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

Percentage Accurate: 74.8% → 82.9%

Time: 30.6s

Alternatives: 27

Speedup: 0.5×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = ((t * (i / z)) - c) * (z * b)
	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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t * Float64(i / z)) - c) * Float64(z * b));
	end
	return tmp
end

MATLAB

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around 0 0.0%

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

   4. Taylor expanded in z around inf 19.9%

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

   5. Taylor expanded in b around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

      3. associate-*l* 51.0%

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

      4. *-commutative 51.0%

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

      5. associate-/l* 54.3%

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

   7. Simplified 54.3%

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

4. Final simplification 85.1%

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

Alternative 2: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ t_3 := \left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -7.3 \cdot 10^{-38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;\left(t\_1 + b \cdot \left(t \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* a c) (* y i))) t_1))
        (t_3 (* (- (* t (/ i z)) c) (* z b))))
   (if (<= b -1.4e+220)
     t_3
     (if (<= b -2.9e+203)
       t_2
       (if (<= b -4.4e+185)
         (* c (- (* a j) (* z b)))
         (if (<= b -7.3e-38)
           (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
           (if (<= b 8.2e-72)
             t_2
             (if (<= b 1.7e+16)
               (- (+ t_1 (* b (* t i))) (* b (* z c)))
               (if (<= b 6.2e+62) 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = ((t * (i / z)) - c) * (z * b);
	double tmp;
	if (b <= -1.4e+220) {
		tmp = t_3;
	} else if (b <= -2.9e+203) {
		tmp = t_2;
	} else if (b <= -4.4e+185) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= -7.3e-38) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else if (b <= 8.2e-72) {
		tmp = t_2;
	} else if (b <= 1.7e+16) {
		tmp = (t_1 + (b * (t * i))) - (b * (z * c));
	} else if (b <= 6.2e+62) {
		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 = x * ((y * z) - (t * a))
    t_2 = (j * ((a * c) - (y * i))) + t_1
    t_3 = ((t * (i / z)) - c) * (z * b)
    if (b <= (-1.4d+220)) then
        tmp = t_3
    else if (b <= (-2.9d+203)) then
        tmp = t_2
    else if (b <= (-4.4d+185)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= (-7.3d-38)) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else if (b <= 8.2d-72) then
        tmp = t_2
    else if (b <= 1.7d+16) then
        tmp = (t_1 + (b * (t * i))) - (b * (z * c))
    else if (b <= 6.2d+62) 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = ((t * (i / z)) - c) * (z * b);
	double tmp;
	if (b <= -1.4e+220) {
		tmp = t_3;
	} else if (b <= -2.9e+203) {
		tmp = t_2;
	} else if (b <= -4.4e+185) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= -7.3e-38) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else if (b <= 8.2e-72) {
		tmp = t_2;
	} else if (b <= 1.7e+16) {
		tmp = (t_1 + (b * (t * i))) - (b * (z * c));
	} else if (b <= 6.2e+62) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (j * ((a * c) - (y * i))) + t_1
	t_3 = ((t * (i / z)) - c) * (z * b)
	tmp = 0
	if b <= -1.4e+220:
		tmp = t_3
	elif b <= -2.9e+203:
		tmp = t_2
	elif b <= -4.4e+185:
		tmp = c * ((a * j) - (z * b))
	elif b <= -7.3e-38:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	elif b <= 8.2e-72:
		tmp = t_2
	elif b <= 1.7e+16:
		tmp = (t_1 + (b * (t * i))) - (b * (z * c))
	elif b <= 6.2e+62:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1)
	t_3 = Float64(Float64(Float64(t * Float64(i / z)) - c) * Float64(z * b))
	tmp = 0.0
	if (b <= -1.4e+220)
		tmp = t_3;
	elseif (b <= -2.9e+203)
		tmp = t_2;
	elseif (b <= -4.4e+185)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= -7.3e-38)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (b <= 8.2e-72)
		tmp = t_2;
	elseif (b <= 1.7e+16)
		tmp = Float64(Float64(t_1 + Float64(b * Float64(t * i))) - Float64(b * Float64(z * c)));
	elseif (b <= 6.2e+62)
		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 = x * ((y * z) - (t * a));
	t_2 = (j * ((a * c) - (y * i))) + t_1;
	t_3 = ((t * (i / z)) - c) * (z * b);
	tmp = 0.0;
	if (b <= -1.4e+220)
		tmp = t_3;
	elseif (b <= -2.9e+203)
		tmp = t_2;
	elseif (b <= -4.4e+185)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= -7.3e-38)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	elseif (b <= 8.2e-72)
		tmp = t_2;
	elseif (b <= 1.7e+16)
		tmp = (t_1 + (b * (t * i))) - (b * (z * c));
	elseif (b <= 6.2e+62)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+220], t$95$3, If[LessEqual[b, -2.9e+203], t$95$2, If[LessEqual[b, -4.4e+185], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.3e-38], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-72], t$95$2, If[LessEqual[b, 1.7e+16], N[(N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+62], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.4e220 or 6.20000000000000029e62 < b

   1. Initial program 65.5%

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

   3. Taylor expanded in i around 0 55.7%

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

   4. Taylor expanded in z around inf 51.0%

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

   5. Taylor expanded in b around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*l* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

   if -1.4e220 < b < -2.90000000000000011e203 or -7.3000000000000001e-38 < b < 8.20000000000000007e-72 or 1.7e16 < b < 6.20000000000000029e62

   1. Initial program 76.0%

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

   3. Taylor expanded in b around 0 78.3%

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

   if -2.90000000000000011e203 < b < -4.4000000000000002e185

   1. Initial program 49.7%

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

   3. Taylor expanded in c around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -4.4000000000000002e185 < b < -7.3000000000000001e-38

   1. Initial program 79.8%

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

   3. Taylor expanded in y around 0 77.5%

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

   5. Simplified 77.5%

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

   if 8.20000000000000007e-72 < b < 1.7e16

   1. Initial program 70.2%

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

   3. Taylor expanded in i around 0 70.3%

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

   4. Taylor expanded in j around 0 75.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;\left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -7.3 \cdot 10^{-38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ t_3 := \left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ t_4 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* a c) (* y i))) t_1))
        (t_3 (* (- (* t (/ i z)) c) (* z b)))
        (t_4 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))
   (if (<= b -1.4e+220)
     t_3
     (if (<= b -2.9e+203)
       t_2
       (if (<= b -4.1e+185)
         (* c (- (* a j) (* z b)))
         (if (<= b -2.6e-37)
           t_4
           (if (<= b 6.8e-102)
             t_2
             (if (<= b 1.6e-29)
               t_4
               (if (<= b 6.6e+41) (- t_1 (* i (* y j))) 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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = ((t * (i / z)) - c) * (z * b);
	double t_4 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -1.4e+220) {
		tmp = t_3;
	} else if (b <= -2.9e+203) {
		tmp = t_2;
	} else if (b <= -4.1e+185) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= -2.6e-37) {
		tmp = t_4;
	} else if (b <= 6.8e-102) {
		tmp = t_2;
	} else if (b <= 1.6e-29) {
		tmp = t_4;
	} else if (b <= 6.6e+41) {
		tmp = t_1 - (i * (y * j));
	} 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) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (j * ((a * c) - (y * i))) + t_1
    t_3 = ((t * (i / z)) - c) * (z * b)
    t_4 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    if (b <= (-1.4d+220)) then
        tmp = t_3
    else if (b <= (-2.9d+203)) then
        tmp = t_2
    else if (b <= (-4.1d+185)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= (-2.6d-37)) then
        tmp = t_4
    else if (b <= 6.8d-102) then
        tmp = t_2
    else if (b <= 1.6d-29) then
        tmp = t_4
    else if (b <= 6.6d+41) then
        tmp = t_1 - (i * (y * j))
    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 = x * ((y * z) - (t * a));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = ((t * (i / z)) - c) * (z * b);
	double t_4 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (b <= -1.4e+220) {
		tmp = t_3;
	} else if (b <= -2.9e+203) {
		tmp = t_2;
	} else if (b <= -4.1e+185) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= -2.6e-37) {
		tmp = t_4;
	} else if (b <= 6.8e-102) {
		tmp = t_2;
	} else if (b <= 1.6e-29) {
		tmp = t_4;
	} else if (b <= 6.6e+41) {
		tmp = t_1 - (i * (y * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (j * ((a * c) - (y * i))) + t_1
	t_3 = ((t * (i / z)) - c) * (z * b)
	t_4 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	tmp = 0
	if b <= -1.4e+220:
		tmp = t_3
	elif b <= -2.9e+203:
		tmp = t_2
	elif b <= -4.1e+185:
		tmp = c * ((a * j) - (z * b))
	elif b <= -2.6e-37:
		tmp = t_4
	elif b <= 6.8e-102:
		tmp = t_2
	elif b <= 1.6e-29:
		tmp = t_4
	elif b <= 6.6e+41:
		tmp = t_1 - (i * (y * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1)
	t_3 = Float64(Float64(Float64(t * Float64(i / z)) - c) * Float64(z * b))
	t_4 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -1.4e+220)
		tmp = t_3;
	elseif (b <= -2.9e+203)
		tmp = t_2;
	elseif (b <= -4.1e+185)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= -2.6e-37)
		tmp = t_4;
	elseif (b <= 6.8e-102)
		tmp = t_2;
	elseif (b <= 1.6e-29)
		tmp = t_4;
	elseif (b <= 6.6e+41)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (j * ((a * c) - (y * i))) + t_1;
	t_3 = ((t * (i / z)) - c) * (z * b);
	t_4 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -1.4e+220)
		tmp = t_3;
	elseif (b <= -2.9e+203)
		tmp = t_2;
	elseif (b <= -4.1e+185)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= -2.6e-37)
		tmp = t_4;
	elseif (b <= 6.8e-102)
		tmp = t_2;
	elseif (b <= 1.6e-29)
		tmp = t_4;
	elseif (b <= 6.6e+41)
		tmp = t_1 - (i * (y * j));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+220], t$95$3, If[LessEqual[b, -2.9e+203], t$95$2, If[LessEqual[b, -4.1e+185], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-37], t$95$4, If[LessEqual[b, 6.8e-102], t$95$2, If[LessEqual[b, 1.6e-29], t$95$4, If[LessEqual[b, 6.6e+41], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.4e220 or 6.6000000000000001e41 < b

