Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.0% → 82.0%

Time: 23.0s

Alternatives: 24

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.0% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* a (* b (- i (/ (* x t) 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * (b * (i - ((x * t) / 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (b * (i - ((x * t) / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (b * (i - ((x * t) / 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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * Float64(i - Float64(Float64(x * t) / 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (b * (i - ((x * t) / 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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(b * N[(i - N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 10.7%

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

      1. fma-define 19.8%

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

      2. associate-/l* 23.4%

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

      3. associate-/l* 23.4%

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

      4. *-commutative 23.4%

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

   5. Simplified 23.4%

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

   6. Taylor expanded in a around inf 54.5%

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

4. Final simplification 83.6%

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

Alternative 2: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+246}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{+76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-34}:\\ \;\;\;\;t\_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+237}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -1.05e+246)
     t_3
     (if (<= a -7.2e+164)
       (* x (* z (- y (* a (/ t z)))))
       (if (<= a -1.06e+76)
         t_3
         (if (<= a -1.55e-90)
           t_2
           (if (<= a -7.8e-305)
             (* c (- (* t j) (* z b)))
             (if (<= a 3.5e-34)
               (- t_1 (* c (* z b)))
               (if (<= a 2.5e+237) t_2 (* a (* b (- i (/ (* x t) b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.05e+246) {
		tmp = t_3;
	} else if (a <= -7.2e+164) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -1.06e+76) {
		tmp = t_3;
	} else if (a <= -1.55e-90) {
		tmp = t_2;
	} else if (a <= -7.8e-305) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 3.5e-34) {
		tmp = t_1 - (c * (z * b));
	} else if (a <= 2.5e+237) {
		tmp = t_2;
	} else {
		tmp = a * (b * (i - ((x * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-1.05d+246)) then
        tmp = t_3
    else if (a <= (-7.2d+164)) then
        tmp = x * (z * (y - (a * (t / z))))
    else if (a <= (-1.06d+76)) then
        tmp = t_3
    else if (a <= (-1.55d-90)) then
        tmp = t_2
    else if (a <= (-7.8d-305)) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 3.5d-34) then
        tmp = t_1 - (c * (z * b))
    else if (a <= 2.5d+237) then
        tmp = t_2
    else
        tmp = a * (b * (i - ((x * 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 t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.05e+246) {
		tmp = t_3;
	} else if (a <= -7.2e+164) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -1.06e+76) {
		tmp = t_3;
	} else if (a <= -1.55e-90) {
		tmp = t_2;
	} else if (a <= -7.8e-305) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 3.5e-34) {
		tmp = t_1 - (c * (z * b));
	} else if (a <= 2.5e+237) {
		tmp = t_2;
	} else {
		tmp = a * (b * (i - ((x * t) / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = (x * ((y * z) - (t * a))) + t_1
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.05e+246:
		tmp = t_3
	elif a <= -7.2e+164:
		tmp = x * (z * (y - (a * (t / z))))
	elif a <= -1.06e+76:
		tmp = t_3
	elif a <= -1.55e-90:
		tmp = t_2
	elif a <= -7.8e-305:
		tmp = c * ((t * j) - (z * b))
	elif a <= 3.5e-34:
		tmp = t_1 - (c * (z * b))
	elif a <= 2.5e+237:
		tmp = t_2
	else:
		tmp = a * (b * (i - ((x * t) / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.05e+246)
		tmp = t_3;
	elseif (a <= -7.2e+164)
		tmp = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))));
	elseif (a <= -1.06e+76)
		tmp = t_3;
	elseif (a <= -1.55e-90)
		tmp = t_2;
	elseif (a <= -7.8e-305)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 3.5e-34)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (a <= 2.5e+237)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(b * Float64(i - Float64(Float64(x * t) / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = (x * ((y * z) - (t * a))) + t_1;
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.05e+246)
		tmp = t_3;
	elseif (a <= -7.2e+164)
		tmp = x * (z * (y - (a * (t / z))));
	elseif (a <= -1.06e+76)
		tmp = t_3;
	elseif (a <= -1.55e-90)
		tmp = t_2;
	elseif (a <= -7.8e-305)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 3.5e-34)
		tmp = t_1 - (c * (z * b));
	elseif (a <= 2.5e+237)
		tmp = t_2;
	else
		tmp = a * (b * (i - ((x * t) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+246], t$95$3, If[LessEqual[a, -7.2e+164], N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.06e+76], t$95$3, If[LessEqual[a, -1.55e-90], t$95$2, If[LessEqual[a, -7.8e-305], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-34], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+237], t$95$2, N[(a * N[(b * N[(i - N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.05e246 or -7.19999999999999981e164 < a < -1.06e76

   1. Initial program 46.1%

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

   3. Taylor expanded in a around -inf 76.3%

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

   if -1.05e246 < a < -7.19999999999999981e164

   1. Initial program 61.0%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 89.3%

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

   8. Simplified 89.3%

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

   if -1.06e76 < a < -1.5500000000000001e-90 or 3.5e-34 < a < 2.5000000000000001e237

   1. Initial program 82.8%

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

   3. Taylor expanded in b around 0 80.3%

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

   if -1.5500000000000001e-90 < a < -7.8000000000000005e-305

   1. Initial program 67.1%

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

   3. Taylor expanded in c around inf 78.1%

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

   if -7.8000000000000005e-305 < a < 3.5e-34

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0 76.2%

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

      1. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in c around inf 72.5%

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

      1. associate-*r* 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 72.4%

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

   8. Simplified 72.4%

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

   if 2.5000000000000001e237 < a

   1. Initial program 56.6%

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

   3. Taylor expanded in b around inf 56.4%

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

      1. fma-define 56.8%

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

      2. associate-/l* 56.8%

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

      3. associate-/l* 52.8%

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

      4. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in a around inf 73.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(i + -1 \cdot \frac{t \cdot x}{b}\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+246}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.1 \cdot 10^{+245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-35}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -6.1e+245)
     t_2
     (if (<= a -3.2e+164)
       (* x (* z (- y (* a (/ t z)))))
       (if (<= a -9.5e+48)
         t_2
         (if (<= a 1.12e-35)
           (+ t_1 (* b (- (* a i) (* z c))))
           (if (<= a 2.65e+237)
             (+ (* x (- (* y z) (* t a))) t_1)
             (* a (* b (- i (/ (* x t) b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.1e+245) {
		tmp = t_2;
	} else if (a <= -3.2e+164) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -9.5e+48) {
		tmp = t_2;
	} else if (a <= 1.12e-35) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (a <= 2.65e+237) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = a * (b * (i - ((x * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-6.1d+245)) then
        tmp = t_2
    else if (a <= (-3.2d+164)) then
        tmp = x * (z * (y - (a * (t / z))))
    else if (a <= (-9.5d+48)) then
        tmp = t_2
    else if (a <= 1.12d-35) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else if (a <= 2.65d+237) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = a * (b * (i - ((x * 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 t_1 = j * ((t * c) - (y * i));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.1e+245) {
		tmp = t_2;
	} else if (a <= -3.2e+164) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -9.5e+48) {
		tmp = t_2;
	} else if (a <= 1.12e-35) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (a <= 2.65e+237) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = a * (b * (i - ((x * t) / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -6.1e+245:
		tmp = t_2
	elif a <= -3.2e+164:
		tmp = x * (z * (y - (a * (t / z))))
	elif a <= -9.5e+48:
		tmp = t_2
	elif a <= 1.12e-35:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	elif a <= 2.65e+237:
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = a * (b * (i - ((x * t) / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.1e+245)
		tmp = t_2;
	elseif (a <= -3.2e+164)
		tmp = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))));
	elseif (a <= -9.5e+48)
		tmp = t_2;
	elseif (a <= 1.12e-35)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (a <= 2.65e+237)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(a * Float64(b * Float64(i - Float64(Float64(x * t) / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -6.1e+245)
		tmp = t_2;
	elseif (a <= -3.2e+164)
		tmp = x * (z * (y - (a * (t / z))));
	elseif (a <= -9.5e+48)
		tmp = t_2;
	elseif (a <= 1.12e-35)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	elseif (a <= 2.65e+237)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = a * (b * (i - ((x * t) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.1e+245], t$95$2, If[LessEqual[a, -3.2e+164], N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e+48], t$95$2, If[LessEqual[a, 1.12e-35], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e+237], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a * N[(b * N[(i - N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.0999999999999999e245 or -3.1999999999999998e164 < a < -9.4999999999999997e48

