 2.3e-129)
                   t_2
                   (if (<= b 0.00032) (* x (- (* y z) (* t a))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -8.5e+83) {
		tmp = t_3;
	} else if (b <= -1.15e-95) {
		tmp = t_1;
	} else if (b <= -3.8e-109) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.4e-111) {
		tmp = t_2;
	} else if (b <= -2.6e-282) {
		tmp = t_1;
	} else if (b <= 3e-242) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (b <= 4.1e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.3e-129) {
		tmp = t_2;
	} else if (b <= 0.00032) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * (z * ((a * (i / z)) - c))
    if (b <= (-8.5d+83)) then
        tmp = t_3
    else if (b <= (-1.15d-95)) then
        tmp = t_1
    else if (b <= (-3.8d-109)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2.4d-111)) then
        tmp = t_2
    else if (b <= (-2.6d-282)) then
        tmp = t_1
    else if (b <= 3d-242) then
        tmp = x * (a * ((y * (z / a)) - t))
    else if (b <= 4.1d-228) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.3d-129) then
        tmp = t_2
    else if (b <= 0.00032d0) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -8.5e+83) {
		tmp = t_3;
	} else if (b <= -1.15e-95) {
		tmp = t_1;
	} else if (b <= -3.8e-109) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.4e-111) {
		tmp = t_2;
	} else if (b <= -2.6e-282) {
		tmp = t_1;
	} else if (b <= 3e-242) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (b <= 4.1e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.3e-129) {
		tmp = t_2;
	} else if (b <= 0.00032) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * (z * ((a * (i / z)) - c))
	tmp = 0
	if b <= -8.5e+83:
		tmp = t_3
	elif b <= -1.15e-95:
		tmp = t_1
	elif b <= -3.8e-109:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2.4e-111:
		tmp = t_2
	elif b <= -2.6e-282:
		tmp = t_1
	elif b <= 3e-242:
		tmp = x * (a * ((y * (z / a)) - t))
	elif b <= 4.1e-228:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.3e-129:
		tmp = t_2
	elif b <= 0.00032:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	tmp = 0.0
	if (b <= -8.5e+83)
		tmp = t_3;
	elseif (b <= -1.15e-95)
		tmp = t_1;
	elseif (b <= -3.8e-109)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2.4e-111)
		tmp = t_2;
	elseif (b <= -2.6e-282)
		tmp = t_1;
	elseif (b <= 3e-242)
		tmp = Float64(x * Float64(a * Float64(Float64(y * Float64(z / a)) - t)));
	elseif (b <= 4.1e-228)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.3e-129)
		tmp = t_2;
	elseif (b <= 0.00032)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * (z * ((a * (i / z)) - c));
	tmp = 0.0;
	if (b <= -8.5e+83)
		tmp = t_3;
	elseif (b <= -1.15e-95)
		tmp = t_1;
	elseif (b <= -3.8e-109)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2.4e-111)
		tmp = t_2;
	elseif (b <= -2.6e-282)
		tmp = t_1;
	elseif (b <= 3e-242)
		tmp = x * (a * ((y * (z / a)) - t));
	elseif (b <= 4.1e-228)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.3e-129)
		tmp = t_2;
	elseif (b <= 0.00032)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+83], t$95$3, If[LessEqual[b, -1.15e-95], t$95$1, If[LessEqual[b, -3.8e-109], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-111], t$95$2, If[LessEqual[b, -2.6e-282], t$95$1, If[LessEqual[b, 3e-242], N[(x * N[(a * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e-228], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-129], t$95$2, If[LessEqual[b, 0.00032], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -8.4999999999999995e83 or 3.20000000000000026e-4 < b

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   if -8.4999999999999995e83 < b < -1.15e-95 or -2.4000000000000001e-111 < b < -2.60000000000000012e-282

   1. Initial program 85.0%

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

   3. Taylor expanded in j around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   if -1.15e-95 < b < -3.80000000000000002e-109

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -3.80000000000000002e-109 < b < -2.4000000000000001e-111 or 4.09999999999999997e-228 < b < 2.3e-129

   1. Initial program 70.6%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

      5. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if -2.60000000000000012e-282 < b < 3e-242

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 65.5%

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

      5. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around -inf 71.0%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around inf 59.5%

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

       1. associate-*r/ 59.5%

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

       2. mul-1-neg 59.5%

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

       3. distribute-rgt-neg-in 59.5%

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

   11. Simplified 59.5%

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

   12. Taylor expanded in a around -inf 59.4%

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

       1. mul-1-neg 59.4%

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

       2. distribute-rgt-neg-in 59.4%

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

       3. mul-1-neg 59.4%

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

       4. unsub-neg 59.4%

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

       5. associate-/l* 65.2%

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

   14. Simplified 65.2%

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

   if 3e-242 < b < 4.09999999999999997e-228

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 2.3e-129 < b < 3.20000000000000026e-4

   1. Initial program 87.1%

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

   3. Taylor expanded in c around 0 87.1%

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

   4. Taylor expanded in x around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. *-commutative 66.0%

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

      3. *-commutative 66.0%

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

   6. Simplified 66.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-109}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 0.00032:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 0.00036:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (* z (- (* a (/ i z)) c)))))
   (if (<= b -5.8e+82)
     t_3
     (if (<= b -1.15e-88)
       t_1
       (if (<= b -2.15e-108)
         (* z (- (* x y) (* b c)))
         (if (<= b -6.2e-114)
           t_2
           (if (<= b -3.2e-281)
             t_1
             (if (<= b 2.3e-243)
               (* x (* a (- (* y (/ z a)) t)))
               (if (<= b 1.28e-228)
                 (* y (- (* x z) (* i j)))
                 (if (<= b 3.7e-131)
                   t_2
                   (if (<= b 0.00036)
                     (* x (* y (- z (/ (* t a) y))))
                     t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -5.8e+82) {
		tmp = t_3;
	} else if (b <= -1.15e-88) {
		tmp = t_1;
	} else if (b <= -2.15e-108) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -6.2e-114) {
		tmp = t_2;
	} else if (b <= -3.2e-281) {
		tmp = t_1;
	} else if (b <= 2.3e-243) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (b <= 1.28e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.7e-131) {
		tmp = t_2;
	} else if (b <= 0.00036) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * (z * ((a * (i / z)) - c))
    if (b <= (-5.8d+82)) then
        tmp = t_3
    else if (b <= (-1.15d-88)) then
        tmp = t_1
    else if (b <= (-2.15d-108)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-6.2d-114)) then
        tmp = t_2
    else if (b <= (-3.2d-281)) then
        tmp = t_1
    else if (b <= 2.3d-243) then
        tmp = x * (a * ((y * (z / a)) - t))
    else if (b <= 1.28d-228) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 3.7d-131) then
        tmp = t_2
    else if (b <= 0.00036d0) then
        tmp = x * (y * (z - ((t * a) / y)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -5.8e+82) {
		tmp = t_3;
	} else if (b <= -1.15e-88) {
		tmp = t_1;
	} else if (b <= -2.15e-108) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -6.2e-114) {
		tmp = t_2;
	} else if (b <= -3.2e-281) {
		tmp = t_1;
	} else if (b <= 2.3e-243) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (b <= 1.28e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.7e-131) {
		tmp = t_2;
	} else if (b <= 0.00036) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * (z * ((a * (i / z)) - c))
	tmp = 0
	if b <= -5.8e+82:
		tmp = t_3
	elif b <= -1.15e-88:
		tmp = t_1
	elif b <= -2.15e-108:
		tmp = z * ((x * y) - (b * c))
	elif b <= -6.2e-114:
		tmp = t_2
	elif b <= -3.2e-281:
		tmp = t_1
	elif b <= 2.3e-243:
		tmp = x * (a * ((y * (z / a)) - t))
	elif b <= 1.28e-228:
		tmp = y * ((x * z) - (i * j))
	elif b <= 3.7e-131:
		tmp = t_2
	elif b <= 0.00036:
		tmp = x * (y * (z - ((t * a) / y)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	tmp = 0.0
	if (b <= -5.8e+82)
		tmp = t_3;
	elseif (b <= -1.15e-88)
		tmp = t_1;
	elseif (b <= -2.15e-108)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -6.2e-114)
		tmp = t_2;
	elseif (b <= -3.2e-281)
		tmp = t_1;
	elseif (b <= 2.3e-243)
		tmp = Float64(x * Float64(a * Float64(Float64(y * Float64(z / a)) - t)));
	elseif (b <= 1.28e-228)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 3.7e-131)
		tmp = t_2;
	elseif (b <= 0.00036)
		tmp = Float64(x * Float64(y * Float64(z - Float64(Float64(t * a) / y))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * (z * ((a * (i / z)) - c));
	tmp = 0.0;
	if (b <= -5.8e+82)
		tmp = t_3;
	elseif (b <= -1.15e-88)
		tmp = t_1;
	elseif (b <= -2.15e-108)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -6.2e-114)
		tmp = t_2;
	elseif (b <= -3.2e-281)
		tmp = t_1;
	elseif (b <= 2.3e-243)
		tmp = x * (a * ((y * (z / a)) - t));
	elseif (b <= 1.28e-228)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 3.7e-131)
		tmp = t_2;
	elseif (b <= 0.00036)
		tmp = x * (y * (z - ((t * a) / y)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+82], t$95$3, If[LessEqual[b, -1.15e-88], t$95$1, If[LessEqual[b, -2.15e-108], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-114], t$95$2, If[LessEqual[b, -3.2e-281], t$95$1, If[LessEqual[b, 2.3e-243], N[(x * N[(a * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.28e-228], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-131], t$95$2, If[LessEqual[b, 0.00036], N[(x * N[(y * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.8000000000000003e82 or 3.60000000000000023e-4 < b

