Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.8% → 83.0%

Time: 22.3s

Alternatives: 23

Speedup: 0.5×

• 58.2% 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: 73.8% accurate, 1.0× speedup

Math

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

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: 83.0% accurate, 0.5× speedup

Math

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

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 (* j (* t (- c (* a (/ x 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 = ((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 = j * (t * (c - (a * (x / j))));
	}
	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 = j * (t * (c - (a * (x / j))));
	}
	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 = j * (t * (c - (a * (x / j))))
	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(j * Float64(t * Float64(c - Float64(a * Float64(x / j)))));
	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 = j * (t * (c - (a * (x / j))));
	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[(j * N[(t * N[(c - N[(a * N[(x / j), $MachinePrecision]), $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 94.5%

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

   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 j around inf 12.1%

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

   4. Taylor expanded in t around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

      3. associate-/l* 53.9%

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

   6. Simplified 53.9%

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

4. Final simplification 85.3%

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

Alternative 2: 47.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.5:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-261}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-68}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= y -1.3e+75)
     (* y (- (* x z) (* i j)))
     (if (<= y -4.5)
       (* c (- (* t j) (* z b)))
       (if (<= y -2.15e-43)
         t_2
         (if (<= y -3e-102)
           t_3
           (if (<= y -1.3e-162)
             t_1
             (if (<= y -2.3e-261)
               t_3
               (if (<= y 1.35e-152)
                 (* t (- (* c j) (* x a)))
                 (if (<= y 3.05e-68)
                   t_3
                   (if (<= y 2.85e+106) t_2 t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -1.3e+75) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -4.5) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= -2.15e-43) {
		tmp = t_2;
	} else if (y <= -3e-102) {
		tmp = t_3;
	} else if (y <= -1.3e-162) {
		tmp = t_1;
	} else if (y <= -2.3e-261) {
		tmp = t_3;
	} else if (y <= 1.35e-152) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 3.05e-68) {
		tmp = t_3;
	} else if (y <= 2.85e+106) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((a * i) - (z * c))
    if (y <= (-1.3d+75)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-4.5d0)) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= (-2.15d-43)) then
        tmp = t_2
    else if (y <= (-3d-102)) then
        tmp = t_3
    else if (y <= (-1.3d-162)) then
        tmp = t_1
    else if (y <= (-2.3d-261)) then
        tmp = t_3
    else if (y <= 1.35d-152) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 3.05d-68) then
        tmp = t_3
    else if (y <= 2.85d+106) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -1.3e+75) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -4.5) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= -2.15e-43) {
		tmp = t_2;
	} else if (y <= -3e-102) {
		tmp = t_3;
	} else if (y <= -1.3e-162) {
		tmp = t_1;
	} else if (y <= -2.3e-261) {
		tmp = t_3;
	} else if (y <= 1.35e-152) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 3.05e-68) {
		tmp = t_3;
	} else if (y <= 2.85e+106) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -1.3e+75:
		tmp = y * ((x * z) - (i * j))
	elif y <= -4.5:
		tmp = c * ((t * j) - (z * b))
	elif y <= -2.15e-43:
		tmp = t_2
	elif y <= -3e-102:
		tmp = t_3
	elif y <= -1.3e-162:
		tmp = t_1
	elif y <= -2.3e-261:
		tmp = t_3
	elif y <= 1.35e-152:
		tmp = t * ((c * j) - (x * a))
	elif y <= 3.05e-68:
		tmp = t_3
	elif y <= 2.85e+106:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -1.3e+75)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -4.5)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= -2.15e-43)
		tmp = t_2;
	elseif (y <= -3e-102)
		tmp = t_3;
	elseif (y <= -1.3e-162)
		tmp = t_1;
	elseif (y <= -2.3e-261)
		tmp = t_3;
	elseif (y <= 1.35e-152)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 3.05e-68)
		tmp = t_3;
	elseif (y <= 2.85e+106)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (y <= -1.3e+75)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -4.5)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= -2.15e-43)
		tmp = t_2;
	elseif (y <= -3e-102)
		tmp = t_3;
	elseif (y <= -1.3e-162)
		tmp = t_1;
	elseif (y <= -2.3e-261)
		tmp = t_3;
	elseif (y <= 1.35e-152)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 3.05e-68)
		tmp = t_3;
	elseif (y <= 2.85e+106)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+75], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-43], t$95$2, If[LessEqual[y, -3e-102], t$95$3, If[LessEqual[y, -1.3e-162], t$95$1, If[LessEqual[y, -2.3e-261], t$95$3, If[LessEqual[y, 1.35e-152], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e-68], t$95$3, If[LessEqual[y, 2.85e+106], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.29999999999999992e75

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. mul-1-neg 79.5%

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

      3. unsub-neg 79.5%

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

      4. *-commutative 79.5%

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

      5. *-commutative 79.5%

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

   5. Simplified 79.5%

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

   if -1.29999999999999992e75 < y < -4.5

   1. Initial program 81.2%

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

   3. Taylor expanded in c around inf 57.8%

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

   if -4.5 < y < -2.14999999999999982e-43 or 3.05e-68 < y < 2.8499999999999999e106

   1. Initial program 74.2%

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

   3. Taylor expanded in x around inf 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -2.14999999999999982e-43 < y < -3e-102 or -1.3e-162 < y < -2.3e-261 or 1.34999999999999999e-152 < y < 3.05e-68

   1. Initial program 75.0%

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

   3. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -3e-102 < y < -1.3e-162 or 2.8499999999999999e106 < y

   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 j around inf 66.6%

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

   if -2.3e-261 < y < 1.34999999999999999e-152

   1. Initial program 80.5%

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

   3. Taylor expanded in t around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

   5. Simplified 65.6%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.5:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-162}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;z \leq -0.0024:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* b (* z c))))
        (t_2 (+ (* j (- (* t c) (* y i))) (* b (* a i)))))
   (if (<= z -0.0024)
     t_1
     (if (<= z 4.9e-135)
       t_2
       (if (<= z 1.45e-94)
         (* t (- (* c j) (* x a)))
         (if (<= z 3.7e-68)
           t_2
           (if (<= z 7.5e+21)
             t_1
             (if (<= z 8e+160) t_2 (* z (- (* x y) (* b c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_2 = (j * ((t * c) - (y * i))) + (b * (a * i));
	double tmp;
	if (z <= -0.0024) {
		tmp = t_1;
	} else if (z <= 4.9e-135) {
		tmp = t_2;
	} else if (z <= 1.45e-94) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.7e-68) {
		tmp = t_2;
	} else if (z <= 7.5e+21) {
		tmp = t_1;
	} else if (z <= 8e+160) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (b * (z * c))
    t_2 = (j * ((t * c) - (y * i))) + (b * (a * i))
    if (z <= (-0.0024d0)) then
        tmp = t_1
    else if (z <= 4.9d-135) then
        tmp = t_2
    else if (z <= 1.45d-94) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.7d-68) then
        tmp = t_2
    else if (z <= 7.5d+21) then
        tmp = t_1
    else if (z <= 8d+160) then
        tmp = t_2
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_2 = (j * ((t * c) - (y * i))) + (b * (a * i));
	double tmp;
	if (z <= -0.0024) {
		tmp = t_1;
	} else if (z <= 4.9e-135) {
		tmp = t_2;
	} else if (z <= 1.45e-94) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.7e-68) {
		tmp = t_2;
	} else if (z <= 7.5e+21) {
		tmp = t_1;
	} else if (z <= 8e+160) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (b * (z * c))
	t_2 = (j * ((t * c) - (y * i))) + (b * (a * i))
	tmp = 0
	if z <= -0.0024:
		tmp = t_1
	elif z <= 4.9e-135:
		tmp = t_2
	elif z <= 1.45e-94:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.7e-68:
		tmp = t_2
	elif z <= 7.5e+21:
		tmp = t_1
	elif z <= 8e+160:
		tmp = t_2
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(a * i)))
	tmp = 0.0
	if (z <= -0.0024)
		tmp = t_1;
	elseif (z <= 4.9e-135)
		tmp = t_2;
	elseif (z <= 1.45e-94)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.7e-68)
		tmp = t_2;
	elseif (z <= 7.5e+21)
		tmp = t_1;
	elseif (z <= 8e+160)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (b * (z * c));
	t_2 = (j * ((t * c) - (y * i))) + (b * (a * i));
	tmp = 0.0;
	if (z <= -0.0024)
		tmp = t_1;
	elseif (z <= 4.9e-135)
		tmp = t_2;
	elseif (z <= 1.45e-94)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.7e-68)
		tmp = t_2;
	elseif (z <= 7.5e+21)
		tmp = t_1;
	elseif (z <= 8e+160)
		tmp = t_2;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0024], t$95$1, If[LessEqual[z, 4.9e-135], t$95$2, If[LessEqual[z, 1.45e-94], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-68], t$95$2, If[LessEqual[z, 7.5e+21], t$95$1, If[LessEqual[z, 8e+160], t$95$2, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.00239999999999999979 or 3.70000000000000002e-68 < z < 7.5e21