   1. Initial program 52.5%

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

   3. Taylor expanded in a around -inf 74.5%

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

   if -6.0999999999999999e245 < a < -3.1999999999999998e164

   1. Initial program 61.0%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 89.3%

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

   8. Simplified 89.3%

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

   if -9.4999999999999997e48 < a < 1.12e-35

   1. Initial program 78.8%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.12e-35 < a < 2.65000000000000016e237

   1. Initial program 81.6%

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

   3. Taylor expanded in b around 0 83.0%

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

   if 2.65000000000000016e237 < a

   1. Initial program 56.6%

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

   3. Taylor expanded in b around inf 56.4%

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

      1. fma-define 56.8%

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

      2. associate-/l* 56.8%

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

      3. associate-/l* 52.8%

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

      4. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in a around inf 73.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(i + -1 \cdot \frac{t \cdot x}{b}\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{+245}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 27.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* a (* x (- t)))))
   (if (<= a -1.02e+197)
     t_2
     (if (<= a -2.4e+14)
       (* b (* a i))
       (if (<= a 4.8e-302)
         (* t (* c j))
         (if (<= a 1.7e-187)
           (* z (* c (- b)))
           (if (<= a 8.6e-100)
             t_1
             (if (<= a 4.4e-60)
               (* t (* x (- a)))
               (if (<= a 1.3e+211) 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 * (y * -j);
	double t_2 = a * (x * -t);
	double tmp;
	if (a <= -1.02e+197) {
		tmp = t_2;
	} else if (a <= -2.4e+14) {
		tmp = b * (a * i);
	} else if (a <= 4.8e-302) {
		tmp = t * (c * j);
	} else if (a <= 1.7e-187) {
		tmp = z * (c * -b);
	} else if (a <= 8.6e-100) {
		tmp = t_1;
	} else if (a <= 4.4e-60) {
		tmp = t * (x * -a);
	} else if (a <= 1.3e+211) {
		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 * (y * -j)
    t_2 = a * (x * -t)
    if (a <= (-1.02d+197)) then
        tmp = t_2
    else if (a <= (-2.4d+14)) then
        tmp = b * (a * i)
    else if (a <= 4.8d-302) then
        tmp = t * (c * j)
    else if (a <= 1.7d-187) then
        tmp = z * (c * -b)
    else if (a <= 8.6d-100) then
        tmp = t_1
    else if (a <= 4.4d-60) then
        tmp = t * (x * -a)
    else if (a <= 1.3d+211) 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 * (y * -j);
	double t_2 = a * (x * -t);
	double tmp;
	if (a <= -1.02e+197) {
		tmp = t_2;
	} else if (a <= -2.4e+14) {
		tmp = b * (a * i);
	} else if (a <= 4.8e-302) {
		tmp = t * (c * j);
	} else if (a <= 1.7e-187) {
		tmp = z * (c * -b);
	} else if (a <= 8.6e-100) {
		tmp = t_1;
	} else if (a <= 4.4e-60) {
		tmp = t * (x * -a);
	} else if (a <= 1.3e+211) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = a * (x * -t)
	tmp = 0
	if a <= -1.02e+197:
		tmp = t_2
	elif a <= -2.4e+14:
		tmp = b * (a * i)
	elif a <= 4.8e-302:
		tmp = t * (c * j)
	elif a <= 1.7e-187:
		tmp = z * (c * -b)
	elif a <= 8.6e-100:
		tmp = t_1
	elif a <= 4.4e-60:
		tmp = t * (x * -a)
	elif a <= 1.3e+211:
		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(y * Float64(-j)))
	t_2 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (a <= -1.02e+197)
		tmp = t_2;
	elseif (a <= -2.4e+14)
		tmp = Float64(b * Float64(a * i));
	elseif (a <= 4.8e-302)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 1.7e-187)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (a <= 8.6e-100)
		tmp = t_1;
	elseif (a <= 4.4e-60)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= 1.3e+211)
		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 * (y * -j);
	t_2 = a * (x * -t);
	tmp = 0.0;
	if (a <= -1.02e+197)
		tmp = t_2;
	elseif (a <= -2.4e+14)
		tmp = b * (a * i);
	elseif (a <= 4.8e-302)
		tmp = t * (c * j);
	elseif (a <= 1.7e-187)
		tmp = z * (c * -b);
	elseif (a <= 8.6e-100)
		tmp = t_1;
	elseif (a <= 4.4e-60)
		tmp = t * (x * -a);
	elseif (a <= 1.3e+211)
		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[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.02e+197], t$95$2, If[LessEqual[a, -2.4e+14], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-302], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-187], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e-100], t$95$1, If[LessEqual[a, 4.4e-60], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+211], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.02000000000000008e197 or 1.2999999999999999e211 < a

   1. Initial program 56.1%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-rgt-neg-in 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

   8. Simplified 58.5%

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

   if -1.02000000000000008e197 < a < -2.4e14

   1. Initial program 68.6%

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

   3. Taylor expanded in b around inf 50.9%

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

      1. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in i around inf 50.9%

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

      1. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -2.4e14 < a < 4.80000000000000044e-302

   1. Initial program 72.4%

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

   3. Taylor expanded in i around 0 64.4%

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

   4. Taylor expanded in j around inf 45.4%

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

      1. associate-*r* 47.3%

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

      2. *-commutative 47.3%

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

   6. Simplified 47.3%

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

   if 4.80000000000000044e-302 < a < 1.7000000000000001e-187

   1. Initial program 85.1%

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

   3. Taylor expanded in z around inf 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around 0 61.6%

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

      1. neg-mul-1 61.6%

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

      2. distribute-rgt-neg-in 61.6%

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

   8. Simplified 61.6%

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

   if 1.7000000000000001e-187 < a < 8.59999999999999997e-100 or 4.3999999999999998e-60 < a < 1.2999999999999999e211

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 60.2%

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

      1. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in y around inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   8. Simplified 41.2%

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

   if 8.59999999999999997e-100 < a < 4.3999999999999998e-60

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

      4. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in j around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-lft-neg-out 59.2%

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

      3. *-commutative 59.2%

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

   8. Simplified 59.2%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-100}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4100:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -9.5e+62)
     t_3
     (if (<= j -2.5e+33)
       t_1
       (if (<= j -4100.0)
         (* c (- (* t j) (* z b)))
         (if (<= j -4.5e-249)
           t_2
           (if (<= j 4.6e-217) t_1 (if (<= j 3.5e-53) 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 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -9.5e+62) {
		tmp = t_3;
	} else if (j <= -2.5e+33) {
		tmp = t_1;
	} else if (j <= -4100.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -4.5e-249) {
		tmp = t_2;
	} else if (j <= 4.6e-217) {
		tmp = t_1;
	} else if (j <= 3.5e-53) {
		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 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-9.5d+62)) then
        tmp = t_3
    else if (j <= (-2.5d+33)) then
        tmp = t_1
    else if (j <= (-4100.0d0)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= (-4.5d-249)) then
        tmp = t_2
    else if (j <= 4.6d-217) then
        tmp = t_1
    else if (j <= 3.5d-53) 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 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -9.5e+62) {
		tmp = t_3;
	} else if (j <= -2.5e+33) {
		tmp = t_1;
	} else if (j <= -4100.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -4.5e-249) {
		tmp = t_2;
	} else if (j <= 4.6e-217) {
		tmp = t_1;
	} else if (j <= 3.5e-53) {
		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 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -9.5e+62:
		tmp = t_3
	elif j <= -2.5e+33:
		tmp = t_1
	elif j <= -4100.0:
		tmp = c * ((t * j) - (z * b))
	elif j <= -4.5e-249:
		tmp = t_2
	elif j <= 4.6e-217:
		tmp = t_1
	elif j <= 3.5e-53:
		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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9.5e+62)
		tmp = t_3;
	elseif (j <= -2.5e+33)
		tmp = t_1;
	elseif (j <= -4100.0)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= -4.5e-249)
		tmp = t_2;
	elseif (j <= 4.6e-217)
		tmp = t_1;
	elseif (j <= 3.5e-53)
		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 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -9.5e+62)
		tmp = t_3;
	elseif (j <= -2.5e+33)
		tmp = t_1;
	elseif (j <= -4100.0)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= -4.5e-249)
		tmp = t_2;
	elseif (j <= 4.6e-217)
		tmp = t_1;
	elseif (j <= 3.5e-53)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+62], t$95$3, If[LessEqual[j, -2.5e+33], t$95$1, If[LessEqual[j, -4100.0], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-249], t$95$2, If[LessEqual[j, 4.6e-217], t$95$1, If[LessEqual[j, 3.5e-53], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.5000000000000003e62 or 3.49999999999999993e-53 < j