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   if -5.8000000000000003e82 < b < -1.14999999999999993e-88 or -6.2e-114 < b < -3.2000000000000001e-281

   1. Initial program 85.0%

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

   3. Taylor expanded in j around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   if -1.14999999999999993e-88 < b < -2.15e-108

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -2.15e-108 < b < -6.2e-114 or 1.28000000000000006e-228 < b < 3.7000000000000002e-131

   1. Initial program 70.6%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

      5. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if -3.2000000000000001e-281 < b < 2.3e-243

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 65.5%

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

      5. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around -inf 71.0%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around inf 59.5%

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

       1. associate-*r/ 59.5%

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

       2. mul-1-neg 59.5%

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

       3. distribute-rgt-neg-in 59.5%

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

   11. Simplified 59.5%

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

   12. Taylor expanded in a around -inf 59.4%

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

       1. mul-1-neg 59.4%

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

       2. distribute-rgt-neg-in 59.4%

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

       3. mul-1-neg 59.4%

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

       4. unsub-neg 59.4%

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

       5. associate-/l* 65.2%

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

   14. Simplified 65.2%

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

   if 2.3e-243 < b < 1.28000000000000006e-228

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 3.7000000000000002e-131 < b < 3.60000000000000023e-4

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. associate-/l* 70.5%

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

      5. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in y around -inf 74.3%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in x around inf 70.2%

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

       1. associate-*r/ 70.2%

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

       2. mul-1-neg 70.2%

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

       3. distribute-rgt-neg-in 70.2%

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

   11. Simplified 70.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 0.00036:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-140}:\\ \;\;\;\;z \cdot \left(x \cdot y - a \cdot \frac{x \cdot t}{z}\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 0.00036:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (* z (- (* a (/ i z)) c)))))
   (if (<= b -8e+82)
     t_2
     (if (<= b -8.5e-91)
       t_1
       (if (<= b -9.2e-108)
         (* z (- (* x y) (* b c)))
         (if (<= b -1e-140)
           (* z (- (* x y) (* a (/ (* x t) z))))
           (if (<= b -1.22e-282)
             t_1
             (if (<= b 4.8e-242)
               (* x (* a (- (* y (/ z a)) t)))
               (if (<= b 2.9e-228)
                 (* y (- (* x z) (* i j)))
                 (if (<= b 1.35e-129)
                   (* t (- (* c j) (* x a)))
                   (if (<= b 0.00036)
                     (* x (* y (- z (/ (* t a) y))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -8e+82) {
		tmp = t_2;
	} else if (b <= -8.5e-91) {
		tmp = t_1;
	} else if (b <= -9.2e-108) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -1e-140) {
		tmp = z * ((x * y) - (a * ((x * t) / z)));
	} else if (b <= -1.22e-282) {
		tmp = t_1;
	} else if (b <= 4.8e-242) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (b <= 2.9e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.35e-129) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 0.00036) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * (z * ((a * (i / z)) - c))
    if (b <= (-8d+82)) then
        tmp = t_2
    else if (b <= (-8.5d-91)) then
        tmp = t_1
    else if (b <= (-9.2d-108)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-1d-140)) then
        tmp = z * ((x * y) - (a * ((x * t) / z)))
    else if (b <= (-1.22d-282)) then
        tmp = t_1
    else if (b <= 4.8d-242) then
        tmp = x * (a * ((y * (z / a)) - t))
    else if (b <= 2.9d-228) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.35d-129) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 0.00036d0) then
        tmp = x * (y * (z - ((t * a) / y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -8e+82) {
		tmp = t_2;
	} else if (b <= -8.5e-91) {
		tmp = t_1;
	} else if (b <= -9.2e-108) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -1e-140) {
		tmp = z * ((x * y) - (a * ((x * t) / z)));
	} else if (b <= -1.22e-282) {
		tmp = t_1;
	} else if (b <= 4.8e-242) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (b <= 2.9e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.35e-129) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 0.00036) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * (z * ((a * (i / z)) - c))
	tmp = 0
	if b <= -8e+82:
		tmp = t_2
	elif b <= -8.5e-91:
		tmp = t_1
	elif b <= -9.2e-108:
		tmp = z * ((x * y) - (b * c))
	elif b <= -1e-140:
		tmp = z * ((x * y) - (a * ((x * t) / z)))
	elif b <= -1.22e-282:
		tmp = t_1
	elif b <= 4.8e-242:
		tmp = x * (a * ((y * (z / a)) - t))
	elif b <= 2.9e-228:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.35e-129:
		tmp = t * ((c * j) - (x * a))
	elif b <= 0.00036:
		tmp = x * (y * (z - ((t * a) / y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	tmp = 0.0
	if (b <= -8e+82)
		tmp = t_2;
	elseif (b <= -8.5e-91)
		tmp = t_1;
	elseif (b <= -9.2e-108)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -1e-140)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(a * Float64(Float64(x * t) / z))));
	elseif (b <= -1.22e-282)
		tmp = t_1;
	elseif (b <= 4.8e-242)
		tmp = Float64(x * Float64(a * Float64(Float64(y * Float64(z / a)) - t)));
	elseif (b <= 2.9e-228)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.35e-129)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 0.00036)
		tmp = Float64(x * Float64(y * Float64(z - Float64(Float64(t * a) / y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * (z * ((a * (i / z)) - c));
	tmp = 0.0;
	if (b <= -8e+82)
		tmp = t_2;
	elseif (b <= -8.5e-91)
		tmp = t_1;
	elseif (b <= -9.2e-108)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -1e-140)
		tmp = z * ((x * y) - (a * ((x * t) / z)));
	elseif (b <= -1.22e-282)
		tmp = t_1;
	elseif (b <= 4.8e-242)
		tmp = x * (a * ((y * (z / a)) - t));
	elseif (b <= 2.9e-228)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.35e-129)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 0.00036)
		tmp = x * (y * (z - ((t * a) / y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+82], t$95$2, If[LessEqual[b, -8.5e-91], t$95$1, If[LessEqual[b, -9.2e-108], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-140], N[(z * N[(N[(x * y), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.22e-282], t$95$1, If[LessEqual[b, 4.8e-242], N[(x * N[(a * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-228], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e-129], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00036], N[(x * N[(y * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -7.9999999999999997e82 or 3.60000000000000023e-4 < b

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   if -7.9999999999999997e82 < b < -8.49999999999999985e-91 or -9.9999999999999998e-141 < b < -1.22e-282

   1. Initial program 83.9%

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

   3. Taylor expanded in j around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if -8.49999999999999985e-91 < b < -9.19999999999999983e-108

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   if -9.19999999999999983e-108 < b < -9.9999999999999998e-141

   1. Initial program 76.5%

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

   3. Taylor expanded in c around 0 76.5%

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

   4. Taylor expanded in x around inf 41.4%

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

      1. *-commutative 41.4%

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

      2. *-commutative 41.4%

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

      3. *-commutative 41.4%

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

   6. Simplified 41.4%

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

   7. Taylor expanded in z around inf 75.3%

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

      1. +-commutative 88.2%

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

      2. mul-1-neg 88.2%

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

      3. unsub-neg 88.2%

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

      4. associate-/l* 88.4%

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

      5. *-commutative 88.4%

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

   9. Simplified 75.5%

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

   if -1.22e-282 < b < 4.8000000000000002e-242

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 65.5%

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

      5. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around -inf 71.0%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around inf 59.5%