   1. Initial program 72.5%

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

   3. Taylor expanded in t around 0 71.5%

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

      1. associate-*r* 73.8%

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

      2. associate-*r* 73.8%

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

      3. *-commutative 73.8%

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

      4. associate-*r* 71.6%

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

      5. distribute-rgt-in 74.0%

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

      6. +-commutative 74.0%

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

      7. mul-1-neg 74.0%

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

      8. unsub-neg 74.0%

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

      9. *-commutative 74.0%

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

      10. *-commutative 74.0%

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

      11. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in c around inf 67.4%

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

   if -0.00239999999999999979 < z < 4.9000000000000003e-135 or 1.44999999999999998e-94 < z < 3.70000000000000002e-68 or 7.5e21 < z < 8.00000000000000005e160

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-*r* 74.7%

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

   5. Simplified 74.7%

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

   if 4.9000000000000003e-135 < z < 1.44999999999999998e-94

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 89.7%

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

      1. +-commutative 89.7%

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

      2. mul-1-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. *-commutative 89.7%

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

   5. Simplified 89.7%

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

   if 8.00000000000000005e160 < z

   1. Initial program 47.0%

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

   3. Taylor expanded in z around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0024:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-135}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.02 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq -1.85 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.02e+53)
     t_2
     (if (<= i -6e-26)
       (* b (* c (- (* a (/ i c)) z)))
       (if (<= i -1.85e-60)
         (* y (- (* x z) (* i j)))
         (if (<= i -2.3e-210)
           t_1
           (if (<= i -2.1e-264)
             (* j (- (* t c) (* y i)))
             (if (<= i 9e-122)
               (* t (- (* c j) (* x a)))
               (if (<= i 3.9e+30) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.02e+53) {
		tmp = t_2;
	} else if (i <= -6e-26) {
		tmp = b * (c * ((a * (i / c)) - z));
	} else if (i <= -1.85e-60) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -2.3e-210) {
		tmp = t_1;
	} else if (i <= -2.1e-264) {
		tmp = j * ((t * c) - (y * i));
	} else if (i <= 9e-122) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 3.9e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.02d+53)) then
        tmp = t_2
    else if (i <= (-6d-26)) then
        tmp = b * (c * ((a * (i / c)) - z))
    else if (i <= (-1.85d-60)) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= (-2.3d-210)) then
        tmp = t_1
    else if (i <= (-2.1d-264)) then
        tmp = j * ((t * c) - (y * i))
    else if (i <= 9d-122) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 3.9d+30) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.02e+53) {
		tmp = t_2;
	} else if (i <= -6e-26) {
		tmp = b * (c * ((a * (i / c)) - z));
	} else if (i <= -1.85e-60) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -2.3e-210) {
		tmp = t_1;
	} else if (i <= -2.1e-264) {
		tmp = j * ((t * c) - (y * i));
	} else if (i <= 9e-122) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 3.9e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.02e+53:
		tmp = t_2
	elif i <= -6e-26:
		tmp = b * (c * ((a * (i / c)) - z))
	elif i <= -1.85e-60:
		tmp = y * ((x * z) - (i * j))
	elif i <= -2.3e-210:
		tmp = t_1
	elif i <= -2.1e-264:
		tmp = j * ((t * c) - (y * i))
	elif i <= 9e-122:
		tmp = t * ((c * j) - (x * a))
	elif i <= 3.9e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.02e+53)
		tmp = t_2;
	elseif (i <= -6e-26)
		tmp = Float64(b * Float64(c * Float64(Float64(a * Float64(i / c)) - z)));
	elseif (i <= -1.85e-60)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= -2.3e-210)
		tmp = t_1;
	elseif (i <= -2.1e-264)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (i <= 9e-122)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 3.9e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.02e+53)
		tmp = t_2;
	elseif (i <= -6e-26)
		tmp = b * (c * ((a * (i / c)) - z));
	elseif (i <= -1.85e-60)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= -2.3e-210)
		tmp = t_1;
	elseif (i <= -2.1e-264)
		tmp = j * ((t * c) - (y * i));
	elseif (i <= 9e-122)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 3.9e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.02e+53], t$95$2, If[LessEqual[i, -6e-26], N[(b * N[(c * N[(N[(a * N[(i / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.85e-60], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.3e-210], t$95$1, If[LessEqual[i, -2.1e-264], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e-122], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.9e+30], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.01999999999999999e53 or 3.90000000000000011e30 < i

   1. Initial program 65.1%

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

   3. Taylor expanded in i around inf 71.7%

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

      1. distribute-lft-out-- 71.7%

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

      2. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in i around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

      4. distribute-rgt-neg-out 71.7%

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

      5. sub-neg 71.7%

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

      6. *-commutative 71.7%

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

      7. distribute-neg-in 71.7%

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

      8. distribute-lft-neg-in 71.7%

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

      9. remove-double-neg 71.7%

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

   8. Simplified 71.7%

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

   if -1.01999999999999999e53 < i < -6.00000000000000023e-26

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in c around inf 61.8%

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

      1. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

   if -6.00000000000000023e-26 < i < -1.85000000000000012e-60

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

      4. *-commutative 76.3%

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

      5. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -1.85000000000000012e-60 < i < -2.3e-210 or 8.99999999999999959e-122 < i < 3.90000000000000011e30

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 62.4%

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

      1. *-commutative 62.4%

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

      2. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   if -2.3e-210 < i < -2.1000000000000002e-264

   1. Initial program 94.4%

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

   3. Taylor expanded in j around inf 72.0%

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

   if -2.1000000000000002e-264 < i < 8.99999999999999959e-122

   1. Initial program 84.1%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.02 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq -1.85 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-122}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 28.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;y \leq -2000000:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= y -2000000.0)
     (* i (* j (- y)))
     (if (<= y -2.4e-98)
       (* c (* z (- b)))
       (if (<= y -4.9e-166)
         t_1
         (if (<= y -9.5e-289)
           (* b (* z (- c)))
           (if (<= y 1.1e-67)
             (* b (* a i))
             (if (<= y 2.5e+106)
               (* t (* x (- a)))
               (if (<= y 1.6e+207) t_1 (* x (* y z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (y <= -2000000.0) {
		tmp = i * (j * -y);
	} else if (y <= -2.4e-98) {
		tmp = c * (z * -b);
	} else if (y <= -4.9e-166) {
		tmp = t_1;
	} else if (y <= -9.5e-289) {
		tmp = b * (z * -c);
	} else if (y <= 1.1e-67) {
		tmp = b * (a * i);
	} else if (y <= 2.5e+106) {
		tmp = t * (x * -a);
	} else if (y <= 1.6e+207) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (y <= (-2000000.0d0)) then
        tmp = i * (j * -y)
    else if (y <= (-2.4d-98)) then
        tmp = c * (z * -b)
    else if (y <= (-4.9d-166)) then
        tmp = t_1
    else if (y <= (-9.5d-289)) then
        tmp = b * (z * -c)
    else if (y <= 1.1d-67) then
        tmp = b * (a * i)
    else if (y <= 2.5d+106) then
        tmp = t * (x * -a)
    else if (y <= 1.6d+207) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (y <= -2000000.0) {
		tmp = i * (j * -y);
	} else if (y <= -2.4e-98) {
		tmp = c * (z * -b);
	} else if (y <= -4.9e-166) {
		tmp = t_1;
	} else if (y <= -9.5e-289) {
		tmp = b * (z * -c);
	} else if (y <= 1.1e-67) {
		tmp = b * (a * i);
	} else if (y <= 2.5e+106) {
		tmp = t * (x * -a);
	} else if (y <= 1.6e+207) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if y <= -2000000.0:
		tmp = i * (j * -y)
	elif y <= -2.4e-98:
		tmp = c * (z * -b)
	elif y <= -4.9e-166:
		tmp = t_1
	elif y <= -9.5e-289:
		tmp = b * (z * -c)
	elif y <= 1.1e-67:
		tmp = b * (a * i)
	elif y <= 2.5e+106:
		tmp = t * (x * -a)
	elif y <= 1.6e+207:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (y <= -2000000.0)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (y <= -2.4e-98)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (y <= -4.9e-166)
		tmp = t_1;
	elseif (y <= -9.5e-289)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (y <= 1.1e-67)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 2.5e+106)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 1.6e+207)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (y <= -2000000.0)
		tmp = i * (j * -y);
	elseif (y <= -2.4e-98)
		tmp = c * (z * -b);
	elseif (y <= -4.9e-166)
		tmp = t_1;
	elseif (y <= -9.5e-289)
		tmp = b * (z * -c);
	elseif (y <= 1.1e-67)
		tmp = b * (a * i);
	elseif (y <= 2.5e+106)
		tmp = t * (x * -a);
	elseif (y <= 1.6e+207)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2000000.0], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-98], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.9e-166], t$95$1, If[LessEqual[y, -9.5e-289], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-67], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+106], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+207], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2e6