   1. Initial program 66.0%

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

   3. Taylor expanded in i around 0 56.8%

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

   4. Taylor expanded in z around inf 53.9%

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

   5. Taylor expanded in b around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*l* 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-/l* 78.9%

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

   7. Simplified 78.9%

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

   if -1.4e220 < b < -2.90000000000000011e203 or -2.5999999999999998e-37 < b < 6.80000000000000026e-102

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 77.8%

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

   if -2.90000000000000011e203 < b < -4.1e185

   1. Initial program 49.7%

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

   3. Taylor expanded in c around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -4.1e185 < b < -2.5999999999999998e-37 or 6.80000000000000026e-102 < b < 1.6e-29

   1. Initial program 79.2%

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

   3. Taylor expanded in y around 0 77.4%

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

   5. Simplified 78.9%

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

   if 1.6e-29 < b < 6.6000000000000001e41

   1. Initial program 69.0%

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

   3. Taylor expanded in b around 0 69.5%

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

   4. Taylor expanded in a around 0 77.3%

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

      1. associate-*r* 77.3%

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

      2. neg-mul-1 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+220}:\\ \;\;\;\;\left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -7.1 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -5.5e-51)
     t_2
     (if (<= c -7.1e-261)
       t_1
       (if (<= c 4.7e-284)
         (* y (* x z))
         (if (<= c 1.5e-128)
           t_1
           (if (<= c 7.5e-41)
             (* x (* t (- a)))
             (if (<= c 7.8e-19)
               (* x (* y z))
               (if (<= c 1.22e+54) (* b (- (* t i) (* z c))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.5e-51) {
		tmp = t_2;
	} else if (c <= -7.1e-261) {
		tmp = t_1;
	} else if (c <= 4.7e-284) {
		tmp = y * (x * z);
	} else if (c <= 1.5e-128) {
		tmp = t_1;
	} else if (c <= 7.5e-41) {
		tmp = x * (t * -a);
	} else if (c <= 7.8e-19) {
		tmp = x * (y * z);
	} else if (c <= 1.22e+54) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-5.5d-51)) then
        tmp = t_2
    else if (c <= (-7.1d-261)) then
        tmp = t_1
    else if (c <= 4.7d-284) then
        tmp = y * (x * z)
    else if (c <= 1.5d-128) then
        tmp = t_1
    else if (c <= 7.5d-41) then
        tmp = x * (t * -a)
    else if (c <= 7.8d-19) then
        tmp = x * (y * z)
    else if (c <= 1.22d+54) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.5e-51) {
		tmp = t_2;
	} else if (c <= -7.1e-261) {
		tmp = t_1;
	} else if (c <= 4.7e-284) {
		tmp = y * (x * z);
	} else if (c <= 1.5e-128) {
		tmp = t_1;
	} else if (c <= 7.5e-41) {
		tmp = x * (t * -a);
	} else if (c <= 7.8e-19) {
		tmp = x * (y * z);
	} else if (c <= 1.22e+54) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -5.5e-51:
		tmp = t_2
	elif c <= -7.1e-261:
		tmp = t_1
	elif c <= 4.7e-284:
		tmp = y * (x * z)
	elif c <= 1.5e-128:
		tmp = t_1
	elif c <= 7.5e-41:
		tmp = x * (t * -a)
	elif c <= 7.8e-19:
		tmp = x * (y * z)
	elif c <= 1.22e+54:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5.5e-51)
		tmp = t_2;
	elseif (c <= -7.1e-261)
		tmp = t_1;
	elseif (c <= 4.7e-284)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 1.5e-128)
		tmp = t_1;
	elseif (c <= 7.5e-41)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= 7.8e-19)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1.22e+54)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.5e-51)
		tmp = t_2;
	elseif (c <= -7.1e-261)
		tmp = t_1;
	elseif (c <= 4.7e-284)
		tmp = y * (x * z);
	elseif (c <= 1.5e-128)
		tmp = t_1;
	elseif (c <= 7.5e-41)
		tmp = x * (t * -a);
	elseif (c <= 7.8e-19)
		tmp = x * (y * z);
	elseif (c <= 1.22e+54)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e-51], t$95$2, If[LessEqual[c, -7.1e-261], t$95$1, If[LessEqual[c, 4.7e-284], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e-128], t$95$1, If[LessEqual[c, 7.5e-41], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.8e-19], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.22e+54], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.4999999999999997e-51 or 1.22e54 < c

   1. Initial program 66.5%

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

   3. Taylor expanded in c around inf 69.3%

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

      1. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -5.4999999999999997e-51 < c < -7.10000000000000021e-261 or 4.70000000000000022e-284 < c < 1.49999999999999989e-128

   1. Initial program 80.1%

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

   3. Taylor expanded in i around 0 77.5%

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

   4. Taylor expanded in i around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   if -7.10000000000000021e-261 < c < 4.70000000000000022e-284

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in z around inf 51.1%

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

   if 1.49999999999999989e-128 < c < 7.50000000000000049e-41

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 77.0%

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

   4. Taylor expanded in y around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-lft-neg-out 70.2%

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

      3. *-commutative 70.2%

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

   6. Simplified 70.2%

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

   if 7.50000000000000049e-41 < c < 7.7999999999999999e-19

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 41.2%

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

   4. Taylor expanded in y around inf 61.2%

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

   if 7.7999999999999999e-19 < c < 1.22e54

   1. Initial program 50.4%

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

   3. Taylor expanded in b around inf 50.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.1 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-170}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= c -5.5e-6)
     (* c (- (* a j) (* z b)))
     (if (<= c -7.8e-170)
       (+ (* j (- (* a c) (* y i))) (* x (* y z)))
       (if (<= c -9.5e-229)
         t_1
         (if (<= c 4.8e-174)
           (- (* x (- (* y z) (* t a))) (* i (* y j)))
           (if (<= c 9.5e-129)
             t_1
             (if (<= c 2.8e+16)
               (* x (* a (- (/ (* y z) a) t)))
               (* z (- (* x y) (* b 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 = i * ((t * b) - (y * j));
	double tmp;
	if (c <= -5.5e-6) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -7.8e-170) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (c <= -9.5e-229) {
		tmp = t_1;
	} else if (c <= 4.8e-174) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (c <= 9.5e-129) {
		tmp = t_1;
	} else if (c <= 2.8e+16) {
		tmp = x * (a * (((y * z) / a) - t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (c <= (-5.5d-6)) then
        tmp = c * ((a * j) - (z * b))
    else if (c <= (-7.8d-170)) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else if (c <= (-9.5d-229)) then
        tmp = t_1
    else if (c <= 4.8d-174) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (c <= 9.5d-129) then
        tmp = t_1
    else if (c <= 2.8d+16) then
        tmp = x * (a * (((y * z) / a) - t))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (c <= -5.5e-6) {
		tmp = c * ((a * j) - (z * b));
	} else if (c <= -7.8e-170) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (c <= -9.5e-229) {
		tmp = t_1;
	} else if (c <= 4.8e-174) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (c <= 9.5e-129) {
		tmp = t_1;
	} else if (c <= 2.8e+16) {
		tmp = x * (a * (((y * z) / a) - t));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if c <= -5.5e-6:
		tmp = c * ((a * j) - (z * b))
	elif c <= -7.8e-170:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	elif c <= -9.5e-229:
		tmp = t_1
	elif c <= 4.8e-174:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif c <= 9.5e-129:
		tmp = t_1
	elif c <= 2.8e+16:
		tmp = x * (a * (((y * z) / a) - t))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (c <= -5.5e-6)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (c <= -7.8e-170)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (c <= -9.5e-229)
		tmp = t_1;
	elseif (c <= 4.8e-174)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (c <= 9.5e-129)
		tmp = t_1;
	elseif (c <= 2.8e+16)
		tmp = Float64(x * Float64(a * Float64(Float64(Float64(y * z) / a) - t)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (c <= -5.5e-6)
		tmp = c * ((a * j) - (z * b));
	elseif (c <= -7.8e-170)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	elseif (c <= -9.5e-229)
		tmp = t_1;
	elseif (c <= 4.8e-174)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (c <= 9.5e-129)
		tmp = t_1;
	elseif (c <= 2.8e+16)
		tmp = x * (a * (((y * z) / a) - t));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e-6], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.8e-170], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.5e-229], t$95$1, If[LessEqual[c, 4.8e-174], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-129], t$95$1, If[LessEqual[c, 2.8e+16], N[(x * N[(a * N[(N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.4999999999999999e-6