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

       1. associate-*r/ 59.5%

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

       2. mul-1-neg 59.5%

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

       3. distribute-rgt-neg-in 59.5%

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

   11. Simplified 59.5%

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

   12. Taylor expanded in a around -inf 59.4%

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

       1. mul-1-neg 59.4%

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

       2. distribute-rgt-neg-in 59.4%

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

       3. mul-1-neg 59.4%

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

       4. unsub-neg 59.4%

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

       5. associate-/l* 65.2%

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

   14. Simplified 65.2%

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

   if 4.8000000000000002e-242 < b < 2.9000000000000001e-228

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 2.9000000000000001e-228 < b < 1.35e-129

   1. Initial program 72.3%

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

   3. Taylor expanded in t around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   if 1.35e-129 < b < 3.60000000000000023e-4

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. associate-/l* 70.5%

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

      5. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in y around -inf 74.3%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in x around inf 70.2%

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

       1. associate-*r/ 70.2%

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

       2. mul-1-neg 70.2%

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

       3. distribute-rgt-neg-in 70.2%

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

   11. Simplified 70.2%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{a \cdot \left(-t\right)}{y}\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+82}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-140}:\\ \;\;\;\;z \cdot \left(x \cdot y - a \cdot \frac{x \cdot t}{z}\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 0.00036:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-281}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 0.0028:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (+ (* x (- (* y z) (* t a))) (* t (* c j)))))
   (if (<= b -1.05e+80)
     (* b (* z (- (* a (/ i z)) c)))
     (if (<= b -2.6e-78)
       t_2
       (if (<= b -3e-108)
         t_1
         (if (<= b -1.85e-208)
           t_3
           (if (<= b -7.2e-281)
             t_2
             (if (<= b 0.0028)
               t_3
               (if (<= b 2.85e+57)
                 t_1
                 (if (<= b 2.9e+72) t_2 (* b (- (* a i) (* z c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = (x * ((y * z) - (t * a))) + (t * (c * j));
	double tmp;
	if (b <= -1.05e+80) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -2.6e-78) {
		tmp = t_2;
	} else if (b <= -3e-108) {
		tmp = t_1;
	} else if (b <= -1.85e-208) {
		tmp = t_3;
	} else if (b <= -7.2e-281) {
		tmp = t_2;
	} else if (b <= 0.0028) {
		tmp = t_3;
	} else if (b <= 2.85e+57) {
		tmp = t_1;
	} else if (b <= 2.9e+72) {
		tmp = t_2;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = j * ((t * c) - (y * i))
    t_3 = (x * ((y * z) - (t * a))) + (t * (c * j))
    if (b <= (-1.05d+80)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (b <= (-2.6d-78)) then
        tmp = t_2
    else if (b <= (-3d-108)) then
        tmp = t_1
    else if (b <= (-1.85d-208)) then
        tmp = t_3
    else if (b <= (-7.2d-281)) then
        tmp = t_2
    else if (b <= 0.0028d0) then
        tmp = t_3
    else if (b <= 2.85d+57) then
        tmp = t_1
    else if (b <= 2.9d+72) then
        tmp = t_2
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = (x * ((y * z) - (t * a))) + (t * (c * j));
	double tmp;
	if (b <= -1.05e+80) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -2.6e-78) {
		tmp = t_2;
	} else if (b <= -3e-108) {
		tmp = t_1;
	} else if (b <= -1.85e-208) {
		tmp = t_3;
	} else if (b <= -7.2e-281) {
		tmp = t_2;
	} else if (b <= 0.0028) {
		tmp = t_3;
	} else if (b <= 2.85e+57) {
		tmp = t_1;
	} else if (b <= 2.9e+72) {
		tmp = t_2;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((t * c) - (y * i))
	t_3 = (x * ((y * z) - (t * a))) + (t * (c * j))
	tmp = 0
	if b <= -1.05e+80:
		tmp = b * (z * ((a * (i / z)) - c))
	elif b <= -2.6e-78:
		tmp = t_2
	elif b <= -3e-108:
		tmp = t_1
	elif b <= -1.85e-208:
		tmp = t_3
	elif b <= -7.2e-281:
		tmp = t_2
	elif b <= 0.0028:
		tmp = t_3
	elif b <= 2.85e+57:
		tmp = t_1
	elif b <= 2.9e+72:
		tmp = t_2
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(t * Float64(c * j)))
	tmp = 0.0
	if (b <= -1.05e+80)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (b <= -2.6e-78)
		tmp = t_2;
	elseif (b <= -3e-108)
		tmp = t_1;
	elseif (b <= -1.85e-208)
		tmp = t_3;
	elseif (b <= -7.2e-281)
		tmp = t_2;
	elseif (b <= 0.0028)
		tmp = t_3;
	elseif (b <= 2.85e+57)
		tmp = t_1;
	elseif (b <= 2.9e+72)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = j * ((t * c) - (y * i));
	t_3 = (x * ((y * z) - (t * a))) + (t * (c * j));
	tmp = 0.0;
	if (b <= -1.05e+80)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (b <= -2.6e-78)
		tmp = t_2;
	elseif (b <= -3e-108)
		tmp = t_1;
	elseif (b <= -1.85e-208)
		tmp = t_3;
	elseif (b <= -7.2e-281)
		tmp = t_2;
	elseif (b <= 0.0028)
		tmp = t_3;
	elseif (b <= 2.85e+57)
		tmp = t_1;
	elseif (b <= 2.9e+72)
		tmp = t_2;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+80], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-78], t$95$2, If[LessEqual[b, -3e-108], t$95$1, If[LessEqual[b, -1.85e-208], t$95$3, If[LessEqual[b, -7.2e-281], t$95$2, If[LessEqual[b, 0.0028], t$95$3, If[LessEqual[b, 2.85e+57], t$95$1, If[LessEqual[b, 2.9e+72], t$95$2, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.05000000000000001e80

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in z around inf 84.4%

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

      1. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   if -1.05000000000000001e80 < b < -2.6000000000000001e-78 or -1.8500000000000001e-208 < b < -7.20000000000000013e-281 or 2.8499999999999999e57 < b < 2.90000000000000017e72

   1. Initial program 84.5%

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

   3. Taylor expanded in j around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -2.6000000000000001e-78 < b < -2.99999999999999993e-108 or 0.00279999999999999997 < b < 2.8499999999999999e57

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -2.99999999999999993e-108 < b < -1.8500000000000001e-208 or -7.20000000000000013e-281 < b < 0.00279999999999999997