   1. Initial program 71.3%

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

   3. Taylor expanded in i around inf 53.8%

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

      1. distribute-lft-out-- 53.8%

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

      2. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in b around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. *-commutative 48.5%

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

      3. mul-1-neg 48.5%

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

      4. unsub-neg 48.5%

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

      5. *-commutative 48.5%

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

      6. associate-/l* 51.1%

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

      7. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in b around 0 46.3%

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

       1. associate-*r* 46.3%

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

       2. neg-mul-1 46.3%

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

       3. *-commutative 46.3%

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

   11. Simplified 46.3%

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

   if -2e6 < y < -2.40000000000000005e-98

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 70.8%

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

      1. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in i around 0 51.6%

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

      1. associate-*r* 51.6%

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

      2. neg-mul-1 51.6%

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

   8. Simplified 51.6%

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

   9. Taylor expanded in b around 0 51.6%

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

       1. neg-mul-1 51.6%

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

       2. distribute-lft-neg-in 51.6%

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

       3. *-commutative 51.6%

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

       4. associate-*l* 55.8%

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

   11. Simplified 55.8%

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

   if -2.40000000000000005e-98 < y < -4.8999999999999999e-166 or 2.4999999999999999e106 < y < 1.6000000000000001e207

   1. Initial program 71.0%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 47.9%

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

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if -4.8999999999999999e-166 < y < -9.4999999999999995e-289

   1. Initial program 71.9%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in i around 0 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

   8. Simplified 52.4%

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

   if -9.4999999999999995e-289 < y < 1.1000000000000001e-67

   1. Initial program 82.0%

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

   3. Taylor expanded in b around inf 56.7%

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

      1. *-commutative 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in i around inf 39.2%

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

   if 1.1000000000000001e-67 < y < 2.4999999999999999e106

   1. Initial program 75.1%

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

   3. Taylor expanded in t around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in j around 0 44.3%

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

      1. associate-*r* 44.3%

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

      2. *-commutative 44.3%

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

      3. neg-mul-1 44.3%

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

   8. Simplified 44.3%

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

   if 1.6000000000000001e207 < y

   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 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around inf 56.6%

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

      1. *-commutative 56.6%

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

   8. Simplified 56.6%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2000000:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -8.2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-78}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* a (* b i))))
   (if (<= i -8.2e+107)
     t_2
     (if (<= i -1.95e-78)
       (* b (* z (- c)))
       (if (<= i -3.2e-210)
         t_1
         (if (<= i -8.2e-302)
           (* c (* t j))
           (if (<= i 9e-124)
             (* a (* t (- x)))
             (if (<= i 2.2e+47) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -8.2e+107) {
		tmp = t_2;
	} else if (i <= -1.95e-78) {
		tmp = b * (z * -c);
	} else if (i <= -3.2e-210) {
		tmp = t_1;
	} else if (i <= -8.2e-302) {
		tmp = c * (t * j);
	} else if (i <= 9e-124) {
		tmp = a * (t * -x);
	} else if (i <= 2.2e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = a * (b * i)
    if (i <= (-8.2d+107)) then
        tmp = t_2
    else if (i <= (-1.95d-78)) then
        tmp = b * (z * -c)
    else if (i <= (-3.2d-210)) then
        tmp = t_1
    else if (i <= (-8.2d-302)) then
        tmp = c * (t * j)
    else if (i <= 9d-124) then
        tmp = a * (t * -x)
    else if (i <= 2.2d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -8.2e+107) {
		tmp = t_2;
	} else if (i <= -1.95e-78) {
		tmp = b * (z * -c);
	} else if (i <= -3.2e-210) {
		tmp = t_1;
	} else if (i <= -8.2e-302) {
		tmp = c * (t * j);
	} else if (i <= 9e-124) {
		tmp = a * (t * -x);
	} else if (i <= 2.2e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -8.2e+107:
		tmp = t_2
	elif i <= -1.95e-78:
		tmp = b * (z * -c)
	elif i <= -3.2e-210:
		tmp = t_1
	elif i <= -8.2e-302:
		tmp = c * (t * j)
	elif i <= 9e-124:
		tmp = a * (t * -x)
	elif i <= 2.2e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -8.2e+107)
		tmp = t_2;
	elseif (i <= -1.95e-78)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (i <= -3.2e-210)
		tmp = t_1;
	elseif (i <= -8.2e-302)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 9e-124)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 2.2e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -8.2e+107)
		tmp = t_2;
	elseif (i <= -1.95e-78)
		tmp = b * (z * -c);
	elseif (i <= -3.2e-210)
		tmp = t_1;
	elseif (i <= -8.2e-302)
		tmp = c * (t * j);
	elseif (i <= 9e-124)
		tmp = a * (t * -x);
	elseif (i <= 2.2e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.2e+107], t$95$2, If[LessEqual[i, -1.95e-78], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.2e-210], t$95$1, If[LessEqual[i, -8.2e-302], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e-124], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e+47], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -8.1999999999999998e107 or 2.1999999999999999e47 < i

   1. Initial program 61.2%

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

   3. Taylor expanded in b around inf 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%

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

   6. Taylor expanded in i around inf 48.2%

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

   if -8.1999999999999998e107 < i < -1.9500000000000001e-78

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 45.7%

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

      1. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in i around 0 31.9%

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

      1. associate-*r* 31.9%

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

      2. neg-mul-1 31.9%

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

   8. Simplified 31.9%

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

   if -1.9500000000000001e-78 < i < -3.20000000000000028e-210 or 8.9999999999999992e-124 < i < 2.1999999999999999e47