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 79.0%

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

      1. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -5.4999999999999999e-6 < c < -7.80000000000000042e-170

   1. Initial program 72.4%

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

   3. Taylor expanded in i around 0 72.4%

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

   4. Taylor expanded in y around inf 72.8%

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

   if -7.80000000000000042e-170 < c < -9.4999999999999997e-229 or 4.8e-174 < c < 9.5000000000000006e-129

   1. Initial program 69.6%

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

   3. Taylor expanded in i around 0 63.6%

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

   4. Taylor expanded in i around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

      4. *-commutative 76.3%

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

   6. Simplified 76.3%

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

   if -9.4999999999999997e-229 < c < 4.8e-174

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 79.4%

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

   4. Taylor expanded in a around 0 75.3%

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

      1. associate-*r* 75.3%

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

      2. neg-mul-1 75.3%

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

   6. Simplified 75.3%

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

   if 9.5000000000000006e-129 < c < 2.8e16

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 62.6%

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

   4. Taylor expanded in a around inf 66.6%

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

   if 2.8e16 < c

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. *-commutative 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-170}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-165}:\\ \;\;\;\;\left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (* y z)))))
   (if (<= y -1.7e-67)
     t_1
     (if (<= y -3.8e-165)
       (* (- (* t (/ i z)) c) (* z b))
       (if (<= y -4.2e-204)
         (+ (* x (- (* y z) (* t a))) (* j (* a c)))
         (if (<= y 3.8e-32)
           (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
           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 * ((a * c) - (y * i))) + (x * (y * z));
	double tmp;
	if (y <= -1.7e-67) {
		tmp = t_1;
	} else if (y <= -3.8e-165) {
		tmp = ((t * (i / z)) - c) * (z * b);
	} else if (y <= -4.2e-204) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (y <= 3.8e-32) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
    if (y <= (-1.7d-67)) then
        tmp = t_1
    else if (y <= (-3.8d-165)) then
        tmp = ((t * (i / z)) - c) * (z * b)
    else if (y <= (-4.2d-204)) then
        tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
    else if (y <= 3.8d-32) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double tmp;
	if (y <= -1.7e-67) {
		tmp = t_1;
	} else if (y <= -3.8e-165) {
		tmp = ((t * (i / z)) - c) * (z * b);
	} else if (y <= -4.2e-204) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (y <= 3.8e-32) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
	tmp = 0
	if y <= -1.7e-67:
		tmp = t_1
	elif y <= -3.8e-165:
		tmp = ((t * (i / z)) - c) * (z * b)
	elif y <= -4.2e-204:
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
	elif y <= 3.8e-32:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	tmp = 0.0
	if (y <= -1.7e-67)
		tmp = t_1;
	elseif (y <= -3.8e-165)
		tmp = Float64(Float64(Float64(t * Float64(i / z)) - c) * Float64(z * b));
	elseif (y <= -4.2e-204)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(a * c)));
	elseif (y <= 3.8e-32)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	tmp = 0.0;
	if (y <= -1.7e-67)
		tmp = t_1;
	elseif (y <= -3.8e-165)
		tmp = ((t * (i / z)) - c) * (z * b);
	elseif (y <= -4.2e-204)
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	elseif (y <= 3.8e-32)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	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[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-67], t$95$1, If[LessEqual[y, -3.8e-165], N[(N[(N[(t * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision] * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-204], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-32], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.70000000000000005e-67 or 3.80000000000000008e-32 < y

   1. Initial program 67.2%

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

   3. Taylor expanded in i around 0 66.4%

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

   4. Taylor expanded in y around inf 68.8%

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

   if -1.70000000000000005e-67 < y < -3.80000000000000018e-165

   1. Initial program 69.7%

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

   3. Taylor expanded in i around 0 65.4%

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

   4. Taylor expanded in z around inf 69.4%

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

   5. Taylor expanded in b around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*l* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

   if -3.80000000000000018e-165 < y < -4.20000000000000018e-204

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 83.9%

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

   4. Taylor expanded in a around inf 83.9%

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

   if -4.20000000000000018e-204 < y < 3.80000000000000008e-32

   1. Initial program 82.0%

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

   3. Taylor expanded in y around 0 71.5%

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

   5. Simplified 73.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-165}:\\ \;\;\;\;\left(t \cdot \frac{i}{z} - c\right) \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -4.2e+74)
     t_2
     (if (<= z -6.2e-170)
       (* a (- (* c j) (* x t)))
       (if (<= z 3.7e-252)
         t_1
         (if (<= z 4e-174)
           (+ (* x (- (* y z) (* t a))) (* j (* a c)))
           (if (<= z 1.05e+53) 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 = i * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.2e+74) {
		tmp = t_2;
	} else if (z <= -6.2e-170) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 3.7e-252) {
		tmp = t_1;
	} else if (z <= 4e-174) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (z <= 1.05e+53) {
		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 = i * ((t * b) - (y * j))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-4.2d+74)) then
        tmp = t_2
    else if (z <= (-6.2d-170)) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 3.7d-252) then
        tmp = t_1
    else if (z <= 4d-174) then
        tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
    else if (z <= 1.05d+53) 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 = i * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.2e+74) {
		tmp = t_2;
	} else if (z <= -6.2e-170) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 3.7e-252) {
		tmp = t_1;
	} else if (z <= 4e-174) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} else if (z <= 1.05e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -4.2e+74:
		tmp = t_2
	elif z <= -6.2e-170:
		tmp = a * ((c * j) - (x * t))
	elif z <= 3.7e-252:
		tmp = t_1
	elif z <= 4e-174:
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
	elif z <= 1.05e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -4.2e+74)
		tmp = t_2;
	elseif (z <= -6.2e-170)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 3.7e-252)
		tmp = t_1;
	elseif (z <= 4e-174)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(a * c)));
	elseif (z <= 1.05e+53)
		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 = i * ((t * b) - (y * j));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -4.2e+74)
		tmp = t_2;
	elseif (z <= -6.2e-170)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 3.7e-252)
		tmp = t_1;
	elseif (z <= 4e-174)
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	elseif (z <= 1.05e+53)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+74], t$95$2, If[LessEqual[z, -6.2e-170], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-252], t$95$1, If[LessEqual[z, 4e-174], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+53], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1999999999999998e74 or 1.0500000000000001e53 < z

   1. Initial program 62.7%

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

   3. Taylor expanded in z around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -4.1999999999999998e74 < z < -6.19999999999999971e-170

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -6.19999999999999971e-170 < z < 3.7000000000000001e-252 or 4e-174 < z < 1.0500000000000001e53

   1. Initial program 84.2%

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

   3. Taylor expanded in i around 0 83.0%

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

   4. Taylor expanded in i around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   6. Simplified 63.1%

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

   if 3.7000000000000001e-252 < z < 4e-174

   1. Initial program 81.5%

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

   3. Taylor expanded in b around 0 75.9%

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

   4. Taylor expanded in a around inf 69.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-252}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -3.5e+75)
     t_1
     (if (<= z -2.5e-167)
       (* a (- (* c j) (* x t)))
       (if (<= z 2.4e-243)
         (* i (- (* t b) (* y j)))
         (if (<= z 5.6e+49)
           (+ (* j (- (* a c) (* y i))) (* x (* y z)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.5e+75) {
		tmp = t_1;
	} else if (z <= -2.5e-167) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 2.4e-243) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 5.6e+49) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-3.5d+75)) then
        tmp = t_1
    else if (z <= (-2.5d-167)) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= 2.4d-243) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 5.6d+49) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.5e+75) {
		tmp = t_1;
	} else if (z <= -2.5e-167) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= 2.4e-243) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 5.6e+49) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -3.5e+75:
		tmp = t_1
	elif z <= -2.5e-167:
		tmp = a * ((c * j) - (x * t))
	elif z <= 2.4e-243:
		tmp = i * ((t * b) - (y * j))
	elif z <= 5.6e+49:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -3.5e+75)
		tmp = t_1;
	elseif (z <= -2.5e-167)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= 2.4e-243)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 5.6e+49)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -3.5e+75)
		tmp = t_1;
	elseif (z <= -2.5e-167)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= 2.4e-243)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 5.6e+49)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+75], t$95$1, If[LessEqual[z, -2.5e-167], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-243], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+49], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999998e75 or 5.5999999999999996e49 < z

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -3.4999999999999998e75 < z < -2.5000000000000001e-167

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -2.5000000000000001e-167 < z < 2.4000000000000001e-243