   1. Initial program 77.0%

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

   3. Taylor expanded in b around 0 78.1%

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

   4. Taylor expanded in c around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*r* 65.0%

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

   6. Simplified 65.0%

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

   if 2.90000000000000017e72 < b

   1. Initial program 73.4%

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

   3. Taylor expanded in b around inf 72.5%

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

      1. *-commutative 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.0028:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.7 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* t (* c j))))
        (t_2 (* y (+ (* x z) (- (/ (* a (* b i)) y) (* i j))))))
   (if (<= b -7.4e+87)
     (* b (* z (- (* a (/ i z)) c)))
     (if (<= b -2.05e-77)
       t_2
       (if (<= b -8.7e-209)
         t_1
         (if (<= b -3.2e-281)
           (* j (- (* t c) (* y i)))
           (if (<= b 8.8e-89)
             t_1
             (if (<= b 1.28e+42) t_2 (* b (- (* a i) (* z c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (t * (c * j));
	double t_2 = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	double tmp;
	if (b <= -7.4e+87) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -2.05e-77) {
		tmp = t_2;
	} else if (b <= -8.7e-209) {
		tmp = t_1;
	} else if (b <= -3.2e-281) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 8.8e-89) {
		tmp = t_1;
	} else if (b <= 1.28e+42) {
		tmp = t_2;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (t * (c * j))
    t_2 = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
    if (b <= (-7.4d+87)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (b <= (-2.05d-77)) then
        tmp = t_2
    else if (b <= (-8.7d-209)) then
        tmp = t_1
    else if (b <= (-3.2d-281)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 8.8d-89) then
        tmp = t_1
    else if (b <= 1.28d+42) then
        tmp = t_2
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (t * (c * j));
	double t_2 = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	double tmp;
	if (b <= -7.4e+87) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -2.05e-77) {
		tmp = t_2;
	} else if (b <= -8.7e-209) {
		tmp = t_1;
	} else if (b <= -3.2e-281) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 8.8e-89) {
		tmp = t_1;
	} else if (b <= 1.28e+42) {
		tmp = t_2;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (t * (c * j))
	t_2 = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
	tmp = 0
	if b <= -7.4e+87:
		tmp = b * (z * ((a * (i / z)) - c))
	elif b <= -2.05e-77:
		tmp = t_2
	elif b <= -8.7e-209:
		tmp = t_1
	elif b <= -3.2e-281:
		tmp = j * ((t * c) - (y * i))
	elif b <= 8.8e-89:
		tmp = t_1
	elif b <= 1.28e+42:
		tmp = t_2
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(t * Float64(c * j)))
	t_2 = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(b * i)) / y) - Float64(i * j))))
	tmp = 0.0
	if (b <= -7.4e+87)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (b <= -2.05e-77)
		tmp = t_2;
	elseif (b <= -8.7e-209)
		tmp = t_1;
	elseif (b <= -3.2e-281)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 8.8e-89)
		tmp = t_1;
	elseif (b <= 1.28e+42)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (t * (c * j));
	t_2 = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	tmp = 0.0;
	if (b <= -7.4e+87)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (b <= -2.05e-77)
		tmp = t_2;
	elseif (b <= -8.7e-209)
		tmp = t_1;
	elseif (b <= -3.2e-281)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 8.8e-89)
		tmp = t_1;
	elseif (b <= 1.28e+42)
		tmp = t_2;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+87], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.05e-77], t$95$2, If[LessEqual[b, -8.7e-209], t$95$1, If[LessEqual[b, -3.2e-281], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e-89], t$95$1, If[LessEqual[b, 1.28e+42], t$95$2, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.40000000000000005e87

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 83.7%

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

      1. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in z around inf 83.7%

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

      1. associate-/l* 83.7%

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

   8. Simplified 83.7%

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

   if -7.40000000000000005e87 < b < -2.04999999999999981e-77 or 8.80000000000000048e-89 < b < 1.28000000000000004e42

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. +-commutative 79.6%

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

      2. mul-1-neg 79.6%

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

      3. unsub-neg 79.6%

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

      4. associate-/l* 79.6%

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

      5. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in y around -inf 75.0%

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

   8. Simplified 71.7%

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

   9. Taylor expanded in i around inf 59.7%

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

   if -2.04999999999999981e-77 < b < -8.7000000000000002e-209 or -3.2000000000000001e-281 < b < 8.80000000000000048e-89

   1. Initial program 76.9%

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

   3. Taylor expanded in b around 0 79.6%

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

   4. Taylor expanded in c around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 69.0%

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

   6. Simplified 69.0%

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

   if -8.7000000000000002e-209 < b < -3.2000000000000001e-281

   1. Initial program 71.2%

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

   3. Taylor expanded in j around inf 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   if 1.28000000000000004e42 < b

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8.7 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 0.00083:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+197} \lor \neg \left(b \leq 1.35 \cdot 10^{+235}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* b (* z (- c)))))
   (if (<= b -8.2e+113)
     t_2
     (if (<= b -8.6e-18)
       t_1
       (if (<= b -5.2e-109)
         t_2
         (if (<= b 1.15e-231)
           (* c (* t j))
           (if (<= b 0.00083)
             (* a (* x (- t)))
             (if (or (<= b 1.35e+197) (not (<= b 1.35e+235))) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = b * (z * -c);
	double tmp;
	if (b <= -8.2e+113) {
		tmp = t_2;
	} else if (b <= -8.6e-18) {
		tmp = t_1;
	} else if (b <= -5.2e-109) {
		tmp = t_2;
	} else if (b <= 1.15e-231) {
		tmp = c * (t * j);
	} else if (b <= 0.00083) {
		tmp = a * (x * -t);
	} else if ((b <= 1.35e+197) || !(b <= 1.35e+235)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * i)
    t_2 = b * (z * -c)
    if (b <= (-8.2d+113)) then
        tmp = t_2
    else if (b <= (-8.6d-18)) then
        tmp = t_1
    else if (b <= (-5.2d-109)) then
        tmp = t_2
    else if (b <= 1.15d-231) then
        tmp = c * (t * j)
    else if (b <= 0.00083d0) then
        tmp = a * (x * -t)
    else if ((b <= 1.35d+197) .or. (.not. (b <= 1.35d+235))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = b * (z * -c);
	double tmp;
	if (b <= -8.2e+113) {
		tmp = t_2;
	} else if (b <= -8.6e-18) {
		tmp = t_1;
	} else if (b <= -5.2e-109) {
		tmp = t_2;
	} else if (b <= 1.15e-231) {
		tmp = c * (t * j);
	} else if (b <= 0.00083) {
		tmp = a * (x * -t);
	} else if ((b <= 1.35e+197) || !(b <= 1.35e+235)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = b * (z * -c)
	tmp = 0
	if b <= -8.2e+113:
		tmp = t_2
	elif b <= -8.6e-18:
		tmp = t_1
	elif b <= -5.2e-109:
		tmp = t_2
	elif b <= 1.15e-231:
		tmp = c * (t * j)
	elif b <= 0.00083:
		tmp = a * (x * -t)
	elif (b <= 1.35e+197) or not (b <= 1.35e+235):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (b <= -8.2e+113)
		tmp = t_2;
	elseif (b <= -8.6e-18)
		tmp = t_1;
	elseif (b <= -5.2e-109)
		tmp = t_2;
	elseif (b <= 1.15e-231)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 0.00083)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif ((b <= 1.35e+197) || !(b <= 1.35e+235))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	t_2 = b * (z * -c);
	tmp = 0.0;
	if (b <= -8.2e+113)
		tmp = t_2;
	elseif (b <= -8.6e-18)
		tmp = t_1;
	elseif (b <= -5.2e-109)
		tmp = t_2;
	elseif (b <= 1.15e-231)
		tmp = c * (t * j);
	elseif (b <= 0.00083)
		tmp = a * (x * -t);
	elseif ((b <= 1.35e+197) || ~((b <= 1.35e+235)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+113], t$95$2, If[LessEqual[b, -8.6e-18], t$95$1, If[LessEqual[b, -5.2e-109], t$95$2, If[LessEqual[b, 1.15e-231], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00083], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.35e+197], N[Not[LessEqual[b, 1.35e+235]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.19999999999999985e113 or -8.6000000000000005e-18 < b < -5.1999999999999997e-109 or 8.3000000000000001e-4 < b < 1.35e197 or 1.3499999999999999e235 < b

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in a around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-rgt-neg-in 51.1%

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

      3. *-commutative 51.1%

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

      4. distribute-rgt-neg-in 51.1%

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

   8. Simplified 51.1%

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

   if -8.19999999999999985e113 < b < -8.6000000000000005e-18 or 1.35e197 < b < 1.3499999999999999e235

   1. Initial program 73.1%

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

   3. Taylor expanded in b around inf 46.9%

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

      1. *-commutative 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in a around inf 41.9%

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

      1. *-commutative 41.9%

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

   8. Simplified 41.9%

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

   if -5.1999999999999997e-109 < b < 1.15e-231

   1. Initial program 73.6%

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

   3. Taylor expanded in b around 0 80.1%

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

   4. Taylor expanded in c around inf 37.0%

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

   if 1.15e-231 < b < 8.3000000000000001e-4

   1. Initial program 78.9%

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

   3. Taylor expanded in c around 0 81.1%

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

   4. Taylor expanded in x around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

      3. *-commutative 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in y around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. *-commutative 43.0%