   1. Initial program 76.2%

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

   3. Taylor expanded in x around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in y around inf 39.9%

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

      1. *-commutative 39.9%

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

      2. associate-*l* 42.8%

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

   8. Simplified 42.8%

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

   if -3.20000000000000028e-210 < i < -8.1999999999999996e-302

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 52.8%

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

   if -8.1999999999999996e-302 < i < 8.9999999999999992e-124

   1. Initial program 78.7%

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

   3. Taylor expanded in x around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

      3. distribute-rgt-neg-in 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.2 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-78}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -8.6 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 6.9 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* a (* b i))))
   (if (<= i -8.6e+107)
     t_2
     (if (<= i -1.8e-79)
       (* c (* z (- b)))
       (if (<= i -8.2e-210)
         t_1
         (if (<= i -1.15e-299)
           (* c (* t j))
           (if (<= i 6.9e-124)
             (* a (* t (- x)))
             (if (<= i 2.6e+48) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -8.6e+107) {
		tmp = t_2;
	} else if (i <= -1.8e-79) {
		tmp = c * (z * -b);
	} else if (i <= -8.2e-210) {
		tmp = t_1;
	} else if (i <= -1.15e-299) {
		tmp = c * (t * j);
	} else if (i <= 6.9e-124) {
		tmp = a * (t * -x);
	} else if (i <= 2.6e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = a * (b * i)
    if (i <= (-8.6d+107)) then
        tmp = t_2
    else if (i <= (-1.8d-79)) then
        tmp = c * (z * -b)
    else if (i <= (-8.2d-210)) then
        tmp = t_1
    else if (i <= (-1.15d-299)) then
        tmp = c * (t * j)
    else if (i <= 6.9d-124) then
        tmp = a * (t * -x)
    else if (i <= 2.6d+48) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -8.6e+107) {
		tmp = t_2;
	} else if (i <= -1.8e-79) {
		tmp = c * (z * -b);
	} else if (i <= -8.2e-210) {
		tmp = t_1;
	} else if (i <= -1.15e-299) {
		tmp = c * (t * j);
	} else if (i <= 6.9e-124) {
		tmp = a * (t * -x);
	} else if (i <= 2.6e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -8.6e+107:
		tmp = t_2
	elif i <= -1.8e-79:
		tmp = c * (z * -b)
	elif i <= -8.2e-210:
		tmp = t_1
	elif i <= -1.15e-299:
		tmp = c * (t * j)
	elif i <= 6.9e-124:
		tmp = a * (t * -x)
	elif i <= 2.6e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -8.6e+107)
		tmp = t_2;
	elseif (i <= -1.8e-79)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= -8.2e-210)
		tmp = t_1;
	elseif (i <= -1.15e-299)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 6.9e-124)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 2.6e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -8.6e+107)
		tmp = t_2;
	elseif (i <= -1.8e-79)
		tmp = c * (z * -b);
	elseif (i <= -8.2e-210)
		tmp = t_1;
	elseif (i <= -1.15e-299)
		tmp = c * (t * j);
	elseif (i <= 6.9e-124)
		tmp = a * (t * -x);
	elseif (i <= 2.6e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.6e+107], t$95$2, If[LessEqual[i, -1.8e-79], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.2e-210], t$95$1, If[LessEqual[i, -1.15e-299], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.9e-124], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+48], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -8.5999999999999999e107 or 2.59999999999999995e48 < i

   1. Initial program 61.2%

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

   3. Taylor expanded in b around inf 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%

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

   6. Taylor expanded in i around inf 48.2%

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

   if -8.5999999999999999e107 < i < -1.8000000000000001e-79

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 45.7%

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

      1. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in i around 0 31.9%

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

      1. associate-*r* 31.9%

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

      2. neg-mul-1 31.9%

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

   8. Simplified 31.9%

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

   9. Taylor expanded in b around 0 31.9%

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

       1. neg-mul-1 31.9%

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

       2. distribute-lft-neg-in 31.9%

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

       3. *-commutative 31.9%

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

       4. associate-*l* 31.5%

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

   11. Simplified 31.5%

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

   if -1.8000000000000001e-79 < i < -8.19999999999999982e-210 or 6.9e-124 < i < 2.59999999999999995e48

   1. Initial program 76.2%

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

   3. Taylor expanded in x around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in y around inf 39.9%

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

      1. *-commutative 39.9%

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

      2. associate-*l* 42.8%

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

   8. Simplified 42.8%

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

   if -8.19999999999999982e-210 < i < -1.15e-299

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 52.8%

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

   if -1.15e-299 < i < 6.9e-124

   1. Initial program 78.7%

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

   3. Taylor expanded in x around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

      3. distribute-rgt-neg-in 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 6.9 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+112} \lor \neg \left(j \leq -1.75 \cdot 10^{-129}\right) \land j \leq 1.35 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -2.2e+185)
     t_1
     (if (or (<= j -3.2e+112) (and (not (<= j -1.75e-129)) (<= j 1.35e+20)))
       (- (* z (* x y)) (* b (- (* z c) (* a i))))
       (+ t_1 (* b (* a i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.2e+185) {
		tmp = t_1;
	} else if ((j <= -3.2e+112) || (!(j <= -1.75e-129) && (j <= 1.35e+20))) {
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	} else {
		tmp = t_1 + (b * (a * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-2.2d+185)) then
        tmp = t_1
    else if ((j <= (-3.2d+112)) .or. (.not. (j <= (-1.75d-129))) .and. (j <= 1.35d+20)) then
        tmp = (z * (x * y)) - (b * ((z * c) - (a * i)))
    else
        tmp = t_1 + (b * (a * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.2e+185) {
		tmp = t_1;
	} else if ((j <= -3.2e+112) || (!(j <= -1.75e-129) && (j <= 1.35e+20))) {
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	} else {
		tmp = t_1 + (b * (a * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.2e+185:
		tmp = t_1
	elif (j <= -3.2e+112) or (not (j <= -1.75e-129) and (j <= 1.35e+20)):
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)))
	else:
		tmp = t_1 + (b * (a * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.2e+185)
		tmp = t_1;
	elseif ((j <= -3.2e+112) || (!(j <= -1.75e-129) && (j <= 1.35e+20)))
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.2e+185)
		tmp = t_1;
	elseif ((j <= -3.2e+112) || (~((j <= -1.75e-129)) && (j <= 1.35e+20)))
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	else
		tmp = t_1 + (b * (a * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+185], t$95$1, If[Or[LessEqual[j, -3.2e+112], And[N[Not[LessEqual[j, -1.75e-129]], $MachinePrecision], LessEqual[j, 1.35e+20]]], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.2000000000000001e185

   1. Initial program 63.9%

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

   3. Taylor expanded in j around inf 81.2%

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

   if -2.2000000000000001e185 < j < -3.19999999999999986e112 or -1.7499999999999999e-129 < j < 1.35e20

   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 t around 0 69.3%

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

      1. associate-*r* 69.4%

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

      2. associate-*r* 69.4%

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

      3. *-commutative 69.4%

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

      4. associate-*r* 73.1%

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

      5. distribute-rgt-in 75.0%

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

      6. +-commutative 75.0%

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

      7. mul-1-neg 75.0%

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

      8. unsub-neg 75.0%

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

      9. *-commutative 75.0%

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

      10. *-commutative 75.0%

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

      11. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around inf 68.7%

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

      1. associate-*r* 72.2%

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

      2. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   if -3.19999999999999986e112 < j < -1.7499999999999999e-129 or 1.35e20 < 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 inf 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-*r* 67.4%

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

   5. Simplified 67.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+185}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+112} \lor \neg \left(j \leq -1.75 \cdot 10^{-129}\right) \land j \leq 1.35 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - c \cdot \frac{z}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= i -4.1e+86)
     (* i (- (* a b) (* y j)))
     (if (<= i 2.15e-103)
       (+ (* x (- (* y z) (* t a))) t_1)
       (if (<= i 2.1e+105)
         (- (* y (- (* x z) (* i j))) (* b (* z c)))
         (if (<= i 2e+296)
           (+ t_1 (* b (* a i)))
           (* b (* a (- i (* c (/ z a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -4.1e+86) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= 2.15e-103) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (i <= 2.1e+105) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (i <= 2e+296) {
		tmp = t_1 + (b * (a * i));
	} else {
		tmp = b * (a * (i - (c * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (i <= (-4.1d+86)) then
        tmp = i * ((a * b) - (y * j))
    else if (i <= 2.15d-103) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (i <= 2.1d+105) then
        tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
    else if (i <= 2d+296) then
        tmp = t_1 + (b * (a * i))
    else
        tmp = b * (a * (i - (c * (z / 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 t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -4.1e+86) {
		tmp = i * ((a * b) - (y * j));
	} else if (i <= 2.15e-103) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (i <= 2.1e+105) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (i <= 2e+296) {
		tmp = t_1 + (b * (a * i));
	} else {
		tmp = b * (a * (i - (c * (z / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if i <= -4.1e+86:
		tmp = i * ((a * b) - (y * j))
	elif i <= 2.15e-103:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif i <= 2.1e+105:
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
	elif i <= 2e+296:
		tmp = t_1 + (b * (a * i))
	else:
		tmp = b * (a * (i - (c * (z / a))))
	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)))
	tmp = 0.0
	if (i <= -4.1e+86)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (i <= 2.15e-103)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (i <= 2.1e+105)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)));
	elseif (i <= 2e+296)
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	else
		tmp = Float64(b * Float64(a * Float64(i - Float64(c * Float64(z / a)))));
	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));
	tmp = 0.0;
	if (i <= -4.1e+86)
		tmp = i * ((a * b) - (y * j));
	elseif (i <= 2.15e-103)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (i <= 2.1e+105)
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	elseif (i <= 2e+296)
		tmp = t_1 + (b * (a * i));
	else
		tmp = b * (a * (i - (c * (z / a))));
	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]}, If[LessEqual[i, -4.1e+86], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e-103], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[i, 2.1e+105], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e+296], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * N[(i - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.0999999999999999e86