   1. Initial program 83.6%

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

   3. Taylor expanded in i around 0 83.6%

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

   4. Taylor expanded in i around inf 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. unsub-neg 73.2%

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

      4. *-commutative 73.2%

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

   6. Simplified 73.2%

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

   if 2.4000000000000001e-243 < z < 5.5999999999999996e49

   1. Initial program 85.2%

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

   3. Taylor expanded in i around 0 83.5%

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

   4. Taylor expanded in y around inf 55.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-201}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -2.4e+73)
     t_1
     (if (<= z -3.5e-170)
       (* a (- (* c j) (* x t)))
       (if (<= z -1.35e-201)
         (* i (- (* t b) (* y j)))
         (if (<= z 1.7e+42)
           (- (* j (- (* a c) (* y i))) (* 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.4e+73) {
		tmp = t_1;
	} else if (z <= -3.5e-170) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -1.35e-201) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 1.7e+42) {
		tmp = (j * ((a * c) - (y * i))) - (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 = z * ((x * y) - (b * c))
    if (z <= (-2.4d+73)) then
        tmp = t_1
    else if (z <= (-3.5d-170)) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= (-1.35d-201)) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 1.7d+42) then
        tmp = (j * ((a * c) - (y * i))) - (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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.4e+73) {
		tmp = t_1;
	} else if (z <= -3.5e-170) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -1.35e-201) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 1.7e+42) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.4e+73:
		tmp = t_1
	elif z <= -3.5e-170:
		tmp = a * ((c * j) - (x * t))
	elif z <= -1.35e-201:
		tmp = i * ((t * b) - (y * j))
	elif z <= 1.7e+42:
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (z <= -2.4e+73)
		tmp = t_1;
	elseif (z <= -3.5e-170)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= -1.35e-201)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 1.7e+42)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.4e+73)
		tmp = t_1;
	elseif (z <= -3.5e-170)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= -1.35e-201)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 1.7e+42)
		tmp = (j * ((a * c) - (y * i))) - (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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+73], t$95$1, If[LessEqual[z, -3.5e-170], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-201], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+42], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000002e73 or 1.69999999999999988e42 < z

   1. Initial program 62.8%

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

   3. Taylor expanded in z around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -2.40000000000000002e73 < z < -3.49999999999999985e-170

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -3.49999999999999985e-170 < z < -1.35000000000000003e-201

   1. Initial program 87.5%

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

   3. Taylor expanded in i around 0 87.5%

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

   4. Taylor expanded in i around inf 87.6%

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

      1. +-commutative 87.6%

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

      2. mul-1-neg 87.6%

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

      3. unsub-neg 87.6%

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

      4. *-commutative 87.6%

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

   6. Simplified 87.6%

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

   if -1.35000000000000003e-201 < z < 1.69999999999999988e42

   1. Initial program 84.0%

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

   3. Taylor expanded in i around 0 82.8%

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

   4. Taylor expanded in a around inf 63.9%

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

      1. associate-*r* 63.9%

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

      2. neg-mul-1 63.9%

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

      3. *-commutative 63.9%

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

   6. Simplified 63.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-201}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -5.3 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= b -5.3e+185)
     (* b (* z (- c)))
     (if (<= b -2.5e+61)
       (* i (* t b))
       (if (<= b -3.4e-162)
         t_1
         (if (<= b -3.3e-228)
           (* x (* y z))
           (if (<= b 2.15e+43) t_1 (* c (* 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 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -5.3e+185) {
		tmp = b * (z * -c);
	} else if (b <= -2.5e+61) {
		tmp = i * (t * b);
	} else if (b <= -3.4e-162) {
		tmp = t_1;
	} else if (b <= -3.3e-228) {
		tmp = x * (y * z);
	} else if (b <= 2.15e+43) {
		tmp = t_1;
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (b <= (-5.3d+185)) then
        tmp = b * (z * -c)
    else if (b <= (-2.5d+61)) then
        tmp = i * (t * b)
    else if (b <= (-3.4d-162)) then
        tmp = t_1
    else if (b <= (-3.3d-228)) then
        tmp = x * (y * z)
    else if (b <= 2.15d+43) then
        tmp = t_1
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -5.3e+185) {
		tmp = b * (z * -c);
	} else if (b <= -2.5e+61) {
		tmp = i * (t * b);
	} else if (b <= -3.4e-162) {
		tmp = t_1;
	} else if (b <= -3.3e-228) {
		tmp = x * (y * z);
	} else if (b <= 2.15e+43) {
		tmp = t_1;
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -5.3e+185:
		tmp = b * (z * -c)
	elif b <= -2.5e+61:
		tmp = i * (t * b)
	elif b <= -3.4e-162:
		tmp = t_1
	elif b <= -3.3e-228:
		tmp = x * (y * z)
	elif b <= 2.15e+43:
		tmp = t_1
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (b <= -5.3e+185)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (b <= -2.5e+61)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -3.4e-162)
		tmp = t_1;
	elseif (b <= -3.3e-228)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2.15e+43)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -5.3e+185)
		tmp = b * (z * -c);
	elseif (b <= -2.5e+61)
		tmp = i * (t * b);
	elseif (b <= -3.4e-162)
		tmp = t_1;
	elseif (b <= -3.3e-228)
		tmp = x * (y * z);
	elseif (b <= 2.15e+43)
		tmp = t_1;
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.3e+185], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e+61], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-162], t$95$1, If[LessEqual[b, -3.3e-228], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+43], t$95$1, N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.30000000000000007e185

   1. Initial program 66.6%

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

   3. Taylor expanded in i around 0 53.2%

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

   4. Taylor expanded in z around inf 36.9%

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

   5. Taylor expanded in b around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*l* 73.9%

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

      4. *-commutative 73.9%

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

      5. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in t around 0 63.8%

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

      1. associate-*r* 63.8%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. mul-1-neg 63.8%

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

   10. Simplified 63.8%

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

   if -5.30000000000000007e185 < b < -2.50000000000000009e61

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 55.4%

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

      1. distribute-lft-out-- 55.4%

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

      2. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in a around 0 48.0%

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

      1. neg-mul-1 48.0%

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

      2. *-commutative 48.0%

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

      3. distribute-rgt-neg-in 48.0%

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

   8. Simplified 48.0%

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

   9. Taylor expanded in t around 0 51.3%

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

       1. *-commutative 51.3%

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

   11. Simplified 51.3%

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

   12. Taylor expanded in b around 0 51.3%

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

       1. *-commutative 51.3%

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

       2. associate-*r* 51.4%

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

   14. Simplified 51.4%

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

   if -2.50000000000000009e61 < b < -3.4e-162 or -3.30000000000000006e-228 < b < 2.15e43

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   if -3.4e-162 < b < -3.30000000000000006e-228

   1. Initial program 70.0%

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

   3. Taylor expanded in x around inf 51.8%

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

   4. Taylor expanded in y around inf 51.1%

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

   if 2.15e43 < b

   1. Initial program 66.5%

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

   3. Taylor expanded in i around 0 62.1%

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

   4. Taylor expanded in z around inf 62.4%

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

   5. Taylor expanded in b around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*l* 71.6%

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

      4. *-commutative 71.6%

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

      5. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in t around 0 50.1%

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

      1. neg-mul-1 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.3 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.75 \cdot 10^{-48}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -7.7 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -1.75e-48)
     t_3
     (if (<= c -7.7e-261)
       t_2
       (if (<= c 8.5e-261)
         t_1
         (if (<= c 1.9e-129) t_2 (if (<= c 1.55e+157) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.75e-48) {
		tmp = t_3;
	} else if (c <= -7.7e-261) {
		tmp = t_2;
	} else if (c <= 8.5e-261) {
		tmp = t_1;
	} else if (c <= 1.9e-129) {
		tmp = t_2;
	} else if (c <= 1.55e+157) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-1.75d-48)) then
        tmp = t_3
    else if (c <= (-7.7d-261)) then
        tmp = t_2
    else if (c <= 8.5d-261) then
        tmp = t_1
    else if (c <= 1.9d-129) then
        tmp = t_2
    else if (c <= 1.55d+157) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.75e-48) {
		tmp = t_3;
	} else if (c <= -7.7e-261) {
		tmp = t_2;
	} else if (c <= 8.5e-261) {
		tmp = t_1;
	} else if (c <= 1.9e-129) {
		tmp = t_2;
	} else if (c <= 1.55e+157) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.75e-48:
		tmp = t_3
	elif c <= -7.7e-261:
		tmp = t_2
	elif c <= 8.5e-261:
		tmp = t_1
	elif c <= 1.9e-129:
		tmp = t_2
	elif c <= 1.55e+157:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.75e-48)
		tmp = t_3;
	elseif (c <= -7.7e-261)
		tmp = t_2;
	elseif (c <= 8.5e-261)
		tmp = t_1;
	elseif (c <= 1.9e-129)
		tmp = t_2;
	elseif (c <= 1.55e+157)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.75e-48)
		tmp = t_3;
	elseif (c <= -7.7e-261)
		tmp = t_2;
	elseif (c <= 8.5e-261)
		tmp = t_1;
	elseif (c <= 1.9e-129)
		tmp = t_2;
	elseif (c <= 1.55e+157)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.75e-48], t$95$3, If[LessEqual[c, -7.7e-261], t$95$2, If[LessEqual[c, 8.5e-261], t$95$1, If[LessEqual[c, 1.9e-129], t$95$2, If[LessEqual[c, 1.55e+157], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.74999999999999996e-48 or 1.5499999999999999e157 < c

   1. Initial program 64.5%

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

   3. Taylor expanded in c around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -1.74999999999999996e-48 < c < -7.6999999999999997e-261 or 8.4999999999999996e-261 < c < 1.89999999999999992e-129

   1. Initial program 78.7%

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

   3. Taylor expanded in i around 0 75.8%

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

   4. Taylor expanded in i around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   6. Simplified 62.6%

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

   if -7.6999999999999997e-261 < c < 8.4999999999999996e-261 or 1.89999999999999992e-129 < c < 1.5499999999999999e157