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

   9. Simplified 43.0%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 0.00083:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+197} \lor \neg \left(b \leq 1.35 \cdot 10^{+235}\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.00097:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (* z (- (* a (/ i z)) c)))))
   (if (<= b -1.8e+76)
     t_2
     (if (<= b -5.2e-90)
       t_1
       (if (<= b -8.5e-110)
         (* z (- (* x y) (* b c)))
         (if (<= b -2e-113)
           (* t (- (* c j) (* x a)))
           (if (<= b -5e-308)
             t_1
             (if (<= b 0.00097) (* x (- (* y z) (* t a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -1.8e+76) {
		tmp = t_2;
	} else if (b <= -5.2e-90) {
		tmp = t_1;
	} else if (b <= -8.5e-110) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2e-113) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -5e-308) {
		tmp = t_1;
	} else if (b <= 0.00097) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * (z * ((a * (i / z)) - c))
    if (b <= (-1.8d+76)) then
        tmp = t_2
    else if (b <= (-5.2d-90)) then
        tmp = t_1
    else if (b <= (-8.5d-110)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2d-113)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= (-5d-308)) then
        tmp = t_1
    else if (b <= 0.00097d0) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (b <= -1.8e+76) {
		tmp = t_2;
	} else if (b <= -5.2e-90) {
		tmp = t_1;
	} else if (b <= -8.5e-110) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2e-113) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -5e-308) {
		tmp = t_1;
	} else if (b <= 0.00097) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * (z * ((a * (i / z)) - c))
	tmp = 0
	if b <= -1.8e+76:
		tmp = t_2
	elif b <= -5.2e-90:
		tmp = t_1
	elif b <= -8.5e-110:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2e-113:
		tmp = t * ((c * j) - (x * a))
	elif b <= -5e-308:
		tmp = t_1
	elif b <= 0.00097:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	tmp = 0.0
	if (b <= -1.8e+76)
		tmp = t_2;
	elseif (b <= -5.2e-90)
		tmp = t_1;
	elseif (b <= -8.5e-110)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2e-113)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= -5e-308)
		tmp = t_1;
	elseif (b <= 0.00097)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * (z * ((a * (i / z)) - c));
	tmp = 0.0;
	if (b <= -1.8e+76)
		tmp = t_2;
	elseif (b <= -5.2e-90)
		tmp = t_1;
	elseif (b <= -8.5e-110)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2e-113)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= -5e-308)
		tmp = t_1;
	elseif (b <= 0.00097)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+76], t$95$2, If[LessEqual[b, -5.2e-90], t$95$1, If[LessEqual[b, -8.5e-110], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-113], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5e-308], t$95$1, If[LessEqual[b, 0.00097], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.8000000000000001e76 or 9.70000000000000051e-4 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in z around inf 74.2%

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

      1. associate-/l* 73.4%

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

   8. Simplified 73.4%

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

   if -1.8000000000000001e76 < b < -5.2000000000000001e-90 or -1.99999999999999996e-113 < b < -4.99999999999999955e-308

   1. Initial program 84.5%

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

   3. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -5.2000000000000001e-90 < b < -8.50000000000000029e-110

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -8.50000000000000029e-110 < b < -1.99999999999999996e-113

   1. Initial program 51.7%

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

   3. Taylor expanded in t around inf 99.2%

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

      1. +-commutative 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   if -4.99999999999999955e-308 < b < 9.70000000000000051e-4

   1. Initial program 74.8%

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

   3. Taylor expanded in c around 0 78.0%

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

   4. Taylor expanded in x around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. *-commutative 56.0%

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

   6. Simplified 56.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-90}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-308}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00097:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-205}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-214}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 0.00057:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* a (* x (- t)))))
   (if (<= b -2.05e+73)
     t_1
     (if (<= b -5.5e-130)
       t_2
       (if (<= b -1e-138)
         (* x (* y z))
         (if (<= b -2.1e-205)
           t_3
           (if (<= b 1.6e-214) t_2 (if (<= b 0.00057) t_3 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * (x * -t);
	double tmp;
	if (b <= -2.05e+73) {
		tmp = t_1;
	} else if (b <= -5.5e-130) {
		tmp = t_2;
	} else if (b <= -1e-138) {
		tmp = x * (y * z);
	} else if (b <= -2.1e-205) {
		tmp = t_3;
	} else if (b <= 1.6e-214) {
		tmp = t_2;
	} else if (b <= 0.00057) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = c * ((t * j) - (z * b))
    t_3 = a * (x * -t)
    if (b <= (-2.05d+73)) then
        tmp = t_1
    else if (b <= (-5.5d-130)) then
        tmp = t_2
    else if (b <= (-1d-138)) then
        tmp = x * (y * z)
    else if (b <= (-2.1d-205)) then
        tmp = t_3
    else if (b <= 1.6d-214) then
        tmp = t_2
    else if (b <= 0.00057d0) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * (x * -t);
	double tmp;
	if (b <= -2.05e+73) {
		tmp = t_1;
	} else if (b <= -5.5e-130) {
		tmp = t_2;
	} else if (b <= -1e-138) {
		tmp = x * (y * z);
	} else if (b <= -2.1e-205) {
		tmp = t_3;
	} else if (b <= 1.6e-214) {
		tmp = t_2;
	} else if (b <= 0.00057) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * ((t * j) - (z * b))
	t_3 = a * (x * -t)
	tmp = 0
	if b <= -2.05e+73:
		tmp = t_1
	elif b <= -5.5e-130:
		tmp = t_2
	elif b <= -1e-138:
		tmp = x * (y * z)
	elif b <= -2.1e-205:
		tmp = t_3
	elif b <= 1.6e-214:
		tmp = t_2
	elif b <= 0.00057:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (b <= -2.05e+73)
		tmp = t_1;
	elseif (b <= -5.5e-130)
		tmp = t_2;
	elseif (b <= -1e-138)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -2.1e-205)
		tmp = t_3;
	elseif (b <= 1.6e-214)
		tmp = t_2;
	elseif (b <= 0.00057)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = c * ((t * j) - (z * b));
	t_3 = a * (x * -t);
	tmp = 0.0;
	if (b <= -2.05e+73)
		tmp = t_1;
	elseif (b <= -5.5e-130)
		tmp = t_2;
	elseif (b <= -1e-138)
		tmp = x * (y * z);
	elseif (b <= -2.1e-205)
		tmp = t_3;
	elseif (b <= 1.6e-214)
		tmp = t_2;
	elseif (b <= 0.00057)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+73], t$95$1, If[LessEqual[b, -5.5e-130], t$95$2, If[LessEqual[b, -1e-138], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-205], t$95$3, If[LessEqual[b, 1.6e-214], t$95$2, If[LessEqual[b, 0.00057], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.0499999999999999e73 or 5.6999999999999998e-4 < b

   1. Initial program 75.6%

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

   3. Taylor expanded in b around inf 72.6%

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

      1. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -2.0499999999999999e73 < b < -5.50000000000000007e-130 or -2.09999999999999983e-205 < b < 1.60000000000000007e-214

   1. Initial program 76.3%

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

   3. Taylor expanded in c around inf 45.7%

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

      1. *-commutative 45.7%

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

      2. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   if -5.50000000000000007e-130 < b < -1.00000000000000007e-138

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

      4. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 67.2%

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

   if -1.00000000000000007e-138 < b < -2.09999999999999983e-205 or 1.60000000000000007e-214 < b < 5.6999999999999998e-4

   1. Initial program 82.7%

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

   3. Taylor expanded in c around 0 84.6%

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

   4. Taylor expanded in x around inf 58.1%

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

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

      3. *-commutative 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in y around 0 44.7%

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

      1. mul-1-neg 44.7%

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

      2. *-commutative 44.7%

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

   9. Simplified 44.7%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 0.00057:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.00032:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -5.1e+79)
     t_3
     (if (<= b -2.6e-50)
       t_1
       (if (<= b -5e-104)
         (* c (- (* t j) (* z b)))
         (if (<= b -1.7e-207)
           t_2
           (if (<= b -2.1e-307) t_1 (if (<= b 0.00032) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.1e+79) {
		tmp = t_3;
	} else if (b <= -2.6e-50) {
		tmp = t_1;
	} else if (b <= -5e-104) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= -1.7e-207) {
		tmp = t_2;
	} else if (b <= -2.1e-307) {
		tmp = t_1;
	} else if (b <= 0.00032) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-5.1d+79)) then
        tmp = t_3
    else if (b <= (-2.6d-50)) then
        tmp = t_1
    else if (b <= (-5d-104)) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= (-1.7d-207)) then
        tmp = t_2
    else if (b <= (-2.1d-307)) then
        tmp = t_1
    else if (b <= 0.00032d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.1e+79) {
		tmp = t_3;
	} else if (b <= -2.6e-50) {
		tmp = t_1;
	} else if (b <= -5e-104) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= -1.7e-207) {
		tmp = t_2;
	} else if (b <= -2.1e-307) {
		tmp = t_1;
	} else if (b <= 0.00032) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.1e+79:
		tmp = t_3
	elif b <= -2.6e-50:
		tmp = t_1
	elif b <= -5e-104:
		tmp = c * ((t * j) - (z * b))
	elif b <= -1.7e-207:
		tmp = t_2
	elif b <= -2.1e-307:
		tmp = t_1
	elif b <= 0.00032:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.1e+79)
		tmp = t_3;
	elseif (b <= -2.6e-50)
		tmp = t_1;
	elseif (b <= -5e-104)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= -1.7e-207)
		tmp = t_2;
	elseif (b <= -2.1e-307)
		tmp = t_1;
	elseif (b <= 0.00032)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.1e+79)
		tmp = t_3;
	elseif (b <= -2.6e-50)
		tmp = t_1;
	elseif (b <= -5e-104)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= -1.7e-207)
		tmp = t_2;
	elseif (b <= -2.1e-307)
		tmp = t_1;
	elseif (b <= 0.00032)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.1e+79], t$95$3, If[LessEqual[b, -2.6e-50], t$95$1, If[LessEqual[b, -5e-104], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-207], t$95$2, If[LessEqual[b, -2.1e-307], t$95$1, If[LessEqual[b, 0.00032], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.1000000000000001e79 or 3.20000000000000026e-4 < b