   1. Initial program 60.4%

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

   3. Taylor expanded in i around inf 77.3%

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

      1. distribute-lft-out-- 77.3%

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

      2. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in i around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. distribute-rgt-neg-out 77.3%

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

      5. sub-neg 77.3%

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

      6. *-commutative 77.3%

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

      7. distribute-neg-in 77.3%

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

      8. distribute-lft-neg-in 77.3%

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

      9. remove-double-neg 77.3%

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

   8. Simplified 77.3%

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

   if -4.0999999999999999e86 < i < 2.15000000000000011e-103

   1. Initial program 83.0%

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

   3. Taylor expanded in b around 0 69.5%

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

   if 2.15000000000000011e-103 < i < 2.1000000000000001e105

   1. Initial program 68.2%

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

   3. Taylor expanded in t around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. associate-*r* 70.4%

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

      3. *-commutative 70.4%

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

      4. associate-*r* 72.8%

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

      5. distribute-rgt-in 72.8%

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

      6. +-commutative 72.8%

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

      7. mul-1-neg 72.8%

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

      8. unsub-neg 72.8%

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

      9. *-commutative 72.8%

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

      10. *-commutative 72.8%

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

      11. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in c around inf 67.4%

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

   if 2.1000000000000001e105 < i < 1.99999999999999996e296

   1. Initial program 66.5%

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

   3. Taylor expanded in i around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*r* 82.5%

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

   5. Simplified 82.5%

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

   if 1.99999999999999996e296 < i

   1. Initial program 40.0%

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

   3. Taylor expanded in b around inf 60.3%

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

      1. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in c around inf 80.3%

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

      1. associate-/l* 80.0%

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

   8. Simplified 80.0%

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

   9. Taylor expanded in a around inf 60.3%

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

       1. mul-1-neg 60.3%

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

       2. unsub-neg 60.3%

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

       3. associate-/l* 80.3%

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

   11. Simplified 80.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{+296}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - c \cdot \frac{z}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -0.00178:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* b (* a i))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -0.00178)
     t_2
     (if (<= z 4.8e-135)
       t_1
       (if (<= z 4.3e-94)
         (* t (- (* c j) (* x a)))
         (if (<= z 9.5e+169) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (b * (a * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -0.00178) {
		tmp = t_2;
	} else if (z <= 4.8e-135) {
		tmp = t_1;
	} else if (z <= 4.3e-94) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 9.5e+169) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (b * (a * i))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-0.00178d0)) then
        tmp = t_2
    else if (z <= 4.8d-135) then
        tmp = t_1
    else if (z <= 4.3d-94) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 9.5d+169) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (b * (a * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -0.00178) {
		tmp = t_2;
	} else if (z <= 4.8e-135) {
		tmp = t_1;
	} else if (z <= 4.3e-94) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 9.5e+169) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (b * (a * i))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -0.00178:
		tmp = t_2
	elif z <= 4.8e-135:
		tmp = t_1
	elif z <= 4.3e-94:
		tmp = t * ((c * j) - (x * a))
	elif z <= 9.5e+169:
		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(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(a * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -0.00178)
		tmp = t_2;
	elseif (z <= 4.8e-135)
		tmp = t_1;
	elseif (z <= 4.3e-94)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 9.5e+169)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (b * (a * i));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -0.00178)
		tmp = t_2;
	elseif (z <= 4.8e-135)
		tmp = t_1;
	elseif (z <= 4.3e-94)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 9.5e+169)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00178], t$95$2, If[LessEqual[z, 4.8e-135], t$95$1, If[LessEqual[z, 4.3e-94], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+169], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0017799999999999999 or 9.4999999999999995e169 < z

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   if -0.0017799999999999999 < z < 4.7999999999999997e-135 or 4.2999999999999998e-94 < z < 9.4999999999999995e169

   1. Initial program 81.4%

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

   3. Taylor expanded in i around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-*r* 71.4%

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

   5. Simplified 71.4%

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

   if 4.7999999999999997e-135 < z < 4.2999999999999998e-94

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 89.7%

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

      1. +-commutative 89.7%

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

      2. mul-1-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. *-commutative 89.7%

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

   5. Simplified 89.7%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00178:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-135}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.15 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(t \cdot \left(c - a \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -2.15e+52)
     t_1
     (if (<= i -4.5e-27)
       (* b (* c (- (* a (/ i c)) z)))
       (if (<= i -1.05e-60)
         (* y (- (* x z) (* i j)))
         (if (<= i 7.5e-118)
           (* j (* t (- c (* a (/ x j)))))
           (if (<= i 2.4e+32) (* z (- (* x y) (* b c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.15e+52) {
		tmp = t_1;
	} else if (i <= -4.5e-27) {
		tmp = b * (c * ((a * (i / c)) - z));
	} else if (i <= -1.05e-60) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 7.5e-118) {
		tmp = j * (t * (c - (a * (x / j))));
	} else if (i <= 2.4e+32) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-2.15d+52)) then
        tmp = t_1
    else if (i <= (-4.5d-27)) then
        tmp = b * (c * ((a * (i / c)) - z))
    else if (i <= (-1.05d-60)) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= 7.5d-118) then
        tmp = j * (t * (c - (a * (x / j))))
    else if (i <= 2.4d+32) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.15e+52) {
		tmp = t_1;
	} else if (i <= -4.5e-27) {
		tmp = b * (c * ((a * (i / c)) - z));
	} else if (i <= -1.05e-60) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 7.5e-118) {
		tmp = j * (t * (c - (a * (x / j))));
	} else if (i <= 2.4e+32) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.15e+52:
		tmp = t_1
	elif i <= -4.5e-27:
		tmp = b * (c * ((a * (i / c)) - z))
	elif i <= -1.05e-60:
		tmp = y * ((x * z) - (i * j))
	elif i <= 7.5e-118:
		tmp = j * (t * (c - (a * (x / j))))
	elif i <= 2.4e+32:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.15e+52)
		tmp = t_1;
	elseif (i <= -4.5e-27)
		tmp = Float64(b * Float64(c * Float64(Float64(a * Float64(i / c)) - z)));
	elseif (i <= -1.05e-60)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= 7.5e-118)
		tmp = Float64(j * Float64(t * Float64(c - Float64(a * Float64(x / j)))));
	elseif (i <= 2.4e+32)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.15e+52)
		tmp = t_1;
	elseif (i <= -4.5e-27)
		tmp = b * (c * ((a * (i / c)) - z));
	elseif (i <= -1.05e-60)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= 7.5e-118)
		tmp = j * (t * (c - (a * (x / j))));
	elseif (i <= 2.4e+32)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.15e+52], t$95$1, If[LessEqual[i, -4.5e-27], N[(b * N[(c * N[(N[(a * N[(i / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.05e-60], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e-118], N[(j * N[(t * N[(c - N[(a * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e+32], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.15e52 or 2.39999999999999991e32 < i

   1. Initial program 65.1%

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

   3. Taylor expanded in i around inf 71.7%

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

      1. distribute-lft-out-- 71.7%

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

      2. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in i around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