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 67.6%

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

      1. fma-define 71.5%

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

      2. associate-/l* 73.0%

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

      3. associate-/l* 71.4%

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

      4. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in j around -inf 71.7%

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

   if -9.5000000000000003e62 < j < -2.49999999999999986e33 or -4.49999999999999981e-249 < j < 4.6000000000000001e-217

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf 65.4%

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

      1. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if -2.49999999999999986e33 < j < -4100

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 78.5%

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

   if -4100 < j < -4.49999999999999981e-249 or 4.6000000000000001e-217 < j < 3.49999999999999993e-53

   1. Initial program 63.7%

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

   3. Taylor expanded in b around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -4100:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-249}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -360000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-170}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.6e+197)
   (* a (* x (- t)))
   (if (<= a -360000.0)
     (* b (* a i))
     (if (<= a 4.8e-302)
       (* t (* c j))
       (if (<= a 2.05e-170)
         (* z (* c (- b)))
         (if (<= a 1.35e-28)
           (* c (* t j))
           (if (<= a 1.35e+65) (* x (* y z)) (* x (* t (- a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.6e+197) {
		tmp = a * (x * -t);
	} else if (a <= -360000.0) {
		tmp = b * (a * i);
	} else if (a <= 4.8e-302) {
		tmp = t * (c * j);
	} else if (a <= 2.05e-170) {
		tmp = z * (c * -b);
	} else if (a <= 1.35e-28) {
		tmp = c * (t * j);
	} else if (a <= 1.35e+65) {
		tmp = x * (y * z);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.6d+197)) then
        tmp = a * (x * -t)
    else if (a <= (-360000.0d0)) then
        tmp = b * (a * i)
    else if (a <= 4.8d-302) then
        tmp = t * (c * j)
    else if (a <= 2.05d-170) then
        tmp = z * (c * -b)
    else if (a <= 1.35d-28) then
        tmp = c * (t * j)
    else if (a <= 1.35d+65) then
        tmp = x * (y * z)
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.6e+197) {
		tmp = a * (x * -t);
	} else if (a <= -360000.0) {
		tmp = b * (a * i);
	} else if (a <= 4.8e-302) {
		tmp = t * (c * j);
	} else if (a <= 2.05e-170) {
		tmp = z * (c * -b);
	} else if (a <= 1.35e-28) {
		tmp = c * (t * j);
	} else if (a <= 1.35e+65) {
		tmp = x * (y * z);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.6e+197:
		tmp = a * (x * -t)
	elif a <= -360000.0:
		tmp = b * (a * i)
	elif a <= 4.8e-302:
		tmp = t * (c * j)
	elif a <= 2.05e-170:
		tmp = z * (c * -b)
	elif a <= 1.35e-28:
		tmp = c * (t * j)
	elif a <= 1.35e+65:
		tmp = x * (y * z)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.6e+197)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (a <= -360000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (a <= 4.8e-302)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 2.05e-170)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (a <= 1.35e-28)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 1.35e+65)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.6e+197)
		tmp = a * (x * -t);
	elseif (a <= -360000.0)
		tmp = b * (a * i);
	elseif (a <= 4.8e-302)
		tmp = t * (c * j);
	elseif (a <= 2.05e-170)
		tmp = z * (c * -b);
	elseif (a <= 1.35e-28)
		tmp = c * (t * j);
	elseif (a <= 1.35e+65)
		tmp = x * (y * z);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.6e+197], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -360000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-302], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-170], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-28], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+65], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.59999999999999987e197

   1. Initial program 46.3%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in y around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-rgt-neg-in 54.5%

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

      3. distribute-rgt-neg-in 54.5%

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

   8. Simplified 54.5%

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

   if -2.59999999999999987e197 < a < -3.6e5

   1. Initial program 68.6%

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

   3. Taylor expanded in b around inf 50.9%

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

      1. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in i around inf 50.9%

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

      1. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -3.6e5 < a < 4.80000000000000044e-302

   1. Initial program 72.4%

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

   3. Taylor expanded in i around 0 64.4%

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

   4. Taylor expanded in j around inf 45.4%

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

      1. associate-*r* 47.3%

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

      2. *-commutative 47.3%

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

   6. Simplified 47.3%

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

   if 4.80000000000000044e-302 < a < 2.04999999999999983e-170

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in y around 0 55.8%

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

      1. neg-mul-1 55.8%

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

      2. distribute-rgt-neg-in 55.8%

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

   8. Simplified 55.8%

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

   if 2.04999999999999983e-170 < a < 1.3499999999999999e-28

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 79.0%

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

      1. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in t around inf 35.9%

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

   if 1.3499999999999999e-28 < a < 1.35000000000000009e65

   1. Initial program 80.4%

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

   3. Taylor expanded in x around inf 51.8%

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

      1. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around inf 36.2%

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

   if 1.35000000000000009e65 < a

   1. Initial program 68.9%

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

   3. Taylor expanded in x around inf 52.1%

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

      1. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in y around 0 48.3%

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

      1. neg-mul-1 48.3%

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

      2. *-commutative 48.3%

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

      3. distribute-rgt-neg-in 48.3%

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

   8. Simplified 48.3%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -360000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-170}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -0.0062:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -5e+245)
     t_1
     (if (<= a -6.2e+162)
       (* x (* z (- y (* a (/ t z)))))
       (if (<= a -0.0062)
         t_1
         (if (<= a 1.4e-169)
           (* c (- (* t j) (* z b)))
           (if (<= a 1.3e+211)
             (* j (- (* t c) (* y i)))
             (* a (* b (- i (/ (* x t) 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 * ((b * i) - (x * t));
	double tmp;
	if (a <= -5e+245) {
		tmp = t_1;
	} else if (a <= -6.2e+162) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -0.0062) {
		tmp = t_1;
	} else if (a <= 1.4e-169) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.3e+211) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = a * (b * (i - ((x * 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) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-5d+245)) then
        tmp = t_1
    else if (a <= (-6.2d+162)) then
        tmp = x * (z * (y - (a * (t / z))))
    else if (a <= (-0.0062d0)) then
        tmp = t_1
    else if (a <= 1.4d-169) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 1.3d+211) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = a * (b * (i - ((x * 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 t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -5e+245) {
		tmp = t_1;
	} else if (a <= -6.2e+162) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -0.0062) {
		tmp = t_1;
	} else if (a <= 1.4e-169) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.3e+211) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = a * (b * (i - ((x * t) / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -5e+245:
		tmp = t_1
	elif a <= -6.2e+162:
		tmp = x * (z * (y - (a * (t / z))))
	elif a <= -0.0062:
		tmp = t_1
	elif a <= 1.4e-169:
		tmp = c * ((t * j) - (z * b))
	elif a <= 1.3e+211:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = a * (b * (i - ((x * t) / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5e+245)
		tmp = t_1;
	elseif (a <= -6.2e+162)
		tmp = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))));
	elseif (a <= -0.0062)
		tmp = t_1;
	elseif (a <= 1.4e-169)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 1.3e+211)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(a * Float64(b * Float64(i - Float64(Float64(x * t) / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -5e+245)
		tmp = t_1;
	elseif (a <= -6.2e+162)
		tmp = x * (z * (y - (a * (t / z))));
	elseif (a <= -0.0062)
		tmp = t_1;
	elseif (a <= 1.4e-169)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 1.3e+211)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = a * (b * (i - ((x * t) / 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[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+245], t$95$1, If[LessEqual[a, -6.2e+162], N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.0062], t$95$1, If[LessEqual[a, 1.4e-169], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+211], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(i - N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.00000000000000034e245 or -6.1999999999999999e162 < a < -0.00619999999999999978