   1. Initial program 79.5%

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

   3. Taylor expanded in x around inf 60.7%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.75 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.7 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -9e+74)
     t_3
     (if (<= z -1.5e-167)
       t_2
       (if (<= z 1.8e-250)
         t_1
         (if (<= z 4e-171) t_2 (if (<= z 1.02e+51) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9e+74) {
		tmp = t_3;
	} else if (z <= -1.5e-167) {
		tmp = t_2;
	} else if (z <= 1.8e-250) {
		tmp = t_1;
	} else if (z <= 4e-171) {
		tmp = t_2;
	} else if (z <= 1.02e+51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-9d+74)) then
        tmp = t_3
    else if (z <= (-1.5d-167)) then
        tmp = t_2
    else if (z <= 1.8d-250) then
        tmp = t_1
    else if (z <= 4d-171) then
        tmp = t_2
    else if (z <= 1.02d+51) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9e+74) {
		tmp = t_3;
	} else if (z <= -1.5e-167) {
		tmp = t_2;
	} else if (z <= 1.8e-250) {
		tmp = t_1;
	} else if (z <= 4e-171) {
		tmp = t_2;
	} else if (z <= 1.02e+51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -9e+74:
		tmp = t_3
	elif z <= -1.5e-167:
		tmp = t_2
	elif z <= 1.8e-250:
		tmp = t_1
	elif z <= 4e-171:
		tmp = t_2
	elif z <= 1.02e+51:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -9e+74)
		tmp = t_3;
	elseif (z <= -1.5e-167)
		tmp = t_2;
	elseif (z <= 1.8e-250)
		tmp = t_1;
	elseif (z <= 4e-171)
		tmp = t_2;
	elseif (z <= 1.02e+51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -9e+74)
		tmp = t_3;
	elseif (z <= -1.5e-167)
		tmp = t_2;
	elseif (z <= 1.8e-250)
		tmp = t_1;
	elseif (z <= 4e-171)
		tmp = t_2;
	elseif (z <= 1.02e+51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+74], t$95$3, If[LessEqual[z, -1.5e-167], t$95$2, If[LessEqual[z, 1.8e-250], t$95$1, If[LessEqual[z, 4e-171], t$95$2, If[LessEqual[z, 1.02e+51], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999999e74 or 1.02e51 < z

   1. Initial program 62.7%

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

   3. Taylor expanded in z around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -8.9999999999999999e74 < z < -1.4999999999999999e-167 or 1.79999999999999991e-250 < z < 3.9999999999999999e-171

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if -1.4999999999999999e-167 < z < 1.79999999999999991e-250 or 3.9999999999999999e-171 < z < 1.02e51

   1. Initial program 84.2%

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

   3. Taylor expanded in i around 0 83.0%

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

   4. Taylor expanded in i around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-250}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-171}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))) (t_2 (* y (* x z))))
   (if (<= z -5.1e+73)
     t_2
     (if (<= z -5.5e-169)
       (* c (* a j))
       (if (<= z 2.7e-306)
         t_1
         (if (<= z 1.4e-73) (* t (* b i)) (if (<= z 3.5e+76) 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 = y * (i * -j);
	double t_2 = y * (x * z);
	double tmp;
	if (z <= -5.1e+73) {
		tmp = t_2;
	} else if (z <= -5.5e-169) {
		tmp = c * (a * j);
	} else if (z <= 2.7e-306) {
		tmp = t_1;
	} else if (z <= 1.4e-73) {
		tmp = t * (b * i);
	} else if (z <= 3.5e+76) {
		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 = y * (i * -j)
    t_2 = y * (x * z)
    if (z <= (-5.1d+73)) then
        tmp = t_2
    else if (z <= (-5.5d-169)) then
        tmp = c * (a * j)
    else if (z <= 2.7d-306) then
        tmp = t_1
    else if (z <= 1.4d-73) then
        tmp = t * (b * i)
    else if (z <= 3.5d+76) 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 = y * (i * -j);
	double t_2 = y * (x * z);
	double tmp;
	if (z <= -5.1e+73) {
		tmp = t_2;
	} else if (z <= -5.5e-169) {
		tmp = c * (a * j);
	} else if (z <= 2.7e-306) {
		tmp = t_1;
	} else if (z <= 1.4e-73) {
		tmp = t * (b * i);
	} else if (z <= 3.5e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = y * (x * z)
	tmp = 0
	if z <= -5.1e+73:
		tmp = t_2
	elif z <= -5.5e-169:
		tmp = c * (a * j)
	elif z <= 2.7e-306:
		tmp = t_1
	elif z <= 1.4e-73:
		tmp = t * (b * i)
	elif z <= 3.5e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -5.1e+73)
		tmp = t_2;
	elseif (z <= -5.5e-169)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 2.7e-306)
		tmp = t_1;
	elseif (z <= 1.4e-73)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 3.5e+76)
		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 = y * (i * -j);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (z <= -5.1e+73)
		tmp = t_2;
	elseif (z <= -5.5e-169)
		tmp = c * (a * j);
	elseif (z <= 2.7e-306)
		tmp = t_1;
	elseif (z <= 1.4e-73)
		tmp = t * (b * i);
	elseif (z <= 3.5e+76)
		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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+73], t$95$2, If[LessEqual[z, -5.5e-169], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-306], t$95$1, If[LessEqual[z, 1.4e-73], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+76], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.10000000000000024e73 or 3.5e76 < z

   1. Initial program 63.1%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

      4. *-commutative 46.2%

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

      5. *-commutative 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in z around inf 41.8%

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

   if -5.10000000000000024e73 < z < -5.4999999999999994e-169

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in j around inf 39.4%

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

      1. *-commutative 39.4%

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

   8. Simplified 39.4%

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

   9. Taylor expanded in a around 0 39.4%

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

       1. associate-*r* 40.9%

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

       2. *-commutative 40.9%

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

       3. associate-*l* 43.1%

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

   11. Simplified 43.1%

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

   if -5.4999999999999994e-169 < z < 2.70000000000000009e-306 or 1.40000000000000006e-73 < z < 3.5e76

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

      5. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in z around 0 45.9%

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

      1. neg-mul-1 45.9%

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

      2. distribute-lft-neg-in 45.9%

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

   8. Simplified 45.9%

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

   if 2.70000000000000009e-306 < z < 1.40000000000000006e-73

   1. Initial program 77.3%

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

   3. Taylor expanded in t around inf 50.2%

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

      1. distribute-lft-out-- 50.2%

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

      2. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in a around 0 29.5%

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

      1. neg-mul-1 29.5%

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

      2. *-commutative 29.5%

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

      3. distribute-rgt-neg-in 29.5%

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

   8. Simplified 29.5%

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

   9. Taylor expanded in t around 0 24.8%

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

       1. *-commutative 24.8%

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

       2. associate-*r* 24.5%

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

       3. *-commutative 24.5%

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

       4. associate-*r* 29.5%

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

   11. Simplified 29.5%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* b (* z (- c)))))
   (if (<= z -2.35e+180)
     t_2
     (if (<= z -3.3e+140)
       t_1
       (if (<= z -4.9e+38)
         t_2
         (if (<= z -4e-169)
           (* c (* a j))
           (if (<= z 7e+78) (* y (* i (- j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = b * (z * -c);
	double tmp;
	if (z <= -2.35e+180) {
		tmp = t_2;
	} else if (z <= -3.3e+140) {
		tmp = t_1;
	} else if (z <= -4.9e+38) {
		tmp = t_2;
	} else if (z <= -4e-169) {
		tmp = c * (a * j);
	} else if (z <= 7e+78) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = b * (z * -c)
    if (z <= (-2.35d+180)) then
        tmp = t_2
    else if (z <= (-3.3d+140)) then
        tmp = t_1
    else if (z <= (-4.9d+38)) then
        tmp = t_2
    else if (z <= (-4d-169)) then
        tmp = c * (a * j)
    else if (z <= 7d+78) then
        tmp = y * (i * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = b * (z * -c);
	double tmp;
	if (z <= -2.35e+180) {
		tmp = t_2;
	} else if (z <= -3.3e+140) {
		tmp = t_1;
	} else if (z <= -4.9e+38) {
		tmp = t_2;
	} else if (z <= -4e-169) {
		tmp = c * (a * j);
	} else if (z <= 7e+78) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = b * (z * -c)
	tmp = 0
	if z <= -2.35e+180:
		tmp = t_2
	elif z <= -3.3e+140:
		tmp = t_1
	elif z <= -4.9e+38:
		tmp = t_2
	elif z <= -4e-169:
		tmp = c * (a * j)
	elif z <= 7e+78:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (z <= -2.35e+180)
		tmp = t_2;
	elseif (z <= -3.3e+140)
		tmp = t_1;
	elseif (z <= -4.9e+38)
		tmp = t_2;
	elseif (z <= -4e-169)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 7e+78)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = b * (z * -c);
	tmp = 0.0;
	if (z <= -2.35e+180)
		tmp = t_2;
	elseif (z <= -3.3e+140)
		tmp = t_1;
	elseif (z <= -4.9e+38)
		tmp = t_2;
	elseif (z <= -4e-169)
		tmp = c * (a * j);
	elseif (z <= 7e+78)
		tmp = y * (i * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+180], t$95$2, If[LessEqual[z, -3.3e+140], t$95$1, If[LessEqual[z, -4.9e+38], t$95$2, If[LessEqual[z, -4e-169], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+78], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.34999999999999986e180 or -3.3000000000000002e140 < z < -4.90000000000000002e38