      4. distribute-rgt-neg-out 71.7%

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

      5. sub-neg 71.7%

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

      6. *-commutative 71.7%

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

      7. distribute-neg-in 71.7%

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

      8. distribute-lft-neg-in 71.7%

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

      9. remove-double-neg 71.7%

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

   8. Simplified 71.7%

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

   if -2.15e52 < i < -4.5000000000000002e-27

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in c around inf 61.8%

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

      1. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

   if -4.5000000000000002e-27 < i < -1.04999999999999996e-60

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

      4. *-commutative 76.3%

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

      5. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -1.04999999999999996e-60 < i < 7.49999999999999978e-118

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf 81.9%

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

   4. Taylor expanded in t around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

      3. associate-/l* 62.3%

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

   6. Simplified 62.3%

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

   if 7.49999999999999978e-118 < i < 2.39999999999999991e32

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. *-commutative 64.4%

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

   5. Simplified 64.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.15 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(c \cdot \left(a \cdot \frac{i}{c} - z\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(t \cdot \left(c - a \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -2.5e-38)
     t_1
     (if (<= i -2.8e-217)
       (* x (- (* y z) (* t a)))
       (if (<= i -2.1e-264)
         (* j (- (* t c) (* y i)))
         (if (<= i 3.7e-123)
           (* t (- (* c j) (* x a)))
           (if (<= i 8.6e+30) (* z (- (* x y) (* b c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.5e-38) {
		tmp = t_1;
	} else if (i <= -2.8e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= -2.1e-264) {
		tmp = j * ((t * c) - (y * i));
	} else if (i <= 3.7e-123) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 8.6e+30) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-2.5d-38)) then
        tmp = t_1
    else if (i <= (-2.8d-217)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= (-2.1d-264)) then
        tmp = j * ((t * c) - (y * i))
    else if (i <= 3.7d-123) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 8.6d+30) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.5e-38) {
		tmp = t_1;
	} else if (i <= -2.8e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= -2.1e-264) {
		tmp = j * ((t * c) - (y * i));
	} else if (i <= 3.7e-123) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 8.6e+30) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.5e-38:
		tmp = t_1
	elif i <= -2.8e-217:
		tmp = x * ((y * z) - (t * a))
	elif i <= -2.1e-264:
		tmp = j * ((t * c) - (y * i))
	elif i <= 3.7e-123:
		tmp = t * ((c * j) - (x * a))
	elif i <= 8.6e+30:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.5e-38)
		tmp = t_1;
	elseif (i <= -2.8e-217)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= -2.1e-264)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (i <= 3.7e-123)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 8.6e+30)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.5e-38)
		tmp = t_1;
	elseif (i <= -2.8e-217)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= -2.1e-264)
		tmp = j * ((t * c) - (y * i));
	elseif (i <= 3.7e-123)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 8.6e+30)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.5e-38], t$95$1, If[LessEqual[i, -2.8e-217], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.1e-264], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e-123], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.6e+30], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.50000000000000017e-38 or 8.6e30 < i

   1. Initial program 66.1%

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

   3. Taylor expanded in i around inf 67.8%

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

      1. distribute-lft-out-- 67.8%

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

      2. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in i around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. *-commutative 67.8%

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

      3. *-commutative 67.8%

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

      4. distribute-rgt-neg-out 67.8%

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

      5. sub-neg 67.8%

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

      6. *-commutative 67.8%

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

      7. distribute-neg-in 67.8%

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

      8. distribute-lft-neg-in 67.8%

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

      9. remove-double-neg 67.8%

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

   8. Simplified 67.8%

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

   if -2.50000000000000017e-38 < i < -2.8e-217

   1. Initial program 79.5%

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

   3. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -2.8e-217 < i < -2.1000000000000002e-264

   1. Initial program 94.0%

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

   3. Taylor expanded in j around inf 76.0%

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

   if -2.1000000000000002e-264 < i < 3.70000000000000015e-123

   1. Initial program 84.1%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if 3.70000000000000015e-123 < i < 8.6e30

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. *-commutative 64.4%

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

   5. Simplified 64.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -3.4e+100)
     t_3
     (if (<= x -1.25e-190)
       t_2
       (if (<= x -6.5e-238)
         t_1
         (if (<= x -5.2e-308) t_2 (if (<= x 6000.0) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.4e+100) {
		tmp = t_3;
	} else if (x <= -1.25e-190) {
		tmp = t_2;
	} else if (x <= -6.5e-238) {
		tmp = t_1;
	} else if (x <= -5.2e-308) {
		tmp = t_2;
	} else if (x <= 6000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-3.4d+100)) then
        tmp = t_3
    else if (x <= (-1.25d-190)) then
        tmp = t_2
    else if (x <= (-6.5d-238)) then
        tmp = t_1
    else if (x <= (-5.2d-308)) then
        tmp = t_2
    else if (x <= 6000.0d0) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.4e+100) {
		tmp = t_3;
	} else if (x <= -1.25e-190) {
		tmp = t_2;
	} else if (x <= -6.5e-238) {
		tmp = t_1;
	} else if (x <= -5.2e-308) {
		tmp = t_2;
	} else if (x <= 6000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.4e+100:
		tmp = t_3
	elif x <= -1.25e-190:
		tmp = t_2
	elif x <= -6.5e-238:
		tmp = t_1
	elif x <= -5.2e-308:
		tmp = t_2
	elif x <= 6000.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.4e+100)
		tmp = t_3;
	elseif (x <= -1.25e-190)
		tmp = t_2;
	elseif (x <= -6.5e-238)
		tmp = t_1;
	elseif (x <= -5.2e-308)
		tmp = t_2;
	elseif (x <= 6000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.4e+100)
		tmp = t_3;
	elseif (x <= -1.25e-190)
		tmp = t_2;
	elseif (x <= -6.5e-238)
		tmp = t_1;
	elseif (x <= -5.2e-308)
		tmp = t_2;
	elseif (x <= 6000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+100], t$95$3, If[LessEqual[x, -1.25e-190], t$95$2, If[LessEqual[x, -6.5e-238], t$95$1, If[LessEqual[x, -5.2e-308], t$95$2, If[LessEqual[x, 6000.0], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.39999999999999994e100 or 6e3 < x

   1. Initial program 71.2%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if -3.39999999999999994e100 < x < -1.25000000000000009e-190 or -6.5000000000000006e-238 < x < -5.1999999999999999e-308

   1. Initial program 78.0%

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

   3. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -1.25000000000000009e-190 < x < -6.5000000000000006e-238 or -5.1999999999999999e-308 < x < 6e3

   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 j around inf 63.4%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-308}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 6000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= y -3.1e+20)
     t_2
     (if (<= y -1.6e-103)
       t_1
       (if (<= y -1.7e-162)
         t_2
         (if (<= y 8.8e-70)
           t_1
           (if (<= y 1.55e+106) (* t (- (* c j) (* x a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (y <= -3.1e+20) {
		tmp = t_2;
	} else if (y <= -1.6e-103) {
		tmp = t_1;
	} else if (y <= -1.7e-162) {
		tmp = t_2;
	} else if (y <= 8.8e-70) {
		tmp = t_1;
	} else if (y <= 1.55e+106) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (y <= (-3.1d+20)) then
        tmp = t_2
    else if (y <= (-1.6d-103)) then
        tmp = t_1
    else if (y <= (-1.7d-162)) then
        tmp = t_2
    else if (y <= 8.8d-70) then
        tmp = t_1
    else if (y <= 1.55d+106) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (y <= -3.1e+20) {
		tmp = t_2;
	} else if (y <= -1.6e-103) {
		tmp = t_1;
	} else if (y <= -1.7e-162) {
		tmp = t_2;
	} else if (y <= 8.8e-70) {
		tmp = t_1;
	} else if (y <= 1.55e+106) {
		tmp = t * ((c * j) - (x * a));
	} 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 y <= -3.1e+20:
		tmp = t_2
	elif y <= -1.6e-103:
		tmp = t_1
	elif y <= -1.7e-162:
		tmp = t_2
	elif y <= 8.8e-70:
		tmp = t_1
	elif y <= 1.55e+106:
		tmp = t * ((c * j) - (x * a))
	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 (y <= -3.1e+20)
		tmp = t_2;
	elseif (y <= -1.6e-103)
		tmp = t_1;
	elseif (y <= -1.7e-162)
		tmp = t_2;
	elseif (y <= 8.8e-70)
		tmp = t_1;
	elseif (y <= 1.55e+106)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (y <= -3.1e+20)
		tmp = t_2;
	elseif (y <= -1.6e-103)
		tmp = t_1;
	elseif (y <= -1.7e-162)
		tmp = t_2;
	elseif (y <= 8.8e-70)
		tmp = t_1;
	elseif (y <= 1.55e+106)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(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[y, -3.1e+20], t$95$2, If[LessEqual[y, -1.6e-103], t$95$1, If[LessEqual[y, -1.7e-162], t$95$2, If[LessEqual[y, 8.8e-70], t$95$1, If[LessEqual[y, 1.55e+106], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e20 or -1.59999999999999988e-103 < y < -1.7e-162 or 1.55e106 < y