   1. Initial program 58.5%

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

   3. Taylor expanded in a around -inf 73.8%

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

   if -5.00000000000000034e245 < a < -6.1999999999999999e162

   1. Initial program 61.0%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 89.3%

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

   8. Simplified 89.3%

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

   if -0.00619999999999999978 < a < 1.39999999999999994e-169

   1. Initial program 74.4%

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

   3. Taylor expanded in c around inf 66.6%

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

   if 1.39999999999999994e-169 < a < 1.2999999999999999e211

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 73.1%

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

      1. fma-define 74.5%

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

      2. associate-/l* 73.2%

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

      3. associate-/l* 73.1%

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

      4. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in j around -inf 56.4%

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

   if 1.2999999999999999e211 < a

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 64.7%

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

      1. fma-define 65.0%

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

      2. associate-/l* 61.8%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in a around inf 78.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(i + -1 \cdot \frac{t \cdot x}{b}\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+245}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -0.0062:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 3.85 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.1e+52)
   (* i (- (* a b) (* y j)))
   (if (<= i -1.6e-115)
     (+ (* j (* t c)) (* b (- (* a i) (* z c))))
     (if (<= i 1.3e-119)
       (+ (* x (- (* y z) (* t a))) (* c (* t j)))
       (if (<= i 3.85e-10)
         (* a (- (* b i) (* x t)))
         (if (<= i 5.5e+161)
           (* t (* x (- (* c (/ j x)) a)))
           (* (* b i) (- a (* j (/ y 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 (i <= -3.1e+52) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= -1.6e-115) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else if (i <= 1.3e-119) {
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j));
	} else if (i <= 3.85e-10) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 5.5e+161) {
		tmp = t * (x * ((c * (j / x)) - a));
	} else {
		tmp = (b * i) * (a - (j * (y / 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 (i <= (-3.1d+52)) then
        tmp = i * ((a * b) - (y * j))
    else if (i <= (-1.6d-115)) then
        tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
    else if (i <= 1.3d-119) then
        tmp = (x * ((y * z) - (t * a))) + (c * (t * j))
    else if (i <= 3.85d-10) then
        tmp = a * ((b * i) - (x * t))
    else if (i <= 5.5d+161) then
        tmp = t * (x * ((c * (j / x)) - a))
    else
        tmp = (b * i) * (a - (j * (y / 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 (i <= -3.1e+52) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= -1.6e-115) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else if (i <= 1.3e-119) {
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j));
	} else if (i <= 3.85e-10) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 5.5e+161) {
		tmp = t * (x * ((c * (j / x)) - a));
	} else {
		tmp = (b * i) * (a - (j * (y / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.1e+52:
		tmp = i * ((a * b) - (y * j))
	elif i <= -1.6e-115:
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
	elif i <= 1.3e-119:
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j))
	elif i <= 3.85e-10:
		tmp = a * ((b * i) - (x * t))
	elif i <= 5.5e+161:
		tmp = t * (x * ((c * (j / x)) - a))
	else:
		tmp = (b * i) * (a - (j * (y / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.1e+52)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (i <= -1.6e-115)
		tmp = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (i <= 1.3e-119)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(t * j)));
	elseif (i <= 3.85e-10)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (i <= 5.5e+161)
		tmp = Float64(t * Float64(x * Float64(Float64(c * Float64(j / x)) - a)));
	else
		tmp = Float64(Float64(b * i) * Float64(a - Float64(j * Float64(y / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.1e+52)
		tmp = i * ((a * b) - (y * j));
	elseif (i <= -1.6e-115)
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	elseif (i <= 1.3e-119)
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j));
	elseif (i <= 3.85e-10)
		tmp = a * ((b * i) - (x * t));
	elseif (i <= 5.5e+161)
		tmp = t * (x * ((c * (j / x)) - a));
	else
		tmp = (b * i) * (a - (j * (y / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.1e+52], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.6e-115], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-119], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.85e-10], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+161], N[(t * N[(x * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * i), $MachinePrecision] * N[(a - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.1e52

   1. Initial program 61.8%

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

   3. Taylor expanded in i around inf 75.9%

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

      1. distribute-lft-out-- 75.9%

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

      2. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -3.1e52 < i < -1.6e-115

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 76.6%

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

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in c around inf 68.0%

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

   if -1.6e-115 < i < 1.30000000000000006e-119

   1. Initial program 78.6%

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

   3. Taylor expanded in i around 0 76.1%

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

   4. Taylor expanded in b around 0 69.1%

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

   if 1.30000000000000006e-119 < i < 3.8500000000000001e-10

   1. Initial program 77.9%

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

   3. Taylor expanded in a around -inf 67.9%

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

   if 3.8500000000000001e-10 < i < 5.5000000000000005e161

   1. Initial program 66.8%

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

   3. Taylor expanded in t around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in x around inf 65.0%

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

      1. associate-/l* 64.9%

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

   8. Simplified 64.9%

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

   if 5.5000000000000005e161 < i

   1. Initial program 54.0%

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

   3. Taylor expanded in b around inf 49.9%

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

      1. fma-define 53.8%

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

      2. associate-/l* 57.6%

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

      3. associate-/l* 53.8%

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

      4. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in i around inf 62.8%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

      3. mul-1-neg 66.3%

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

      4. unsub-neg 66.3%

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

      5. associate-/l* 66.3%

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

   8. Simplified 66.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 3.85 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -4.1e+245)
     t_1
     (if (<= a -4.5e+160)
       (* x (* z (- y (* a (/ t z)))))
       (if (<= a -2.6e+14)
         t_1
         (if (<= a 1.42e+211)
           (- (* j (- (* t c) (* y i))) (* c (* z b)))
           (* a (* b (- i (/ (* x t) 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 * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+245) {
		tmp = t_1;
	} else if (a <= -4.5e+160) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -2.6e+14) {
		tmp = t_1;
	} else if (a <= 1.42e+211) {
		tmp = (j * ((t * c) - (y * i))) - (c * (z * b));
	} else {
		tmp = a * (b * (i - ((x * 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) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-4.1d+245)) then
        tmp = t_1
    else if (a <= (-4.5d+160)) then
        tmp = x * (z * (y - (a * (t / z))))
    else if (a <= (-2.6d+14)) then
        tmp = t_1
    else if (a <= 1.42d+211) then
        tmp = (j * ((t * c) - (y * i))) - (c * (z * b))
    else
        tmp = a * (b * (i - ((x * 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 t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+245) {
		tmp = t_1;
	} else if (a <= -4.5e+160) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -2.6e+14) {
		tmp = t_1;
	} else if (a <= 1.42e+211) {
		tmp = (j * ((t * c) - (y * i))) - (c * (z * b));
	} else {
		tmp = a * (b * (i - ((x * t) / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.1e+245:
		tmp = t_1
	elif a <= -4.5e+160:
		tmp = x * (z * (y - (a * (t / z))))
	elif a <= -2.6e+14:
		tmp = t_1
	elif a <= 1.42e+211:
		tmp = (j * ((t * c) - (y * i))) - (c * (z * b))
	else:
		tmp = a * (b * (i - ((x * t) / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e+245)
		tmp = t_1;
	elseif (a <= -4.5e+160)
		tmp = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))));
	elseif (a <= -2.6e+14)
		tmp = t_1;
	elseif (a <= 1.42e+211)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(c * Float64(z * b)));
	else
		tmp = Float64(a * Float64(b * Float64(i - Float64(Float64(x * t) / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e+245)
		tmp = t_1;
	elseif (a <= -4.5e+160)
		tmp = x * (z * (y - (a * (t / z))));
	elseif (a <= -2.6e+14)
		tmp = t_1;
	elseif (a <= 1.42e+211)
		tmp = (j * ((t * c) - (y * i))) - (c * (z * b));
	else
		tmp = a * (b * (i - ((x * t) / 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[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+245], t$95$1, If[LessEqual[a, -4.5e+160], N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e+14], t$95$1, If[LessEqual[a, 1.42e+211], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(i - N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.10000000000000005e245 or -4.4999999999999998e160 < a < -2.6e14