   1. Initial program 64.5%

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

   3. Taylor expanded in i around 0 60.9%

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

   4. Taylor expanded in z around inf 75.1%

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

   5. Taylor expanded in b around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*l* 63.4%

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

      4. *-commutative 63.4%

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

      5. associate-/l* 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in t around 0 50.5%

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

      1. associate-*r* 50.5%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. mul-1-neg 50.5%

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

   10. Simplified 50.5%

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

   if -2.34999999999999986e180 < z < -3.3000000000000002e140 or 7.0000000000000003e78 < z

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in z around inf 50.4%

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

   if -4.90000000000000002e38 < z < -4.00000000000000008e-169

   1. Initial program 74.4%

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

   3. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in a around 0 42.9%

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

       1. associate-*r* 44.7%

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

       2. *-commutative 44.7%

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

       3. associate-*l* 47.3%

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

   11. Simplified 47.3%

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

   if -4.00000000000000008e-169 < z < 7.0000000000000003e78

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. +-commutative 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

      4. *-commutative 42.1%

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

      5. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in z around 0 35.2%

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

      1. neg-mul-1 35.2%

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

      2. distribute-lft-neg-in 35.2%

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

   8. Simplified 35.2%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= z -4.6e+181)
     (* c (* z (- b)))
     (if (<= z -5.4e+140)
       t_1
       (if (<= z -5.4e+37)
         (* b (* z (- c)))
         (if (<= z -7.2e-167)
           (* c (* a j))
           (if (<= z 2.4e+84) (* y (* i (- j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -4.6e+181) {
		tmp = c * (z * -b);
	} else if (z <= -5.4e+140) {
		tmp = t_1;
	} else if (z <= -5.4e+37) {
		tmp = b * (z * -c);
	} else if (z <= -7.2e-167) {
		tmp = c * (a * j);
	} else if (z <= 2.4e+84) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (z <= (-4.6d+181)) then
        tmp = c * (z * -b)
    else if (z <= (-5.4d+140)) then
        tmp = t_1
    else if (z <= (-5.4d+37)) then
        tmp = b * (z * -c)
    else if (z <= (-7.2d-167)) then
        tmp = c * (a * j)
    else if (z <= 2.4d+84) then
        tmp = y * (i * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -4.6e+181) {
		tmp = c * (z * -b);
	} else if (z <= -5.4e+140) {
		tmp = t_1;
	} else if (z <= -5.4e+37) {
		tmp = b * (z * -c);
	} else if (z <= -7.2e-167) {
		tmp = c * (a * j);
	} else if (z <= 2.4e+84) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if z <= -4.6e+181:
		tmp = c * (z * -b)
	elif z <= -5.4e+140:
		tmp = t_1
	elif z <= -5.4e+37:
		tmp = b * (z * -c)
	elif z <= -7.2e-167:
		tmp = c * (a * j)
	elif z <= 2.4e+84:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -4.6e+181)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= -5.4e+140)
		tmp = t_1;
	elseif (z <= -5.4e+37)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= -7.2e-167)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 2.4e+84)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (z <= -4.6e+181)
		tmp = c * (z * -b);
	elseif (z <= -5.4e+140)
		tmp = t_1;
	elseif (z <= -5.4e+37)
		tmp = b * (z * -c);
	elseif (z <= -7.2e-167)
		tmp = c * (a * j);
	elseif (z <= 2.4e+84)
		tmp = y * (i * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+181], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.4e+140], t$95$1, If[LessEqual[z, -5.4e+37], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-167], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+84], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5999999999999998e181

   1. Initial program 50.4%

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

   3. Taylor expanded in i around 0 47.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   5. Taylor expanded in b around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

      3. associate-*l* 66.7%

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

      4. *-commutative 66.7%

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

      5. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in t around 0 57.0%

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

      1. neg-mul-1 57.0%

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

   10. Simplified 57.0%

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

   if -4.5999999999999998e181 < z < -5.40000000000000036e140 or 2.4e84 < z

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in z around inf 50.4%

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

   if -5.40000000000000036e140 < z < -5.39999999999999973e37

   1. Initial program 83.3%

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

   3. Taylor expanded in i around 0 79.1%

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

   4. Taylor expanded in z around inf 83.1%

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

   5. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*l* 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in t around 0 45.9%

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

      1. associate-*r* 45.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. mul-1-neg 45.9%

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

   10. Simplified 45.9%

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

   if -5.39999999999999973e37 < z < -7.2000000000000002e-167

   1. Initial program 74.4%

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

   3. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in a around 0 42.9%

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

       1. associate-*r* 44.7%

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

       2. *-commutative 44.7%

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

       3. associate-*l* 47.3%

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

   11. Simplified 47.3%

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

   if -7.2000000000000002e-167 < z < 2.4e84

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. +-commutative 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

      4. *-commutative 42.1%

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

      5. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in z around 0 35.2%

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

      1. neg-mul-1 35.2%

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

      2. distribute-lft-neg-in 35.2%

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

   8. Simplified 35.2%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= z -1.56e+180)
     (* c (* z (- b)))
     (if (<= z -4.4e+140)
       t_1
       (if (<= z -4.5e+39)
         (* b (* z (- c)))
         (if (<= z -5.4e-167)
           (* c (* a j))
           (if (<= z 2e+84) (* i (* y (- j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -1.56e+180) {
		tmp = c * (z * -b);
	} else if (z <= -4.4e+140) {
		tmp = t_1;
	} else if (z <= -4.5e+39) {
		tmp = b * (z * -c);
	} else if (z <= -5.4e-167) {
		tmp = c * (a * j);
	} else if (z <= 2e+84) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (z <= (-1.56d+180)) then
        tmp = c * (z * -b)
    else if (z <= (-4.4d+140)) then
        tmp = t_1
    else if (z <= (-4.5d+39)) then
        tmp = b * (z * -c)
    else if (z <= (-5.4d-167)) then
        tmp = c * (a * j)
    else if (z <= 2d+84) then
        tmp = i * (y * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -1.56e+180) {
		tmp = c * (z * -b);
	} else if (z <= -4.4e+140) {
		tmp = t_1;
	} else if (z <= -4.5e+39) {
		tmp = b * (z * -c);
	} else if (z <= -5.4e-167) {
		tmp = c * (a * j);
	} else if (z <= 2e+84) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if z <= -1.56e+180:
		tmp = c * (z * -b)
	elif z <= -4.4e+140:
		tmp = t_1
	elif z <= -4.5e+39:
		tmp = b * (z * -c)
	elif z <= -5.4e-167:
		tmp = c * (a * j)
	elif z <= 2e+84:
		tmp = i * (y * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -1.56e+180)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= -4.4e+140)
		tmp = t_1;
	elseif (z <= -4.5e+39)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= -5.4e-167)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 2e+84)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (z <= -1.56e+180)
		tmp = c * (z * -b);
	elseif (z <= -4.4e+140)
		tmp = t_1;
	elseif (z <= -4.5e+39)
		tmp = b * (z * -c);
	elseif (z <= -5.4e-167)
		tmp = c * (a * j);
	elseif (z <= 2e+84)
		tmp = i * (y * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.56e+180], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e+140], t$95$1, If[LessEqual[z, -4.5e+39], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.4e-167], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+84], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.55999999999999989e180

   1. Initial program 50.4%

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

   3. Taylor expanded in i around 0 47.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   5. Taylor expanded in b around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

      3. associate-*l* 66.7%

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

      4. *-commutative 66.7%

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

      5. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in t around 0 57.0%

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

      1. neg-mul-1 57.0%

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

   10. Simplified 57.0%

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

   if -1.55999999999999989e180 < z < -4.3999999999999997e140 or 2.00000000000000012e84 < z

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf 50.4%

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

      1. +-commutative 50.4%

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

      2. mul-1-neg 50.4%

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

      3. unsub-neg 50.4%

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

      4. *-commutative 50.4%

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

      5. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in z around inf 50.4%

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

   if -4.3999999999999997e140 < z < -4.49999999999999996e39

   1. Initial program 83.3%

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

   3. Taylor expanded in i around 0 79.1%

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

   4. Taylor expanded in z around inf 83.1%

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

   5. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*l* 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in t around 0 45.9%

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

      1. associate-*r* 45.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. mul-1-neg 45.9%

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

   10. Simplified 45.9%

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

   if -4.49999999999999996e39 < z < -5.4000000000000001e-167

   1. Initial program 74.4%

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

   3. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in a around 0 42.9%

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

       1. associate-*r* 44.7%

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

       2. *-commutative 44.7%

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

       3. associate-*l* 47.3%

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

   11. Simplified 47.3%

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

   if -5.4000000000000001e-167 < z < 2.00000000000000012e84

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. +-commutative 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