   1. Initial program 69.7%

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

   3. Taylor expanded in j around inf 60.4%

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

   if -3.1e20 < y < -1.59999999999999988e-103 or -1.7e-162 < y < 8.7999999999999996e-70

   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 b around inf 61.9%

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

      1. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if 8.7999999999999996e-70 < y < 1.55e106

   1. Initial program 75.1%

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

   3. Taylor expanded in t around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. *-commutative 51.2%

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

   5. Simplified 51.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-162}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.32 \cdot 10^{-79} \lor \neg \left(i \leq 1.15 \cdot 10^{-175}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.35e+141)
   (* i (- (* a b) (* y j)))
   (if (or (<= i -1.32e-79) (not (<= i 1.15e-175)))
     (- (* y (- (* x z) (* i j))) (* b (- (* z c) (* a i))))
     (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y 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 <= -1.35e+141) {
		tmp = i * ((a * b) - (y * j));
	} else if ((i <= -1.32e-79) || !(i <= 1.15e-175)) {
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 <= (-1.35d+141)) then
        tmp = i * ((a * b) - (y * j))
    else if ((i <= (-1.32d-79)) .or. (.not. (i <= 1.15d-175))) then
        tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 <= -1.35e+141) {
		tmp = i * ((a * b) - (y * j));
	} else if ((i <= -1.32e-79) || !(i <= 1.15e-175)) {
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.35e+141:
		tmp = i * ((a * b) - (y * j))
	elif (i <= -1.32e-79) or not (i <= 1.15e-175):
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.35e+141)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif ((i <= -1.32e-79) || !(i <= 1.15e-175))
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.35e+141)
		tmp = i * ((a * b) - (y * j));
	elseif ((i <= -1.32e-79) || ~((i <= 1.15e-175)))
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.35e+141], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -1.32e-79], N[Not[LessEqual[i, 1.15e-175]], $MachinePrecision]], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.35e141

   1. Initial program 54.7%

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

   3. Taylor expanded in i around inf 84.9%

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

      1. distribute-lft-out-- 84.9%

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

      2. *-commutative 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in i around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. *-commutative 84.9%

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

      3. *-commutative 84.9%

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

      4. distribute-rgt-neg-out 84.9%

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

      5. sub-neg 84.9%

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

      6. *-commutative 84.9%

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

      7. distribute-neg-in 84.9%

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

      8. distribute-lft-neg-in 84.9%

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

      9. remove-double-neg 84.9%

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

   8. Simplified 84.9%

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

   if -1.35e141 < i < -1.32e-79 or 1.15e-175 < i

   1. Initial program 72.0%

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

   3. Taylor expanded in t around 0 68.6%

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

      1. associate-*r* 67.3%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*r* 68.6%

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

      5. distribute-rgt-in 73.2%

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

      6. +-commutative 73.2%

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

      7. mul-1-neg 73.2%

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

      8. unsub-neg 73.2%

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

      9. *-commutative 73.2%

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

      10. *-commutative 73.2%

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

      11. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -1.32e-79 < i < 1.15e-175

   1. Initial program 84.2%

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

   3. Taylor expanded in b around 0 78.6%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.32 \cdot 10^{-79} \lor \neg \left(i \leq 1.15 \cdot 10^{-175}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 5.3 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* a (* b i))))
   (if (<= i -1.9e+123)
     t_2
     (if (<= i -8.5e-210)
       t_1
       (if (<= i -1.3e-302)
         (* c (* t j))
         (if (<= i 5e-124) (* a (* t (- x))) (if (<= i 5.3e+47) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -1.9e+123) {
		tmp = t_2;
	} else if (i <= -8.5e-210) {
		tmp = t_1;
	} else if (i <= -1.3e-302) {
		tmp = c * (t * j);
	} else if (i <= 5e-124) {
		tmp = a * (t * -x);
	} else if (i <= 5.3e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = a * (b * i)
    if (i <= (-1.9d+123)) then
        tmp = t_2
    else if (i <= (-8.5d-210)) then
        tmp = t_1
    else if (i <= (-1.3d-302)) then
        tmp = c * (t * j)
    else if (i <= 5d-124) then
        tmp = a * (t * -x)
    else if (i <= 5.3d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -1.9e+123) {
		tmp = t_2;
	} else if (i <= -8.5e-210) {
		tmp = t_1;
	} else if (i <= -1.3e-302) {
		tmp = c * (t * j);
	} else if (i <= 5e-124) {
		tmp = a * (t * -x);
	} else if (i <= 5.3e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = a * (b * i)
	tmp = 0
	if i <= -1.9e+123:
		tmp = t_2
	elif i <= -8.5e-210:
		tmp = t_1
	elif i <= -1.3e-302:
		tmp = c * (t * j)
	elif i <= 5e-124:
		tmp = a * (t * -x)
	elif i <= 5.3e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -1.9e+123)
		tmp = t_2;
	elseif (i <= -8.5e-210)
		tmp = t_1;
	elseif (i <= -1.3e-302)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 5e-124)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 5.3e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -1.9e+123)
		tmp = t_2;
	elseif (i <= -8.5e-210)
		tmp = t_1;
	elseif (i <= -1.3e-302)
		tmp = c * (t * j);
	elseif (i <= 5e-124)
		tmp = a * (t * -x);
	elseif (i <= 5.3e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.9e+123], t$95$2, If[LessEqual[i, -8.5e-210], t$95$1, If[LessEqual[i, -1.3e-302], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-124], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.3e+47], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.89999999999999997e123 or 5.3e47 < i

   1. Initial program 60.6%

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

   3. Taylor expanded in b around inf 53.4%

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

      1. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in i around inf 49.2%

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

   if -1.89999999999999997e123 < i < -8.4999999999999997e-210 or 5.0000000000000003e-124 < i < 5.3e47

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 42.7%

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

      1. *-commutative 42.7%

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

   5. Simplified 42.7%

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

   6. Taylor expanded in y around inf 31.0%

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

      1. *-commutative 31.0%

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

      2. associate-*l* 32.9%

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

   8. Simplified 32.9%

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

   if -8.4999999999999997e-210 < i < -1.30000000000000006e-302

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 52.8%

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

   if -1.30000000000000006e-302 < i < 5.0000000000000003e-124

   1. Initial program 78.7%

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

   3. Taylor expanded in x around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in y around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

      3. distribute-rgt-neg-in 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 5.3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+19} \lor \neg \left(y \leq -1.4 \cdot 10^{-101} \lor \neg \left(y \leq -1.12 \cdot 10^{-162}\right) \land y \leq 3 \cdot 10^{-39}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.1e+19)
         (not
          (or (<= y -1.4e-101) (and (not (<= y -1.12e-162)) (<= y 3e-39)))))
   (* j (- (* t c) (* y i)))
   (* b (- (* a i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.1e+19) || !((y <= -1.4e-101) || (!(y <= -1.12e-162) && (y <= 3e-39)))) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-1.1d+19)) .or. (.not. (y <= (-1.4d-101)) .or. (.not. (y <= (-1.12d-162))) .and. (y <= 3d-39))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.1e+19) || !((y <= -1.4e-101) || (!(y <= -1.12e-162) && (y <= 3e-39)))) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -1.1e+19) or not ((y <= -1.4e-101) or (not (y <= -1.12e-162) and (y <= 3e-39))):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.1e+19) || !((y <= -1.4e-101) || (!(y <= -1.12e-162) && (y <= 3e-39))))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -1.1e+19) || ~(((y <= -1.4e-101) || (~((y <= -1.12e-162)) && (y <= 3e-39)))))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.1e+19], N[Not[Or[LessEqual[y, -1.4e-101], And[N[Not[LessEqual[y, -1.12e-162]], $MachinePrecision], LessEqual[y, 3e-39]]]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e19 or -1.39999999999999995e-101 < y < -1.12e-162 or 3.00000000000000028e-39 < y