   1. Initial program 58.5%

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

   3. Taylor expanded in a around -inf 73.8%

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

   if -4.10000000000000005e245 < a < -4.4999999999999998e160

   1. Initial program 61.0%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 89.3%

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

   8. Simplified 89.3%

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

   if -2.6e14 < a < 1.42000000000000005e211

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0 66.8%

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

      1. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in c around inf 63.2%

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

      1. associate-*r* 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-*r* 65.6%

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

   8. Simplified 65.6%

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

   if 1.42000000000000005e211 < a

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 64.7%

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

      1. fma-define 65.0%

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

      2. associate-/l* 61.8%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in a around inf 78.4%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+245}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(i - \frac{x \cdot t}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -8000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -4.1e+245)
     t_1
     (if (<= a -2.9e+165)
       (* x (* z (- y (* a (/ t z)))))
       (if (<= a -8000000000000.0)
         t_1
         (if (<= a 4.4e-169)
           (* c (- (* t j) (* z b)))
           (if (<= a 1.3e+211) (* j (- (* t c) (* y i))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+245) {
		tmp = t_1;
	} else if (a <= -2.9e+165) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -8000000000000.0) {
		tmp = t_1;
	} else if (a <= 4.4e-169) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.3e+211) {
		tmp = j * ((t * c) - (y * i));
	} 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 * ((b * i) - (x * t))
    if (a <= (-4.1d+245)) then
        tmp = t_1
    else if (a <= (-2.9d+165)) then
        tmp = x * (z * (y - (a * (t / z))))
    else if (a <= (-8000000000000.0d0)) then
        tmp = t_1
    else if (a <= 4.4d-169) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 1.3d+211) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+245) {
		tmp = t_1;
	} else if (a <= -2.9e+165) {
		tmp = x * (z * (y - (a * (t / z))));
	} else if (a <= -8000000000000.0) {
		tmp = t_1;
	} else if (a <= 4.4e-169) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.3e+211) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.1e+245:
		tmp = t_1
	elif a <= -2.9e+165:
		tmp = x * (z * (y - (a * (t / z))))
	elif a <= -8000000000000.0:
		tmp = t_1
	elif a <= 4.4e-169:
		tmp = c * ((t * j) - (z * b))
	elif a <= 1.3e+211:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e+245)
		tmp = t_1;
	elseif (a <= -2.9e+165)
		tmp = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))));
	elseif (a <= -8000000000000.0)
		tmp = t_1;
	elseif (a <= 4.4e-169)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 1.3e+211)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e+245)
		tmp = t_1;
	elseif (a <= -2.9e+165)
		tmp = x * (z * (y - (a * (t / z))));
	elseif (a <= -8000000000000.0)
		tmp = t_1;
	elseif (a <= 4.4e-169)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 1.3e+211)
		tmp = j * ((t * c) - (y * i));
	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[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+245], t$95$1, If[LessEqual[a, -2.9e+165], N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8000000000000.0], t$95$1, If[LessEqual[a, 4.4e-169], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+211], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.10000000000000005e245 or -2.90000000000000006e165 < a < -8e12 or 1.2999999999999999e211 < a

   1. Initial program 61.0%

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

   3. Taylor expanded in a around -inf 75.6%

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

   if -4.10000000000000005e245 < a < -2.90000000000000006e165

   1. Initial program 61.0%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 89.3%

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

   8. Simplified 89.3%

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

   if -8e12 < a < 4.40000000000000015e-169

   1. Initial program 74.4%

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

   3. Taylor expanded in c around inf 66.6%

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

   if 4.40000000000000015e-169 < a < 1.2999999999999999e211

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 73.1%

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

      1. fma-define 74.5%

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

      2. associate-/l* 73.2%

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

      3. associate-/l* 73.1%

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

      4. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in j around -inf 56.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+245}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;a \leq -8000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* x (- t)))))
   (if (<= a -2.85e+197)
     t_2
     (if (<= a -1e+14)
       (* b (* a i))
       (if (<= a 8.2e-29)
         t_1
         (if (<= a 2.9e+65) (* x (* y z)) (if (<= a 3.4e+127) 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 = c * (t * j);
	double t_2 = a * (x * -t);
	double tmp;
	if (a <= -2.85e+197) {
		tmp = t_2;
	} else if (a <= -1e+14) {
		tmp = b * (a * i);
	} else if (a <= 8.2e-29) {
		tmp = t_1;
	} else if (a <= 2.9e+65) {
		tmp = x * (y * z);
	} else if (a <= 3.4e+127) {
		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 = c * (t * j)
    t_2 = a * (x * -t)
    if (a <= (-2.85d+197)) then
        tmp = t_2
    else if (a <= (-1d+14)) then
        tmp = b * (a * i)
    else if (a <= 8.2d-29) then
        tmp = t_1
    else if (a <= 2.9d+65) then
        tmp = x * (y * z)
    else if (a <= 3.4d+127) 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 = c * (t * j);
	double t_2 = a * (x * -t);
	double tmp;
	if (a <= -2.85e+197) {
		tmp = t_2;
	} else if (a <= -1e+14) {
		tmp = b * (a * i);
	} else if (a <= 8.2e-29) {
		tmp = t_1;
	} else if (a <= 2.9e+65) {
		tmp = x * (y * z);
	} else if (a <= 3.4e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (x * -t)
	tmp = 0
	if a <= -2.85e+197:
		tmp = t_2
	elif a <= -1e+14:
		tmp = b * (a * i)
	elif a <= 8.2e-29:
		tmp = t_1
	elif a <= 2.9e+65:
		tmp = x * (y * z)
	elif a <= 3.4e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (a <= -2.85e+197)
		tmp = t_2;
	elseif (a <= -1e+14)
		tmp = Float64(b * Float64(a * i));
	elseif (a <= 8.2e-29)
		tmp = t_1;
	elseif (a <= 2.9e+65)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 3.4e+127)
		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 = c * (t * j);
	t_2 = a * (x * -t);
	tmp = 0.0;
	if (a <= -2.85e+197)
		tmp = t_2;
	elseif (a <= -1e+14)
		tmp = b * (a * i);
	elseif (a <= 8.2e-29)
		tmp = t_1;
	elseif (a <= 2.9e+65)
		tmp = x * (y * z);
	elseif (a <= 3.4e+127)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e+197], t$95$2, If[LessEqual[a, -1e+14], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-29], t$95$1, If[LessEqual[a, 2.9e+65], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+127], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.85000000000000011e197 or 3.39999999999999977e127 < a

   1. Initial program 58.3%

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

   3. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-rgt-neg-in 54.7%

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

      3. distribute-rgt-neg-in 54.7%

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

   8. Simplified 54.7%

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

   if -2.85000000000000011e197 < a < -1e14

   1. Initial program 68.6%

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

   3. Taylor expanded in b around inf 50.9%

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

      1. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in i around inf 50.9%

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

      1. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -1e14 < a < 8.1999999999999996e-29 or 2.9e65 < a < 3.39999999999999977e127

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around inf 38.0%

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

   if 8.1999999999999996e-29 < a < 2.9e65

   1. Initial program 80.4%

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

   3. Taylor expanded in x around inf 51.8%

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

      1. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around inf 36.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;j \leq -3:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= j -3.0)
     (* c (* t j))
     (if (<= j -5.3e-226)
       t_1
       (if (<= j 1.26e-213)
         (* x (* t (- a)))
         (if (<= j 2.05e-179)
           t_1
           (if (<= j 5.4e+45) (* a (* x (- t))) (* t (* c j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (j <= -3.0) {
		tmp = c * (t * j);
	} else if (j <= -5.3e-226) {
		tmp = t_1;
	} else if (j <= 1.26e-213) {
		tmp = x * (t * -a);
	} else if (j <= 2.05e-179) {
		tmp = t_1;
	} else if (j <= 5.4e+45) {
		tmp = a * (x * -t);
	} else {
		tmp = t * (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) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (j <= (-3.0d0)) then
        tmp = c * (t * j)
    else if (j <= (-5.3d-226)) then
        tmp = t_1
    else if (j <= 1.26d-213) then
        tmp = x * (t * -a)
    else if (j <= 2.05d-179) then
        tmp = t_1
    else if (j <= 5.4d+45) then
        tmp = a * (x * -t)
    else
        tmp = t * (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 t_1 = a * (b * i);
	double tmp;
	if (j <= -3.0) {
		tmp = c * (t * j);
	} else if (j <= -5.3e-226) {
		tmp = t_1;
	} else if (j <= 1.26e-213) {
		tmp = x * (t * -a);
	} else if (j <= 2.05e-179) {
		tmp = t_1;
	} else if (j <= 5.4e+45) {
		tmp = a * (x * -t);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if j <= -3.0:
		tmp = c * (t * j)
	elif j <= -5.3e-226:
		tmp = t_1
	elif j <= 1.26e-213:
		tmp = x * (t * -a)
	elif j <= 2.05e-179:
		tmp = t_1
	elif j <= 5.4e+45:
		tmp = a * (x * -t)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (j <= -3.0)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= -5.3e-226)
		tmp = t_1;
	elseif (j <= 1.26e-213)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 2.05e-179)
		tmp = t_1;
	elseif (j <= 5.4e+45)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (j <= -3.0)
		tmp = c * (t * j);
	elseif (j <= -5.3e-226)
		tmp = t_1;
	elseif (j <= 1.26e-213)
		tmp = x * (t * -a);
	elseif (j <= 2.05e-179)
		tmp = t_1;
	elseif (j <= 5.4e+45)
		tmp = a * (x * -t);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.3e-226], t$95$1, If[LessEqual[j, 1.26e-213], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.05e-179], t$95$1, If[LessEqual[j, 5.4e+45], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around inf 48.3%