      4. *-commutative 42.1%

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

      5. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in z around 0 38.8%

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

      1. associate-*r* 38.8%

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

      2. neg-mul-1 38.8%

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

   8. Simplified 38.8%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -2.3e-49)
     t_1
     (if (<= c 9.5e-284)
       (* y (- (* x z) (* i j)))
       (if (<= c 9.5e-129)
         (* i (- (* t b) (* y j)))
         (if (<= c 1.55e+157) (* x (- (* y z) (* t 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.3e-49) {
		tmp = t_1;
	} else if (c <= 9.5e-284) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 9.5e-129) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 1.55e+157) {
		tmp = x * ((y * z) - (t * 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 = c * ((a * j) - (z * b))
    if (c <= (-2.3d-49)) then
        tmp = t_1
    else if (c <= 9.5d-284) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 9.5d-129) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 1.55d+157) then
        tmp = x * ((y * z) - (t * 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.3e-49) {
		tmp = t_1;
	} else if (c <= 9.5e-284) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 9.5e-129) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 1.55e+157) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.3e-49:
		tmp = t_1
	elif c <= 9.5e-284:
		tmp = y * ((x * z) - (i * j))
	elif c <= 9.5e-129:
		tmp = i * ((t * b) - (y * j))
	elif c <= 1.55e+157:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.3e-49)
		tmp = t_1;
	elseif (c <= 9.5e-284)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 9.5e-129)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 1.55e+157)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * 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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.3e-49)
		tmp = t_1;
	elseif (c <= 9.5e-284)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 9.5e-129)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 1.55e+157)
		tmp = x * ((y * z) - (t * 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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.3e-49], t$95$1, If[LessEqual[c, 9.5e-284], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-129], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e+157], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.2999999999999999e-49 or 1.5499999999999999e157 < c

   1. Initial program 64.5%

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

   3. Taylor expanded in c around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -2.2999999999999999e-49 < c < 9.5000000000000003e-284

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

      5. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if 9.5000000000000003e-284 < c < 9.5000000000000006e-129

   1. Initial program 83.9%

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

   3. Taylor expanded in i around 0 80.6%

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

   4. Taylor expanded in i around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. *-commutative 69.0%

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

   6. Simplified 69.0%

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

   if 9.5000000000000006e-129 < c < 1.5499999999999999e157

   1. Initial program 71.2%

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

   3. Taylor expanded in x around inf 56.2%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-87}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -5e+51)
     t_1
     (if (<= b -8e-87)
       (* c (- (* a j) (* z b)))
       (if (<= b 1.65e-70) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5e+51) {
		tmp = t_1;
	} else if (b <= -8e-87) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1.65e-70) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-5d+51)) then
        tmp = t_1
    else if (b <= (-8d-87)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 1.65d-70) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5e+51) {
		tmp = t_1;
	} else if (b <= -8e-87) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1.65e-70) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5e+51:
		tmp = t_1
	elif b <= -8e-87:
		tmp = c * ((a * j) - (z * b))
	elif b <= 1.65e-70:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5e+51)
		tmp = t_1;
	elseif (b <= -8e-87)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 1.65e-70)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5e+51)
		tmp = t_1;
	elseif (b <= -8e-87)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 1.65e-70)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+51], t$95$1, If[LessEqual[b, -8e-87], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-70], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5e51 or 1.65000000000000008e-70 < b

   1. Initial program 70.1%

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

   3. Taylor expanded in b around inf 63.5%

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

   if -5e51 < b < -8.00000000000000014e-87

   1. Initial program 72.0%

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

   3. Taylor expanded in c around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   if -8.00000000000000014e-87 < b < 1.65000000000000008e-70

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 45.2%

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

      1. +-commutative 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unsub-neg 45.2%

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

      4. *-commutative 45.2%

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

   5. Simplified 45.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-87}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= t -2.3e+232)
     t_1
     (if (<= t -1.2e-14)
       (* b (* t i))
       (if (<= t 2.25e-32) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (t <= -2.3e+232) {
		tmp = t_1;
	} else if (t <= -1.2e-14) {
		tmp = b * (t * i);
	} else if (t <= 2.25e-32) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (t <= (-2.3d+232)) then
        tmp = t_1
    else if (t <= (-1.2d-14)) then
        tmp = b * (t * i)
    else if (t <= 2.25d-32) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (t <= -2.3e+232) {
		tmp = t_1;
	} else if (t <= -1.2e-14) {
		tmp = b * (t * i);
	} else if (t <= 2.25e-32) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if t <= -2.3e+232:
		tmp = t_1
	elif t <= -1.2e-14:
		tmp = b * (t * i)
	elif t <= 2.25e-32:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (t <= -2.3e+232)
		tmp = t_1;
	elseif (t <= -1.2e-14)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 2.25e-32)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (t <= -2.3e+232)
		tmp = t_1;
	elseif (t <= -1.2e-14)
		tmp = b * (t * i);
	elseif (t <= 2.25e-32)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+232], t$95$1, If[LessEqual[t, -1.2e-14], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-32], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.30000000000000006e232 or 2.25000000000000002e-32 < t

   1. Initial program 64.6%

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

   3. Taylor expanded in a around inf 43.8%

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

      1. +-commutative 43.8%

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

      2. mul-1-neg 43.8%

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

      3. unsub-neg 43.8%

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

      4. *-commutative 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in j around 0 38.1%

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

      1. neg-mul-1 38.1%

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

      2. distribute-lft-neg-in 38.1%

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

      3. *-commutative 38.1%

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

   8. Simplified 38.1%

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

   if -2.30000000000000006e232 < t < -1.2e-14

   1. Initial program 61.0%

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

   3. Taylor expanded in t around inf 59.8%

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

      1. distribute-lft-out-- 59.8%

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

      2. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in a around 0 42.9%

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

      1. neg-mul-1 42.9%

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

      2. *-commutative 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in t around 0 45.2%

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

       1. *-commutative 45.2%

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

   11. Simplified 45.2%

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

   if -1.2e-14 < t < 2.25000000000000002e-32

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 33.2%

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

   4. Taylor expanded in y around inf 30.8%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+232}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= t -1.1e+232)
     t_1
     (if (<= t -1.5e-13)
       (* b (* t i))
       (if (<= t 3.2e-34) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (t <= -1.1e+232) {
		tmp = t_1;
	} else if (t <= -1.5e-13) {
		tmp = b * (t * i);
	} else if (t <= 3.2e-34) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t * -a)
    if (t <= (-1.1d+232)) then
        tmp = t_1
    else if (t <= (-1.5d-13)) then
        tmp = b * (t * i)
    else if (t <= 3.2d-34) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (t <= -1.1e+232) {
		tmp = t_1;
	} else if (t <= -1.5e-13) {
		tmp = b * (t * i);
	} else if (t <= 3.2e-34) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if t <= -1.1e+232:
		tmp = t_1
	elif t <= -1.5e-13:
		tmp = b * (t * i)
	elif t <= 3.2e-34:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (t <= -1.1e+232)
		tmp = t_1;
	elseif (t <= -1.5e-13)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 3.2e-34)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (t <= -1.1e+232)
		tmp = t_1;
	elseif (t <= -1.5e-13)
		tmp = b * (t * i);
	elseif (t <= 3.2e-34)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+232], t$95$1, If[LessEqual[t, -1.5e-13], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-34], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e232 or 3.20000000000000003e-34 < t

   1. Initial program 64.6%

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

   3. Taylor expanded in x around inf 48.1%

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

   4. Taylor expanded in y around 0 41.4%

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

      1. mul-1-neg 41.4%

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

      2. distribute-lft-neg-out 41.4%

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

      3. *-commutative 41.4%

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

   6. Simplified 41.4%

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

   if -1.1e232 < t < -1.49999999999999992e-13

   1. Initial program 61.0%

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

   3. Taylor expanded in t around inf 59.8%

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

      1. distribute-lft-out-- 59.8%

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

      2. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in a around 0 42.9%

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

      1. neg-mul-1 42.9%

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

      2. *-commutative 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in t around 0 45.2%

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

       1. *-commutative 45.2%

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

   11. Simplified 45.2%

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

   if -1.49999999999999992e-13 < t < 3.20000000000000003e-34

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 33.2%

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

   4. Taylor expanded in y around inf 30.8%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+232}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-80} \lor \neg \left(b \leq 1.65 \cdot 10^{-70}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2e-80) (not (<= b 1.65e-70)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2e-80) || !(b <= 1.65e-70)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2d-80)) .or. (.not. (b <= 1.65d-70))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2e-80) || !(b <= 1.65e-70)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2e-80) or not (b <= 1.65e-70):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2e-80) || !(b <= 1.65e-70))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2e-80) || ~((b <= 1.65e-70)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2e-80], N[Not[LessEqual[b, 1.65e-70]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.99999999999999992e-80 or 1.65000000000000008e-70 < b

   1. Initial program 70.5%

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

   3. Taylor expanded in b around inf 59.0%

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

   if -1.99999999999999992e-80 < b < 1.65000000000000008e-70

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 45.2%

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

      1. +-commutative 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unsub-neg 45.2%

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

      4. *-commutative 45.2%

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

   5. Simplified 45.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-80} \lor \neg \left(b \leq 1.65 \cdot 10^{-70}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+53} \lor \neg \left(t \leq 5.2 \cdot 10^{-68}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -5.8e+53) (not (<= t 5.2e-68))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -5.8e+53) || !(t <= 5.2e-68)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-5.8d+53)) .or. (.not. (t <= 5.2d-68))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -5.8e+53) || !(t <= 5.2e-68)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -5.8e+53) or not (t <= 5.2e-68):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -5.8e+53) || !(t <= 5.2e-68))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -5.8e+53) || ~((t <= 5.2e-68)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -5.8e+53], N[Not[LessEqual[t, 5.2e-68]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8000000000000004e53 or 5.1999999999999996e-68 < t