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -5.1000000000000001e79 < b < -2.6000000000000001e-50 or -1.69999999999999999e-207 < b < -2.1000000000000001e-307

   1. Initial program 82.0%

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

   3. Taylor expanded in j around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if -2.6000000000000001e-50 < b < -4.99999999999999979e-104

   1. Initial program 83.1%

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

   3. Taylor expanded in c around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -4.99999999999999979e-104 < b < -1.69999999999999999e-207 or -2.1000000000000001e-307 < b < 3.20000000000000026e-4

   1. Initial program 77.5%

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

   3. Taylor expanded in c around 0 80.0%

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

   4. Taylor expanded in x around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. *-commutative 56.4%

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

      3. *-commutative 56.4%

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

   6. Simplified 56.4%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00032:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-109}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.00034:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.25e+84)
     t_2
     (if (<= b -4.5e-92)
       t_1
       (if (<= b -1e-109)
         (* z (- (* x y) (* b c)))
         (if (<= b -7.5e-112)
           (* t (- (* c j) (* x a)))
           (if (<= b -1.1e-307)
             t_1
             (if (<= b 0.00034) (* x (- (* y z) (* t a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.25e+84) {
		tmp = t_2;
	} else if (b <= -4.5e-92) {
		tmp = t_1;
	} else if (b <= -1e-109) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -7.5e-112) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -1.1e-307) {
		tmp = t_1;
	} else if (b <= 0.00034) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.25d+84)) then
        tmp = t_2
    else if (b <= (-4.5d-92)) then
        tmp = t_1
    else if (b <= (-1d-109)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-7.5d-112)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= (-1.1d-307)) then
        tmp = t_1
    else if (b <= 0.00034d0) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.25e+84) {
		tmp = t_2;
	} else if (b <= -4.5e-92) {
		tmp = t_1;
	} else if (b <= -1e-109) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -7.5e-112) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -1.1e-307) {
		tmp = t_1;
	} else if (b <= 0.00034) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.25e+84:
		tmp = t_2
	elif b <= -4.5e-92:
		tmp = t_1
	elif b <= -1e-109:
		tmp = z * ((x * y) - (b * c))
	elif b <= -7.5e-112:
		tmp = t * ((c * j) - (x * a))
	elif b <= -1.1e-307:
		tmp = t_1
	elif b <= 0.00034:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.25e+84)
		tmp = t_2;
	elseif (b <= -4.5e-92)
		tmp = t_1;
	elseif (b <= -1e-109)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -7.5e-112)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= -1.1e-307)
		tmp = t_1;
	elseif (b <= 0.00034)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.25e+84)
		tmp = t_2;
	elseif (b <= -4.5e-92)
		tmp = t_1;
	elseif (b <= -1e-109)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -7.5e-112)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= -1.1e-307)
		tmp = t_1;
	elseif (b <= 0.00034)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.25e+84], t$95$2, If[LessEqual[b, -4.5e-92], t$95$1, If[LessEqual[b, -1e-109], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.5e-112], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-307], t$95$1, If[LessEqual[b, 0.00034], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.2499999999999999e84 or 3.4e-4 < b

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -2.2499999999999999e84 < b < -4.5e-92 or -7.5000000000000002e-112 < b < -1.1e-307

   1. Initial program 84.5%

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

   3. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -4.5e-92 < b < -9.9999999999999999e-110

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -9.9999999999999999e-110 < b < -7.5000000000000002e-112

   1. Initial program 51.7%

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

   3. Taylor expanded in t around inf 99.2%

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

      1. +-commutative 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   if -1.1e-307 < b < 3.4e-4

   1. Initial program 75.9%

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

   3. Taylor expanded in c around 0 79.1%

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

   4. Taylor expanded in x around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. *-commutative 56.8%

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

      3. *-commutative 56.8%

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

   6. Simplified 56.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-109}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00034:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-136} \lor \neg \left(b \leq 0.00035\right):\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= b -2.5e+107)
     t_1
     (if (or (<= b -5e-136) (not (<= b 0.00035)))
       (+ t_1 t_2)
       (+ (* x (- (* y z) (* t a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -2.5e+107) {
		tmp = t_1;
	} else if ((b <= -5e-136) || !(b <= 0.00035)) {
		tmp = t_1 + t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + 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 * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (b <= (-2.5d+107)) then
        tmp = t_1
    else if ((b <= (-5d-136)) .or. (.not. (b <= 0.00035d0))) then
        tmp = t_1 + t_2
    else
        tmp = (x * ((y * z) - (t * a))) + 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -2.5e+107) {
		tmp = t_1;
	} else if ((b <= -5e-136) || !(b <= 0.00035)) {
		tmp = t_1 + t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -2.5e+107:
		tmp = t_1
	elif (b <= -5e-136) or not (b <= 0.00035):
		tmp = t_1 + t_2
	else:
		tmp = (x * ((y * z) - (t * a))) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -2.5e+107)
		tmp = t_1;
	elseif ((b <= -5e-136) || !(b <= 0.00035))
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -2.5e+107)
		tmp = t_1;
	elseif ((b <= -5e-136) || ~((b <= 0.00035)))
		tmp = t_1 + t_2;
	else
		tmp = (x * ((y * z) - (t * a))) + 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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+107], t$95$1, If[Or[LessEqual[b, -5e-136], N[Not[LessEqual[b, 0.00035]], $MachinePrecision]], N[(t$95$1 + t$95$2), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5000000000000001e107

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 89.1%

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

      1. *-commutative 89.1%

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

   5. Simplified 89.1%

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

   if -2.5000000000000001e107 < b < -5.0000000000000002e-136 or 3.49999999999999996e-4 < b

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 73.5%

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

   if -5.0000000000000002e-136 < b < 3.49999999999999996e-4

   1. Initial program 76.2%

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

   3. Taylor expanded in b around 0 79.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-136} \lor \neg \left(b \leq 0.00035\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+140}:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-135} \lor \neg \left(b \leq 0.000205\right):\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= b -3.3e+140)
     (+ t_3 t_2)
     (if (or (<= b -1.3e-135) (not (<= b 0.000205)))
       (+ t_2 t_1)
       (+ t_3 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -3.3e+140) {
		tmp = t_3 + t_2;
	} else if ((b <= -1.3e-135) || !(b <= 0.000205)) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = x * ((y * z) - (t * a))
    if (b <= (-3.3d+140)) then
        tmp = t_3 + t_2
    else if ((b <= (-1.3d-135)) .or. (.not. (b <= 0.000205d0))) then
        tmp = t_2 + t_1
    else
        tmp = t_3 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -3.3e+140) {
		tmp = t_3 + t_2;
	} else if ((b <= -1.3e-135) || !(b <= 0.000205)) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if b <= -3.3e+140:
		tmp = t_3 + t_2
	elif (b <= -1.3e-135) or not (b <= 0.000205):
		tmp = t_2 + t_1
	else:
		tmp = t_3 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (b <= -3.3e+140)
		tmp = Float64(t_3 + t_2);
	elseif ((b <= -1.3e-135) || !(b <= 0.000205))
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(t_3 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (b <= -3.3e+140)
		tmp = t_3 + t_2;
	elseif ((b <= -1.3e-135) || ~((b <= 0.000205)))
		tmp = t_2 + t_1;
	else
		tmp = t_3 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+140], N[(t$95$3 + t$95$2), $MachinePrecision], If[Or[LessEqual[b, -1.3e-135], N[Not[LessEqual[b, 0.000205]], $MachinePrecision]], N[(t$95$2 + t$95$1), $MachinePrecision], N[(t$95$3 + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3000000000000002e140