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

   if -3 < j < -5.3000000000000004e-226 or 1.26e-213 < j < 2.05e-179

   1. Initial program 62.2%

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

   3. Taylor expanded in b around inf 59.5%

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

      1. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in i around inf 46.5%

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

   if -5.3000000000000004e-226 < j < 1.26e-213

   1. Initial program 74.9%

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

   3. Taylor expanded in x around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y around 0 40.2%

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

      1. neg-mul-1 40.2%

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

      2. *-commutative 40.2%

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

      3. distribute-rgt-neg-in 40.2%

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

   8. Simplified 40.2%

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

   if 2.05e-179 < j < 5.39999999999999968e45

   1. Initial program 66.8%

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

   3. Taylor expanded in x around inf 48.4%

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

      1. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in y around 0 40.5%

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

      1. mul-1-neg 40.5%

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

      2. distribute-rgt-neg-in 40.5%

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

      3. distribute-rgt-neg-in 40.5%

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

   8. Simplified 40.5%

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

   if 5.39999999999999968e45 < j

   1. Initial program 75.9%

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

   3. Taylor expanded in i around 0 49.2%

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

   4. Taylor expanded in j around inf 36.4%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

   6. Simplified 42.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (* t j))))
   (if (<= j -1e+31)
     t_2
     (if (<= j -1.85e-267)
       t_1
       (if (<= j 8.2e-218)
         (* x (* t (- a)))
         (if (<= j 3.7e-44) t_1 (if (<= j 5.5e+80) t_2 (* i (* y (- j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -1e+31) {
		tmp = t_2;
	} else if (j <= -1.85e-267) {
		tmp = t_1;
	} else if (j <= 8.2e-218) {
		tmp = x * (t * -a);
	} else if (j <= 3.7e-44) {
		tmp = t_1;
	} else if (j <= 5.5e+80) {
		tmp = t_2;
	} else {
		tmp = i * (y * -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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = c * (t * j)
    if (j <= (-1d+31)) then
        tmp = t_2
    else if (j <= (-1.85d-267)) then
        tmp = t_1
    else if (j <= 8.2d-218) then
        tmp = x * (t * -a)
    else if (j <= 3.7d-44) then
        tmp = t_1
    else if (j <= 5.5d+80) then
        tmp = t_2
    else
        tmp = i * (y * -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 t_1 = b * ((a * i) - (z * c));
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -1e+31) {
		tmp = t_2;
	} else if (j <= -1.85e-267) {
		tmp = t_1;
	} else if (j <= 8.2e-218) {
		tmp = x * (t * -a);
	} else if (j <= 3.7e-44) {
		tmp = t_1;
	} else if (j <= 5.5e+80) {
		tmp = t_2;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * (t * j)
	tmp = 0
	if j <= -1e+31:
		tmp = t_2
	elif j <= -1.85e-267:
		tmp = t_1
	elif j <= 8.2e-218:
		tmp = x * (t * -a)
	elif j <= 3.7e-44:
		tmp = t_1
	elif j <= 5.5e+80:
		tmp = t_2
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -1e+31)
		tmp = t_2;
	elseif (j <= -1.85e-267)
		tmp = t_1;
	elseif (j <= 8.2e-218)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 3.7e-44)
		tmp = t_1;
	elseif (j <= 5.5e+80)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = c * (t * j);
	tmp = 0.0;
	if (j <= -1e+31)
		tmp = t_2;
	elseif (j <= -1.85e-267)
		tmp = t_1;
	elseif (j <= 8.2e-218)
		tmp = x * (t * -a);
	elseif (j <= 3.7e-44)
		tmp = t_1;
	elseif (j <= 5.5e+80)
		tmp = t_2;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+31], t$95$2, If[LessEqual[j, -1.85e-267], t$95$1, If[LessEqual[j, 8.2e-218], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-44], t$95$1, If[LessEqual[j, 5.5e+80], t$95$2, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.9999999999999996e30 or 3.7e-44 < j < 5.49999999999999967e80

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around inf 48.0%

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

   if -9.9999999999999996e30 < j < -1.84999999999999993e-267 or 8.1999999999999995e-218 < j < 3.7e-44

   1. Initial program 66.8%

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

   3. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   if -1.84999999999999993e-267 < j < 8.1999999999999995e-218

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around 0 47.1%

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

      1. neg-mul-1 47.1%

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

      2. *-commutative 47.1%

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

      3. distribute-rgt-neg-in 47.1%

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

   8. Simplified 47.1%

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

   if 5.49999999999999967e80 < j

   1. Initial program 73.0%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in y around inf 49.9%

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

      1. associate-*r* 49.9%

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

      2. neg-mul-1 49.9%

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

   8. Simplified 49.9%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.05e-15)
   (* i (- (* a b) (* y j)))
   (if (<= i 1.3e-119)
     (+ (* x (- (* y z) (* t a))) (* c (* t j)))
     (if (<= i 1.3e-9)
       (* a (- (* b i) (* x t)))
       (if (<= i 5.6e+161)
         (* t (* x (- (* c (/ j x)) a)))
         (* (* b i) (- a (* j (/ y 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 (i <= -2.05e-15) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= 1.3e-119) {
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j));
	} else if (i <= 1.3e-9) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 5.6e+161) {
		tmp = t * (x * ((c * (j / x)) - a));
	} else {
		tmp = (b * i) * (a - (j * (y / 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 (i <= (-2.05d-15)) then
        tmp = i * ((a * b) - (y * j))
    else if (i <= 1.3d-119) then
        tmp = (x * ((y * z) - (t * a))) + (c * (t * j))
    else if (i <= 1.3d-9) then
        tmp = a * ((b * i) - (x * t))
    else if (i <= 5.6d+161) then
        tmp = t * (x * ((c * (j / x)) - a))
    else
        tmp = (b * i) * (a - (j * (y / 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 (i <= -2.05e-15) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= 1.3e-119) {
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j));
	} else if (i <= 1.3e-9) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 5.6e+161) {
		tmp = t * (x * ((c * (j / x)) - a));
	} else {
		tmp = (b * i) * (a - (j * (y / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.05e-15:
		tmp = i * ((a * b) - (y * j))
	elif i <= 1.3e-119:
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j))
	elif i <= 1.3e-9:
		tmp = a * ((b * i) - (x * t))
	elif i <= 5.6e+161:
		tmp = t * (x * ((c * (j / x)) - a))
	else:
		tmp = (b * i) * (a - (j * (y / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.05e-15)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (i <= 1.3e-119)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(t * j)));
	elseif (i <= 1.3e-9)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (i <= 5.6e+161)
		tmp = Float64(t * Float64(x * Float64(Float64(c * Float64(j / x)) - a)));
	else
		tmp = Float64(Float64(b * i) * Float64(a - Float64(j * Float64(y / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.05e-15)
		tmp = i * ((a * b) - (y * j));
	elseif (i <= 1.3e-119)
		tmp = (x * ((y * z) - (t * a))) + (c * (t * j));
	elseif (i <= 1.3e-9)
		tmp = a * ((b * i) - (x * t));
	elseif (i <= 5.6e+161)
		tmp = t * (x * ((c * (j / x)) - a));
	else
		tmp = (b * i) * (a - (j * (y / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.05e-15], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-119], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-9], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.6e+161], N[(t * N[(x * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * i), $MachinePrecision] * N[(a - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.05000000000000018e-15

   1. Initial program 65.0%

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

   3. Taylor expanded in i around inf 74.3%

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

      1. distribute-lft-out-- 74.3%

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

      2. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -2.05000000000000018e-15 < i < 1.30000000000000006e-119

   1. Initial program 80.9%

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

   3. Taylor expanded in i around 0 73.2%

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

   4. Taylor expanded in b around 0 63.4%

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

   if 1.30000000000000006e-119 < i < 1.3000000000000001e-9

   1. Initial program 77.9%

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

   3. Taylor expanded in a around -inf 67.9%

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

   if 1.3000000000000001e-9 < i < 5.60000000000000041e161

   1. Initial program 66.8%

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

   3. Taylor expanded in t around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in x around inf 65.0%

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

      1. associate-/l* 64.9%

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

   8. Simplified 64.9%

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

   if 5.60000000000000041e161 < i

   1. Initial program 54.0%

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

   3. Taylor expanded in b around inf 49.9%

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

      1. fma-define 53.8%

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

      2. associate-/l* 57.6%

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

      3. associate-/l* 53.8%

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

      4. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in i around inf 62.8%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