   1. Initial program 61.6%

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

   3. Taylor expanded in t around inf 56.5%

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

      1. distribute-lft-out-- 56.5%

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

      2. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in a around 0 34.1%

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

      1. neg-mul-1 34.1%

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

      2. *-commutative 34.1%

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

      3. distribute-rgt-neg-in 34.1%

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

   8. Simplified 34.1%

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

   9. Taylor expanded in t around 0 34.1%

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

       1. *-commutative 34.1%

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

   11. Simplified 34.1%

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

   if -5.8000000000000004e53 < t < 5.1999999999999996e-68

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf 30.6%

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

      1. +-commutative 30.6%

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

      2. mul-1-neg 30.6%

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

      3. unsub-neg 30.6%

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

      4. *-commutative 30.6%

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

   5. Simplified 30.6%

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

   6. Taylor expanded in j around inf 26.2%

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

      1. *-commutative 26.2%

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

   8. Simplified 26.2%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+53} \lor \neg \left(t \leq 5.2 \cdot 10^{-68}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 27.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+197} \lor \neg \left(j \leq 1.9 \cdot 10^{-42}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1e+197) (not (<= j 1.9e-42))) (* c (* a j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1e+197) || !(j <= 1.9e-42)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1d+197)) .or. (.not. (j <= 1.9d-42))) then
        tmp = c * (a * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1e+197) || !(j <= 1.9e-42)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1e+197) or not (j <= 1.9e-42):
		tmp = c * (a * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1e+197) || !(j <= 1.9e-42))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1e+197) || ~((j <= 1.9e-42)))
		tmp = c * (a * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1e+197], N[Not[LessEqual[j, 1.9e-42]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9.9999999999999995e196 or 1.90000000000000009e-42 < j

   1. Initial program 67.5%

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

   3. Taylor expanded in a around inf 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

   5. Simplified 42.7%

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

   6. Taylor expanded in j around inf 36.0%

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

      1. *-commutative 36.0%

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

   8. Simplified 36.0%

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

   9. Taylor expanded in a around 0 36.0%

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

       1. associate-*r* 38.1%

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

       2. *-commutative 38.1%

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

       3. associate-*l* 39.2%

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

   11. Simplified 39.2%

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

   if -9.9999999999999995e196 < j < 1.90000000000000009e-42

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 43.3%

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

      1. distribute-lft-out-- 43.3%

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

      2. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in a around 0 25.7%

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

      1. neg-mul-1 25.7%

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

      2. *-commutative 25.7%

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

      3. distribute-rgt-neg-in 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in t around 0 25.1%

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

       1. *-commutative 25.1%

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

   11. Simplified 25.1%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+197} \lor \neg \left(j \leq 1.9 \cdot 10^{-42}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 27.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.08 \cdot 10^{+197} \lor \neg \left(j \leq 4.6 \cdot 10^{-43}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.08e+197) (not (<= j 4.6e-43))) (* c (* a j)) (* t (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.08e+197) || !(j <= 4.6e-43)) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.08d+197)) .or. (.not. (j <= 4.6d-43))) then
        tmp = c * (a * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.08e+197) || !(j <= 4.6e-43)) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.08e+197) or not (j <= 4.6e-43):
		tmp = c * (a * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.08e+197) || !(j <= 4.6e-43))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.08e+197) || ~((j <= 4.6e-43)))
		tmp = c * (a * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.08e+197], N[Not[LessEqual[j, 4.6e-43]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.07999999999999998e197 or 4.5999999999999998e-43 < j

   1. Initial program 67.5%

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

   3. Taylor expanded in a around inf 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

   5. Simplified 42.7%

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

   6. Taylor expanded in j around inf 36.0%

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

      1. *-commutative 36.0%

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

   8. Simplified 36.0%

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

   9. Taylor expanded in a around 0 36.0%

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

       1. associate-*r* 38.1%

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

       2. *-commutative 38.1%

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

       3. associate-*l* 39.2%

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

   11. Simplified 39.2%

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

   if -1.07999999999999998e197 < j < 4.5999999999999998e-43

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 43.3%

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

      1. distribute-lft-out-- 43.3%

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

      2. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in a around 0 25.7%

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

      1. neg-mul-1 25.7%

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

      2. *-commutative 25.7%

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

      3. distribute-rgt-neg-in 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in t around 0 25.1%

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

       1. *-commutative 25.1%

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

       2. associate-*r* 25.1%

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

       3. *-commutative 25.1%

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

       4. associate-*r* 25.7%

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

   11. Simplified 25.7%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.08 \cdot 10^{+197} \lor \neg \left(j \leq 4.6 \cdot 10^{-43}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6e+54)
   (* b (* t i))
   (if (<= t 2.1e-68) (* a (* c j)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6e+54) {
		tmp = b * (t * i);
	} else if (t <= 2.1e-68) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-6d+54)) then
        tmp = b * (t * i)
    else if (t <= 2.1d-68) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6e+54) {
		tmp = b * (t * i);
	} else if (t <= 2.1e-68) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6e+54:
		tmp = b * (t * i)
	elif t <= 2.1e-68:
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6e+54)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 2.1e-68)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -6e+54)
		tmp = b * (t * i);
	elseif (t <= 2.1e-68)
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6e+54], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-68], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.9999999999999998e54

   1. Initial program 57.4%

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

   3. Taylor expanded in t around inf 64.9%

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

      1. distribute-lft-out-- 64.9%

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

      2. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in a around 0 40.1%

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

      1. neg-mul-1 40.1%

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

      2. *-commutative 40.1%

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

      3. distribute-rgt-neg-in 40.1%

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

   8. Simplified 40.1%

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

   9. Taylor expanded in t around 0 40.3%

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

       1. *-commutative 40.3%

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

   11. Simplified 40.3%

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

   if -5.9999999999999998e54 < t < 2.10000000000000008e-68

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf 30.6%

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

      1. +-commutative 30.6%

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

      2. mul-1-neg 30.6%

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

      3. unsub-neg 30.6%

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

      4. *-commutative 30.6%

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

   5. Simplified 30.6%

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

   6. Taylor expanded in j around inf 26.2%

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

      1. *-commutative 26.2%

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

   8. Simplified 26.2%

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

   if 2.10000000000000008e-68 < t

   1. Initial program 64.3%

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

   3. Taylor expanded in t around inf 51.1%

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

      1. distribute-lft-out-- 51.1%

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

      2. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in a around 0 30.3%

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

      1. neg-mul-1 30.3%

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

      2. *-commutative 30.3%

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

      3. distribute-rgt-neg-in 30.3%

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

   8. Simplified 30.3%

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

   9. Taylor expanded in t around 0 30.3%

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

       1. *-commutative 30.3%

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

   11. Simplified 30.3%

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

   12. Taylor expanded in b around 0 30.3%

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

       1. *-commutative 30.3%

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

       2. associate-*r* 31.6%

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

   14. Simplified 31.6%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -8.5e-20)
   (* b (* t i))
   (if (<= t 1.32e-18) (* x (* y z)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8.5e-20) {
		tmp = b * (t * i);
	} else if (t <= 1.32e-18) {
		tmp = x * (y * z);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-8.5d-20)) then
        tmp = b * (t * i)
    else if (t <= 1.32d-18) then
        tmp = x * (y * z)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8.5e-20) {
		tmp = b * (t * i);
	} else if (t <= 1.32e-18) {
		tmp = x * (y * z);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -8.5e-20:
		tmp = b * (t * i)
	elif t <= 1.32e-18:
		tmp = x * (y * z)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -8.5e-20)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 1.32e-18)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -8.5e-20)
		tmp = b * (t * i);
	elseif (t <= 1.32e-18)
		tmp = x * (y * z);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -8.5e-20], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e-18], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5000000000000005e-20

   1. Initial program 63.3%

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

   3. Taylor expanded in t around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around 0 38.3%

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

      1. neg-mul-1 38.3%

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

      2. *-commutative 38.3%

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

      3. distribute-rgt-neg-in 38.3%

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

   8. Simplified 38.3%

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

   9. Taylor expanded in t around 0 38.5%

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

       1. *-commutative 38.5%

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

   11. Simplified 38.5%

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

   if -8.5000000000000005e-20 < t < 1.3199999999999999e-18

   1. Initial program 83.2%

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

   3. Taylor expanded in x around inf 34.2%

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

   4. Taylor expanded in y around inf 31.1%

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

   if 1.3199999999999999e-18 < t

   1. Initial program 62.5%

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

   3. Taylor expanded in t around inf 56.2%

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

      1. distribute-lft-out-- 56.2%

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

      2. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in a around 0 32.5%

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

      1. neg-mul-1 32.5%

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

      2. *-commutative 32.5%

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

      3. distribute-rgt-neg-in 32.5%

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

   8. Simplified 32.5%

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

   9. Taylor expanded in t around 0 32.5%

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

       1. *-commutative 32.5%

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

   11. Simplified 32.5%

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

   12. Taylor expanded in b around 0 32.5%

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

       1. *-commutative 32.5%

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

       2. associate-*r* 34.0%

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

   14. Simplified 34.0%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 23.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 34.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 34.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 34.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 34.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 34.3%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 34.3%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 18.9%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-commutative 18.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Simplified 18.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

9. Final simplification 18.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 60.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024066 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))