   1. Initial program 80.5%

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

   3. Taylor expanded in j around 0 90.2%

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

      1. *-commutative 90.2%

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

   5. Simplified 90.2%

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

   if -3.3000000000000002e140 < b < -1.30000000000000002e-135 or 2.05e-4 < b

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 74.6%

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

   if -1.30000000000000002e-135 < b < 2.05e-4

   1. Initial program 76.2%

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

   3. Taylor expanded in b around 0 79.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-135} \lor \neg \left(b \leq 0.000205\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00047:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.1e+80)
     t_1
     (if (<= b 5.3e-211)
       (* j (- (* t c) (* y i)))
       (if (<= b 0.00047)
         (* a (* x (- t)))
         (if (<= b 2.6e+72) (* c (- (* t j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.1e+80) {
		tmp = t_1;
	} else if (b <= 5.3e-211) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 0.00047) {
		tmp = a * (x * -t);
	} else if (b <= 2.6e+72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.1d+80)) then
        tmp = t_1
    else if (b <= 5.3d-211) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 0.00047d0) then
        tmp = a * (x * -t)
    else if (b <= 2.6d+72) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.1e+80) {
		tmp = t_1;
	} else if (b <= 5.3e-211) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 0.00047) {
		tmp = a * (x * -t);
	} else if (b <= 2.6e+72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.1e+80:
		tmp = t_1
	elif b <= 5.3e-211:
		tmp = j * ((t * c) - (y * i))
	elif b <= 0.00047:
		tmp = a * (x * -t)
	elif b <= 2.6e+72:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.1e+80)
		tmp = t_1;
	elseif (b <= 5.3e-211)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 0.00047)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (b <= 2.6e+72)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.1e+80)
		tmp = t_1;
	elseif (b <= 5.3e-211)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 0.00047)
		tmp = a * (x * -t);
	elseif (b <= 2.6e+72)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+80], t$95$1, If[LessEqual[b, 5.3e-211], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00047], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+72], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.10000000000000001e80 or 2.59999999999999981e72 < b

   1. Initial program 75.0%

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

   3. Taylor expanded in b around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -1.10000000000000001e80 < b < 5.29999999999999993e-211

   1. Initial program 78.5%

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

   3. Taylor expanded in j around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   if 5.29999999999999993e-211 < b < 4.69999999999999986e-4

   1. Initial program 80.9%

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

   3. Taylor expanded in c around 0 83.3%

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

   4. Taylor expanded in x around inf 57.3%

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

      1. *-commutative 57.3%

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

      2. *-commutative 57.3%

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

      3. *-commutative 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in y around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. *-commutative 45.6%

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

   9. Simplified 45.6%

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

   if 4.69999999999999986e-4 < b < 2.59999999999999981e72

   1. Initial program 77.5%

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

   3. Taylor expanded in c around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00047:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.65 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.65e+77)
   (* b (* z (- (* a (/ i z)) c)))
   (if (<= b 8.5e+90)
     (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
     (* b (- (* a i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.65e+77) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= 8.5e+90) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3.65d+77)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (b <= 8.5d+90) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.65e+77) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= 8.5e+90) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.65e+77:
		tmp = b * (z * ((a * (i / z)) - c))
	elif b <= 8.5e+90:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.65e+77)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (b <= 8.5e+90)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.65e+77)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (b <= 8.5e+90)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.65e+77], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+90], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.65000000000000012e77

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in z around inf 84.4%

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

      1. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   if -3.65000000000000012e77 < b < 8.5000000000000002e90

   1. Initial program 79.2%

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

   3. Taylor expanded in b around 0 71.9%

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

   if 8.5000000000000002e90 < b

   1. Initial program 72.2%

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

   3. Taylor expanded in b around inf 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.65 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 0.00048:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.25e-108)
     t_1
     (if (<= b 1.35e-229)
       (* c (* t j))
       (if (<= b 0.00048) (* a (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e-108) {
		tmp = t_1;
	} else if (b <= 1.35e-229) {
		tmp = c * (t * j);
	} else if (b <= 0.00048) {
		tmp = a * (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 = b * ((a * i) - (z * c))
    if (b <= (-1.25d-108)) then
        tmp = t_1
    else if (b <= 1.35d-229) then
        tmp = c * (t * j)
    else if (b <= 0.00048d0) then
        tmp = a * (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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e-108) {
		tmp = t_1;
	} else if (b <= 1.35e-229) {
		tmp = c * (t * j);
	} else if (b <= 0.00048) {
		tmp = a * (x * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.25e-108:
		tmp = t_1
	elif b <= 1.35e-229:
		tmp = c * (t * j)
	elif b <= 0.00048:
		tmp = a * (x * -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.25e-108)
		tmp = t_1;
	elseif (b <= 1.35e-229)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 0.00048)
		tmp = Float64(a * Float64(x * Float64(-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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.25e-108)
		tmp = t_1;
	elseif (b <= 1.35e-229)
		tmp = c * (t * j);
	elseif (b <= 0.00048)
		tmp = a * (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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e-108], t$95$1, If[LessEqual[b, 1.35e-229], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00048], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25e-108 or 4.80000000000000012e-4 < b

   1. Initial program 78.7%

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

   3. Taylor expanded in b around inf 63.9%

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

      1. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   if -1.25e-108 < b < 1.3499999999999999e-229

   1. Initial program 73.6%

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

   3. Taylor expanded in b around 0 80.1%

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

   4. Taylor expanded in c around inf 37.0%

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

   if 1.3499999999999999e-229 < b < 4.80000000000000012e-4

   1. Initial program 78.9%

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

   3. Taylor expanded in c around 0 81.1%

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

   4. Taylor expanded in x around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

      3. *-commutative 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in y around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. *-commutative 43.0%

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

   9. Simplified 43.0%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 0.00048:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00047:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -2.15e+83)
     t_1
     (if (<= b -2.75e-297)
       (* j (- (* t c) (* y i)))
       (if (<= b 0.00047) (* t (- (* c j) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.15e+83) {
		tmp = t_1;
	} else if (b <= -2.75e-297) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 0.00047) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-2.15d+83)) then
        tmp = t_1
    else if (b <= (-2.75d-297)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 0.00047d0) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.15e+83) {
		tmp = t_1;
	} else if (b <= -2.75e-297) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 0.00047) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.15e+83:
		tmp = t_1
	elif b <= -2.75e-297:
		tmp = j * ((t * c) - (y * i))
	elif b <= 0.00047:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.15e+83)
		tmp = t_1;
	elseif (b <= -2.75e-297)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 0.00047)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.15e+83)
		tmp = t_1;
	elseif (b <= -2.75e-297)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 0.00047)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+83], t$95$1, If[LessEqual[b, -2.75e-297], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00047], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.15e83 or 4.69999999999999986e-4 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -2.15e83 < b < -2.75000000000000015e-297

   1. Initial program 82.1%

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

   3. Taylor expanded in j around inf 55.3%

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

      1. *-commutative 55.3%

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

      2. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   if -2.75000000000000015e-297 < b < 4.69999999999999986e-4

   1. Initial program 75.2%

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

   3. Taylor expanded in t around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

      5. *-commutative 49.3%

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

   5. Simplified 49.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 0.00047:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -180:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 28500000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -180.0)
   (* b (* a i))
   (if (<= b 1.2e-231)
     (* t (* c j))
     (if (<= b 28500000.0) (* a (* x (- t))) (* a (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -180.0) {
		tmp = b * (a * i);
	} else if (b <= 1.2e-231) {
		tmp = t * (c * j);
	} else if (b <= 28500000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-180.0d0)) then
        tmp = b * (a * i)
    else if (b <= 1.2d-231) then
        tmp = t * (c * j)
    else if (b <= 28500000.0d0) then
        tmp = a * (x * -t)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -180.0) {
		tmp = b * (a * i);
	} else if (b <= 1.2e-231) {
		tmp = t * (c * j);
	} else if (b <= 28500000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -180.0:
		tmp = b * (a * i)
	elif b <= 1.2e-231:
		tmp = t * (c * j)
	elif b <= 28500000.0:
		tmp = a * (x * -t)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -180.0)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 1.2e-231)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 28500000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -180.0)
		tmp = b * (a * i);
	elseif (b <= 1.2e-231)
		tmp = t * (c * j);
	elseif (b <= 28500000.0)
		tmp = a * (x * -t);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -180.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-231], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 28500000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -180