      3. mul-1-neg 66.3%

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

      4. unsub-neg 66.3%

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

      5. associate-/l* 66.3%

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

   8. Simplified 66.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -8.2e+30)
     t_2
     (if (<= j -6.8e-268)
       t_1
       (if (<= j 6.2e-211) (* x (* t (- a))) (if (<= j 5.2e-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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -8.2e+30) {
		tmp = t_2;
	} else if (j <= -6.8e-268) {
		tmp = t_1;
	} else if (j <= 6.2e-211) {
		tmp = x * (t * -a);
	} else if (j <= 5.2e-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 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-8.2d+30)) then
        tmp = t_2
    else if (j <= (-6.8d-268)) then
        tmp = t_1
    else if (j <= 6.2d-211) then
        tmp = x * (t * -a)
    else if (j <= 5.2d-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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -8.2e+30) {
		tmp = t_2;
	} else if (j <= -6.8e-268) {
		tmp = t_1;
	} else if (j <= 6.2e-211) {
		tmp = x * (t * -a);
	} else if (j <= 5.2e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -8.2e+30:
		tmp = t_2
	elif j <= -6.8e-268:
		tmp = t_1
	elif j <= 6.2e-211:
		tmp = x * (t * -a)
	elif j <= 5.2e-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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -8.2e+30)
		tmp = t_2;
	elseif (j <= -6.8e-268)
		tmp = t_1;
	elseif (j <= 6.2e-211)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 5.2e-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 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -8.2e+30)
		tmp = t_2;
	elseif (j <= -6.8e-268)
		tmp = t_1;
	elseif (j <= 6.2e-211)
		tmp = x * (t * -a);
	elseif (j <= 5.2e-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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.2e+30], t$95$2, If[LessEqual[j, -6.8e-268], t$95$1, If[LessEqual[j, 6.2e-211], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e-53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.20000000000000011e30 or 5.19999999999999993e-53 < j

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 67.5%

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

      1. fma-define 71.2%

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

      2. associate-/l* 72.6%

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

      3. associate-/l* 71.1%

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

      4. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in j around -inf 68.7%

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

   if -8.20000000000000011e30 < j < -6.8e-268 or 6.1999999999999999e-211 < j < 5.19999999999999993e-53

   1. Initial program 66.8%

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

   3. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   if -6.8e-268 < j < 6.1999999999999999e-211

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around 0 47.1%

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

      1. neg-mul-1 47.1%

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

      2. *-commutative 47.1%

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

      3. distribute-rgt-neg-in 47.1%

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

   8. Simplified 47.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -2.05e+30)
     t_2
     (if (<= j -1e-267)
       t_1
       (if (<= j 7.2e-213)
         (* t (- (* c j) (* x a)))
         (if (<= j 3.5e-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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.05e+30) {
		tmp = t_2;
	} else if (j <= -1e-267) {
		tmp = t_1;
	} else if (j <= 7.2e-213) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 3.5e-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 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-2.05d+30)) then
        tmp = t_2
    else if (j <= (-1d-267)) then
        tmp = t_1
    else if (j <= 7.2d-213) then
        tmp = t * ((c * j) - (x * a))
    else if (j <= 3.5d-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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.05e+30) {
		tmp = t_2;
	} else if (j <= -1e-267) {
		tmp = t_1;
	} else if (j <= 7.2e-213) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 3.5e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.05e+30:
		tmp = t_2
	elif j <= -1e-267:
		tmp = t_1
	elif j <= 7.2e-213:
		tmp = t * ((c * j) - (x * a))
	elif j <= 3.5e-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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.05e+30)
		tmp = t_2;
	elseif (j <= -1e-267)
		tmp = t_1;
	elseif (j <= 7.2e-213)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (j <= 3.5e-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 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.05e+30)
		tmp = t_2;
	elseif (j <= -1e-267)
		tmp = t_1;
	elseif (j <= 7.2e-213)
		tmp = t * ((c * j) - (x * a));
	elseif (j <= 3.5e-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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.05e+30], t$95$2, If[LessEqual[j, -1e-267], t$95$1, If[LessEqual[j, 7.2e-213], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.05000000000000003e30 or 3.49999999999999993e-53 < j

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 67.5%

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

      1. fma-define 71.2%

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

      2. associate-/l* 72.6%

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

      3. associate-/l* 71.1%

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

      4. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in j around -inf 68.7%

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

   if -2.05000000000000003e30 < j < -9.9999999999999998e-268 or 7.2000000000000002e-213 < j < 3.49999999999999993e-53

   1. Initial program 66.8%

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

   3. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   if -9.9999999999999998e-268 < j < 7.2000000000000002e-213

   1. Initial program 67.6%

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

   3. Taylor expanded in t around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

      4. *-commutative 51.1%

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

   5. Simplified 51.1%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.82 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= a -1.82e+155)
     t_1
     (if (<= a -5.2e-22)
       (* b (- (* a i) (* z c)))
       (if (<= a 1.2e+14)
         (* c (- (* t j) (* z b)))
         (if (<= a 8e+211) (* 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 = a * (x * -t);
	double tmp;
	if (a <= -1.82e+155) {
		tmp = t_1;
	} else if (a <= -5.2e-22) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.2e+14) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 8e+211) {
		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 = a * (x * -t)
    if (a <= (-1.82d+155)) then
        tmp = t_1
    else if (a <= (-5.2d-22)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 1.2d+14) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 8d+211) 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 = a * (x * -t);
	double tmp;
	if (a <= -1.82e+155) {
		tmp = t_1;
	} else if (a <= -5.2e-22) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.2e+14) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 8e+211) {
		tmp = i * (y * -j);
	} 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 a <= -1.82e+155:
		tmp = t_1
	elif a <= -5.2e-22:
		tmp = b * ((a * i) - (z * c))
	elif a <= 1.2e+14:
		tmp = c * ((t * j) - (z * b))
	elif a <= 8e+211:
		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(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (a <= -1.82e+155)
		tmp = t_1;
	elseif (a <= -5.2e-22)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 1.2e+14)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 8e+211)
		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 = a * (x * -t);
	tmp = 0.0;
	if (a <= -1.82e+155)
		tmp = t_1;
	elseif (a <= -5.2e-22)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 1.2e+14)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 8e+211)
		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[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.82e+155], t$95$1, If[LessEqual[a, -5.2e-22], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+14], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+211], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.81999999999999989e155 or 7.9999999999999997e211 < a

   1. Initial program 56.2%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-rgt-neg-in 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   8. Simplified 56.9%

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

   if -1.81999999999999989e155 < a < -5.2e-22

   1. Initial program 70.9%

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

   3. Taylor expanded in b around inf 52.2%

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

      1. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   if -5.2e-22 < a < 1.2e14

   1. Initial program 79.8%

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

   3. Taylor expanded in c around inf 61.1%

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

   if 1.2e14 < a < 7.9999999999999997e211

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 49.7%

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

      1. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in y around inf 40.7%

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

      1. associate-*r* 40.7%

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

      2. neg-mul-1 40.7%

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

   8. Simplified 40.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.82 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.4:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4.4)
   (* c (* t j))
   (if (<= j -8.8e-225)
     (* a (* b i))
     (if (<= j 5.6e-218)
       (* x (* y z))
       (if (<= j 3.7e-44) (* b (* a i)) (* t (* 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 (j <= -4.4) {
		tmp = c * (t * j);
	} else if (j <= -8.8e-225) {
		tmp = a * (b * i);
	} else if (j <= 5.6e-218) {
		tmp = x * (y * z);
	} else if (j <= 3.7e-44) {
		tmp = b * (a * i);
	} else {
		tmp = t * (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 (j <= (-4.4d0)) then
        tmp = c * (t * j)
    else if (j <= (-8.8d-225)) then
        tmp = a * (b * i)
    else if (j <= 5.6d-218) then
        tmp = x * (y * z)
    else if (j <= 3.7d-44) then
        tmp = b * (a * i)
    else
        tmp = t * (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 (j <= -4.4) {
		tmp = c * (t * j);
	} else if (j <= -8.8e-225) {
		tmp = a * (b * i);
	} else if (j <= 5.6e-218) {
		tmp = x * (y * z);
	} else if (j <= 3.7e-44) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -4.4:
		tmp = c * (t * j)
	elif j <= -8.8e-225:
		tmp = a * (b * i)
	elif j <= 5.6e-218:
		tmp = x * (y * z)
	elif j <= 3.7e-44:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4.4)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= -8.8e-225)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 5.6e-218)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 3.7e-44)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * 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 (j <= -4.4)
		tmp = c * (t * j);
	elseif (j <= -8.8e-225)
		tmp = a * (b * i);
	elseif (j <= 5.6e-218)
		tmp = x * (y * z);
	elseif (j <= 3.7e-44)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4.4], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.8e-225], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.6e-218], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-44], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.4000000000000004