   1. Initial program 80.7%

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

   3. Taylor expanded in b around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in a around inf 35.2%

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

      1. *-commutative 35.2%

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

   8. Simplified 35.2%

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

   if -180 < b < 1.19999999999999996e-231

   1. Initial program 76.7%

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

   3. Taylor expanded in b around 0 73.7%

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

   4. Taylor expanded in c around inf 33.7%

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

      1. associate-*r* 33.8%

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

      2. *-commutative 33.8%

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

   6. Simplified 33.8%

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

   if 1.19999999999999996e-231 < b < 2.85e7

   1. Initial program 80.2%

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

   3. Taylor expanded in c around 0 82.2%

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

   4. Taylor expanded in x around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. *-commutative 52.7%

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

      3. *-commutative 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in y around 0 40.5%

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

      1. mul-1-neg 40.5%

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

      2. *-commutative 40.5%

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

   9. Simplified 40.5%

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

   if 2.85e7 < b

   1. Initial program 73.3%

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

   3. Taylor expanded in b around inf 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in a around inf 32.6%

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

      1. *-commutative 32.6%

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

   8. Simplified 32.6%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -180:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 28500000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -145000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -145000.0)
   (* b (* a i))
   (if (<= b 5.2e-128)
     (* j (* t c))
     (if (<= b 7e+95) (* x (* y z)) (* a (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -145000.0) {
		tmp = b * (a * i);
	} else if (b <= 5.2e-128) {
		tmp = j * (t * c);
	} else if (b <= 7e+95) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-145000.0d0)) then
        tmp = b * (a * i)
    else if (b <= 5.2d-128) then
        tmp = j * (t * c)
    else if (b <= 7d+95) then
        tmp = x * (y * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -145000.0) {
		tmp = b * (a * i);
	} else if (b <= 5.2e-128) {
		tmp = j * (t * c);
	} else if (b <= 7e+95) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -145000.0:
		tmp = b * (a * i)
	elif b <= 5.2e-128:
		tmp = j * (t * c)
	elif b <= 7e+95:
		tmp = x * (y * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -145000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 5.2e-128)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= 7e+95)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -145000.0)
		tmp = b * (a * i);
	elseif (b <= 5.2e-128)
		tmp = j * (t * c);
	elseif (b <= 7e+95)
		tmp = x * (y * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -145000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-128], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+95], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -145000

   1. Initial program 80.7%

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

   3. Taylor expanded in b around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in a around inf 35.2%

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

      1. *-commutative 35.2%

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

   8. Simplified 35.2%

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

   if -145000 < b < 5.19999999999999961e-128

   1. Initial program 76.1%

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

   3. Taylor expanded in j around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in t around inf 31.0%

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

   if 5.19999999999999961e-128 < b < 6.99999999999999999e95

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in x around inf 33.0%

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

   if 6.99999999999999999e95 < b

   1. Initial program 71.5%

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

   3. Taylor expanded in b around inf 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -145000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -320000000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -320000000000.0)
   (* b (* a i))
   (if (<= b 5.5e-131)
     (* j (* t c))
     (if (<= b 3.8e+96) (* y (* x z)) (* a (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -320000000000.0) {
		tmp = b * (a * i);
	} else if (b <= 5.5e-131) {
		tmp = j * (t * c);
	} else if (b <= 3.8e+96) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-320000000000.0d0)) then
        tmp = b * (a * i)
    else if (b <= 5.5d-131) then
        tmp = j * (t * c)
    else if (b <= 3.8d+96) then
        tmp = y * (x * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -320000000000.0) {
		tmp = b * (a * i);
	} else if (b <= 5.5e-131) {
		tmp = j * (t * c);
	} else if (b <= 3.8e+96) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -320000000000.0:
		tmp = b * (a * i)
	elif b <= 5.5e-131:
		tmp = j * (t * c)
	elif b <= 3.8e+96:
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -320000000000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 5.5e-131)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= 3.8e+96)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -320000000000.0)
		tmp = b * (a * i);
	elseif (b <= 5.5e-131)
		tmp = j * (t * c);
	elseif (b <= 3.8e+96)
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -320000000000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-131], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+96], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.2e11

   1. Initial program 80.7%

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

   3. Taylor expanded in b around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in a around inf 35.2%

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

      1. *-commutative 35.2%

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

   8. Simplified 35.2%

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

   if -3.2e11 < b < 5.4999999999999997e-131

   1. Initial program 76.1%

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

   3. Taylor expanded in j around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in t around inf 31.0%

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

   if 5.4999999999999997e-131 < b < 3.8000000000000002e96

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in x around inf 34.9%

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

      1. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   if 3.8000000000000002e96 < b

   1. Initial program 71.5%

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

   3. Taylor expanded in b around inf 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -320000000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7500:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7500.0)
   (* b (* a i))
   (if (<= b 1.1e-128)
     (* t (* c j))
     (if (<= b 1.45e+96) (* y (* x z)) (* a (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7500.0) {
		tmp = b * (a * i);
	} else if (b <= 1.1e-128) {
		tmp = t * (c * j);
	} else if (b <= 1.45e+96) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-7500.0d0)) then
        tmp = b * (a * i)
    else if (b <= 1.1d-128) then
        tmp = t * (c * j)
    else if (b <= 1.45d+96) then
        tmp = y * (x * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7500.0) {
		tmp = b * (a * i);
	} else if (b <= 1.1e-128) {
		tmp = t * (c * j);
	} else if (b <= 1.45e+96) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7500.0:
		tmp = b * (a * i)
	elif b <= 1.1e-128:
		tmp = t * (c * j)
	elif b <= 1.45e+96:
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7500.0)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 1.1e-128)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 1.45e+96)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -7500.0)
		tmp = b * (a * i);
	elseif (b <= 1.1e-128)
		tmp = t * (c * j);
	elseif (b <= 1.45e+96)
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7500.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-128], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+96], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7500

   1. Initial program 80.7%

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

   3. Taylor expanded in b around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in a around inf 35.2%

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

      1. *-commutative 35.2%

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

   8. Simplified 35.2%

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

   if -7500 < b < 1.10000000000000005e-128

   1. Initial program 76.1%

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

   3. Taylor expanded in b around 0 73.6%

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

   4. Taylor expanded in c around inf 31.0%

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

      1. associate-*r* 31.1%

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

      2. *-commutative 31.1%

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

   6. Simplified 31.1%

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

   if 1.10000000000000005e-128 < b < 1.44999999999999989e96

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in x around inf 34.9%

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

      1. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   if 1.44999999999999989e96 < b

   1. Initial program 71.5%

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

   3. Taylor expanded in b around inf 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7500:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7.2e-6)
   (* b (* a i))
   (if (<= b 1.6e-30) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.2e-6) {
		tmp = b * (a * i);
	} else if (b <= 1.6e-30) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-7.2d-6)) then
        tmp = b * (a * i)
    else if (b <= 1.6d-30) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.2e-6) {
		tmp = b * (a * i);
	} else if (b <= 1.6e-30) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7.2e-6:
		tmp = b * (a * i)
	elif b <= 1.6e-30:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7.2e-6)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 1.6e-30)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -7.2e-6)
		tmp = b * (a * i);
	elseif (b <= 1.6e-30)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7.2e-6], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-30], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.19999999999999967e-6

   1. Initial program 80.7%

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

   3. Taylor expanded in b around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in a around inf 35.2%

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

      1. *-commutative 35.2%

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

   8. Simplified 35.2%

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

   if -7.19999999999999967e-6 < b < 1.6e-30

   1. Initial program 77.5%

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

   3. Taylor expanded in b around 0 74.7%

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

   4. Taylor expanded in c around inf 29.5%

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

   if 1.6e-30 < b

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 62.8%

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

      1. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in a around inf 31.0%

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

      1. *-commutative 31.0%

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

   8. Simplified 31.0%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.5%

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

3. Taylor expanded in b around inf 41.9%

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

   1. *-commutative 41.9%

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

5. Simplified 41.9%

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

6. Taylor expanded in a around inf 20.0%

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

   1. *-commutative 20.0%

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

8. Simplified 20.0%

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

9. Final simplification 20.0%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Developer target: 68.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))