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around inf 48.3%

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

   if -4.4000000000000004 < j < -8.8e-225

   1. Initial program 62.1%

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

   3. Taylor expanded in b around inf 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in i around inf 41.2%

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

   if -8.8e-225 < j < 5.60000000000000018e-218

   1. Initial program 71.6%

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

   3. Taylor expanded in x around inf 56.8%

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

      1. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y around inf 28.5%

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

   if 5.60000000000000018e-218 < j < 3.7e-44

   1. Initial program 65.4%

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

   3. Taylor expanded in b around inf 61.0%

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

      1. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in i around inf 41.8%

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

      1. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   if 3.7e-44 < j

   1. Initial program 75.2%

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

   3. Taylor expanded in i around 0 54.8%

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

   4. Taylor expanded in j around inf 35.4%

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

      1. associate-*r* 39.7%

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

      2. *-commutative 39.7%

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

   6. Simplified 39.7%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.4:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -29000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -29000.0)
   (* c (* t j))
   (if (<= j -3.7e-225)
     (* a (* b i))
     (if (<= j 6e-218)
       (* z (* x y))
       (if (<= j 3.7e-44) (* b (* a i)) (* t (* 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 (j <= -29000.0) {
		tmp = c * (t * j);
	} else if (j <= -3.7e-225) {
		tmp = a * (b * i);
	} else if (j <= 6e-218) {
		tmp = z * (x * y);
	} else if (j <= 3.7e-44) {
		tmp = b * (a * i);
	} else {
		tmp = t * (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 (j <= (-29000.0d0)) then
        tmp = c * (t * j)
    else if (j <= (-3.7d-225)) then
        tmp = a * (b * i)
    else if (j <= 6d-218) then
        tmp = z * (x * y)
    else if (j <= 3.7d-44) then
        tmp = b * (a * i)
    else
        tmp = t * (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 (j <= -29000.0) {
		tmp = c * (t * j);
	} else if (j <= -3.7e-225) {
		tmp = a * (b * i);
	} else if (j <= 6e-218) {
		tmp = z * (x * y);
	} else if (j <= 3.7e-44) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -29000.0:
		tmp = c * (t * j)
	elif j <= -3.7e-225:
		tmp = a * (b * i)
	elif j <= 6e-218:
		tmp = z * (x * y)
	elif j <= 3.7e-44:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -29000.0)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= -3.7e-225)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 6e-218)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 3.7e-44)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * 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 (j <= -29000.0)
		tmp = c * (t * j);
	elseif (j <= -3.7e-225)
		tmp = a * (b * i);
	elseif (j <= 6e-218)
		tmp = z * (x * y);
	elseif (j <= 3.7e-44)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -29000.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-225], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-218], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-44], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -29000

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around inf 48.3%

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

   if -29000 < j < -3.69999999999999988e-225

   1. Initial program 62.1%

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

   3. Taylor expanded in b around inf 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in i around inf 41.2%

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

   if -3.69999999999999988e-225 < j < 5.9999999999999997e-218

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in y around inf 31.5%

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

   if 5.9999999999999997e-218 < j < 3.7e-44

   1. Initial program 65.4%

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

   3. Taylor expanded in b around inf 61.0%

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

      1. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in i around inf 41.8%

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

      1. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   if 3.7e-44 < j

   1. Initial program 75.2%

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

   3. Taylor expanded in i around 0 54.8%

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

   4. Taylor expanded in j around inf 35.4%

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

      1. associate-*r* 39.7%

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

      2. *-commutative 39.7%

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

   6. Simplified 39.7%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -29000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -200000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -200000.0)
     t_1
     (if (<= a 9.5e-169)
       (* c (- (* t j) (* z b)))
       (if (<= a 1.3e+211) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -200000.0) {
		tmp = t_1;
	} else if (a <= 9.5e-169) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.3e+211) {
		tmp = j * ((t * c) - (y * i));
	} 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 * ((b * i) - (x * t))
    if (a <= (-200000.0d0)) then
        tmp = t_1
    else if (a <= 9.5d-169) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 1.3d+211) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -200000.0) {
		tmp = t_1;
	} else if (a <= 9.5e-169) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.3e+211) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -200000.0:
		tmp = t_1
	elif a <= 9.5e-169:
		tmp = c * ((t * j) - (z * b))
	elif a <= 1.3e+211:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -200000.0)
		tmp = t_1;
	elseif (a <= 9.5e-169)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 1.3e+211)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -200000.0)
		tmp = t_1;
	elseif (a <= 9.5e-169)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 1.3e+211)
		tmp = j * ((t * c) - (y * i));
	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[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -200000.0], t$95$1, If[LessEqual[a, 9.5e-169], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+211], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e5 or 1.2999999999999999e211 < a

   1. Initial program 61.0%

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

   3. Taylor expanded in a around -inf 73.0%

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

   if -2e5 < a < 9.5000000000000001e-169

   1. Initial program 74.4%

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

   3. Taylor expanded in c around inf 66.6%

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

   if 9.5000000000000001e-169 < a < 1.2999999999999999e211

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 73.1%

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

      1. fma-define 74.5%

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

      2. associate-/l* 73.2%

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

      3. associate-/l* 73.1%

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

      4. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in j around -inf 56.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -200000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3900 \lor \neg \left(j \leq 4.2 \cdot 10^{-45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3900.0) (not (<= j 4.2e-45))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3900.0) || !(j <= 4.2e-45)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-3900.0d0)) .or. (.not. (j <= 4.2d-45))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3900.0) || !(j <= 4.2e-45)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -3900.0) or not (j <= 4.2e-45):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -3900.0) || !(j <= 4.2e-45))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -3900.0) || ~((j <= 4.2e-45)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -3900.0], N[Not[LessEqual[j, 4.2e-45]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3900 or 4.1999999999999999e-45 < j

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 69.8%

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

      1. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in t around inf 42.4%

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

   if -3900 < j < 4.1999999999999999e-45

   1. Initial program 65.8%

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

   3. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in i around inf 33.4%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3900 \lor \neg \left(j \leq 4.2 \cdot 10^{-45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -135000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -135000.0)
   (* c (* t j))
   (if (<= j 4.6e-45) (* a (* b i)) (* t (* 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 (j <= -135000.0) {
		tmp = c * (t * j);
	} else if (j <= 4.6e-45) {
		tmp = a * (b * i);
	} else {
		tmp = t * (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 (j <= (-135000.0d0)) then
        tmp = c * (t * j)
    else if (j <= 4.6d-45) then
        tmp = a * (b * i)
    else
        tmp = t * (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 (j <= -135000.0) {
		tmp = c * (t * j);
	} else if (j <= 4.6e-45) {
		tmp = a * (b * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -135000.0:
		tmp = c * (t * j)
	elif j <= 4.6e-45:
		tmp = a * (b * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -135000.0)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= 4.6e-45)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(t * 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 (j <= -135000.0)
		tmp = c * (t * j);
	elseif (j <= 4.6e-45)
		tmp = a * (b * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -135000.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.6e-45], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -135000

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around inf 48.3%

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

   if -135000 < j < 4.59999999999999983e-45

   1. Initial program 65.8%

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

   3. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in i around inf 33.4%

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

   if 4.59999999999999983e-45 < j

   1. Initial program 75.2%

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

   3. Taylor expanded in i around 0 54.8%

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

   4. Taylor expanded in j around inf 35.4%

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

      1. associate-*r* 39.7%

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

      2. *-commutative 39.7%

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

   6. Simplified 39.7%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -135000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.45e+152) (* b (* a i)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.45e+152) {
		tmp = b * (a * i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.45d+152)) then
        tmp = b * (a * i)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.45e+152) {
		tmp = b * (a * i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.45e+152:
		tmp = b * (a * i)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.45e+152)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.45e+152)
		tmp = b * (a * i);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.45e+152], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.4499999999999999e152

   1. Initial program 56.6%

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

   3. Taylor expanded in b around inf 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in i around inf 54.2%

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

      1. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -1.4499999999999999e152 < i

   1. Initial program 73.8%

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

   3. Taylor expanded in b around inf 35.2%

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

      1. *-commutative 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in i around inf 21.6%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.7%

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

3. Taylor expanded in b around inf 37.6%

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

   1. *-commutative 37.6%

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

5. Simplified 37.6%

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

6. Taylor expanded in i around inf 23.4%

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

7. Final simplification 23.4%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024075 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))