   1. Initial program 69.3%

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

   3. Taylor expanded in j around inf 57.0%

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

   if -1.1e19 < y < -1.39999999999999995e-101 or -1.12e-162 < y < 3.00000000000000028e-39

   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 b around inf 58.8%

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

      1. *-commutative 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+19} \lor \neg \left(y \leq -1.4 \cdot 10^{-101} \lor \neg \left(y \leq -1.12 \cdot 10^{-162}\right) \land y \leq 3 \cdot 10^{-39}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.5e+106)
   (* i (* j (- y)))
   (if (<= y 2.3e-67)
     (* b (- (* a i) (* z c)))
     (if (<= y 4.1e+106)
       (* t (* x (- a)))
       (if (<= y 3.3e+208) (* t (* c j)) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.5e+106) {
		tmp = i * (j * -y);
	} else if (y <= 2.3e-67) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 4.1e+106) {
		tmp = t * (x * -a);
	} else if (y <= 3.3e+208) {
		tmp = t * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7.5d+106)) then
        tmp = i * (j * -y)
    else if (y <= 2.3d-67) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 4.1d+106) then
        tmp = t * (x * -a)
    else if (y <= 3.3d+208) then
        tmp = t * (c * j)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.5e+106) {
		tmp = i * (j * -y);
	} else if (y <= 2.3e-67) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 4.1e+106) {
		tmp = t * (x * -a);
	} else if (y <= 3.3e+208) {
		tmp = t * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7.5e+106:
		tmp = i * (j * -y)
	elif y <= 2.3e-67:
		tmp = b * ((a * i) - (z * c))
	elif y <= 4.1e+106:
		tmp = t * (x * -a)
	elif y <= 3.3e+208:
		tmp = t * (c * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.5e+106)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (y <= 2.3e-67)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 4.1e+106)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 3.3e+208)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7.5e+106)
		tmp = i * (j * -y);
	elseif (y <= 2.3e-67)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 4.1e+106)
		tmp = t * (x * -a);
	elseif (y <= 3.3e+208)
		tmp = t * (c * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.5e+106], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-67], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+106], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+208], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.50000000000000058e106

   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 i around inf 57.6%

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

      1. distribute-lft-out-- 57.6%

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

      2. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in b around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. *-commutative 50.3%

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

      3. mul-1-neg 50.3%

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

      4. unsub-neg 50.3%

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

      5. *-commutative 50.3%

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

      6. associate-/l* 55.7%

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

      7. *-commutative 55.7%

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

   8. Simplified 55.7%

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

   9. Taylor expanded in b around 0 50.4%

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

       1. associate-*r* 50.4%

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

       2. neg-mul-1 50.4%

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

       3. *-commutative 50.4%

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

   11. Simplified 50.4%

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

   if -7.50000000000000058e106 < y < 2.3e-67

   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 b around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   if 2.3e-67 < y < 4.1000000000000002e106

   1. Initial program 75.1%

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

   3. Taylor expanded in t around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in j around 0 44.3%

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

      1. associate-*r* 44.3%

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

      2. *-commutative 44.3%

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

      3. neg-mul-1 44.3%

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

   8. Simplified 44.3%

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

   if 4.1000000000000002e106 < y < 3.3e208

   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 t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 50.7%

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

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if 3.3e208 < y

   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 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around inf 56.6%

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

      1. *-commutative 56.6%

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

   8. Simplified 56.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-67}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.3 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-301}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= i -1.9e+123)
     t_1
     (if (<= i -5.3e-210)
       (* y (* x z))
       (if (<= i -2.8e-301)
         (* c (* t j))
         (if (<= i 1.55e+47) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -1.9e+123) {
		tmp = t_1;
	} else if (i <= -5.3e-210) {
		tmp = y * (x * z);
	} else if (i <= -2.8e-301) {
		tmp = c * (t * j);
	} else if (i <= 1.55e+47) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (i <= (-1.9d+123)) then
        tmp = t_1
    else if (i <= (-5.3d-210)) then
        tmp = y * (x * z)
    else if (i <= (-2.8d-301)) then
        tmp = c * (t * j)
    else if (i <= 1.55d+47) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -1.9e+123) {
		tmp = t_1;
	} else if (i <= -5.3e-210) {
		tmp = y * (x * z);
	} else if (i <= -2.8e-301) {
		tmp = c * (t * j);
	} else if (i <= 1.55e+47) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if i <= -1.9e+123:
		tmp = t_1
	elif i <= -5.3e-210:
		tmp = y * (x * z)
	elif i <= -2.8e-301:
		tmp = c * (t * j)
	elif i <= 1.55e+47:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -1.9e+123)
		tmp = t_1;
	elseif (i <= -5.3e-210)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= -2.8e-301)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 1.55e+47)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (i <= -1.9e+123)
		tmp = t_1;
	elseif (i <= -5.3e-210)
		tmp = y * (x * z);
	elseif (i <= -2.8e-301)
		tmp = c * (t * j);
	elseif (i <= 1.55e+47)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.9e+123], t$95$1, If[LessEqual[i, -5.3e-210], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.8e-301], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.55e+47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.89999999999999997e123 or 1.55e47 < i

   1. Initial program 60.6%

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

   3. Taylor expanded in b around inf 53.4%

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

      1. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in i around inf 49.2%

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

   if -1.89999999999999997e123 < i < -5.3000000000000001e-210

   1. Initial program 77.5%

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

   3. Taylor expanded in x around inf 40.4%

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

      1. *-commutative 40.4%

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

   5. Simplified 40.4%

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

   6. Taylor expanded in y around inf 28.0%

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

      1. *-commutative 28.0%

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

      2. associate-*l* 29.7%

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

   8. Simplified 29.7%

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

   if -5.3000000000000001e-210 < i < -2.8000000000000001e-301

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 52.8%

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

   if -2.8000000000000001e-301 < i < 1.55e47

   1. Initial program 76.0%

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

   3. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. *-commutative 35.3%

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

   8. Simplified 35.3%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -5.3 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-301}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (* b i))))
   (if (<= i -1.55e-9)
     t_2
     (if (<= i -2.15e-209)
       t_1
       (if (<= i -1.3e-299) (* c (* t j)) (if (<= i 1.7e+48) 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);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -1.55e-9) {
		tmp = t_2;
	} else if (i <= -2.15e-209) {
		tmp = t_1;
	} else if (i <= -1.3e-299) {
		tmp = c * (t * j);
	} else if (i <= 1.7e+48) {
		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_2 = a * (b * i)
    if (i <= (-1.55d-9)) then
        tmp = t_2
    else if (i <= (-2.15d-209)) then
        tmp = t_1
    else if (i <= (-1.3d-299)) then
        tmp = c * (t * j)
    else if (i <= 1.7d+48) 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);
	double t_2 = a * (b * i);
	double tmp;
	if (i <= -1.55e-9) {
		tmp = t_2;
	} else if (i <= -2.15e-209) {
		tmp = t_1;
	} else if (i <= -1.3e-299) {
		tmp = c * (t * j);
	} else if (i <= 1.7e+48) {
		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_2 = a * (b * i)
	tmp = 0
	if i <= -1.55e-9:
		tmp = t_2
	elif i <= -2.15e-209:
		tmp = t_1
	elif i <= -1.3e-299:
		tmp = c * (t * j)
	elif i <= 1.7e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -1.55e-9)
		tmp = t_2;
	elseif (i <= -2.15e-209)
		tmp = t_1;
	elseif (i <= -1.3e-299)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 1.7e+48)
		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_2 = a * (b * i);
	tmp = 0.0;
	if (i <= -1.55e-9)
		tmp = t_2;
	elseif (i <= -2.15e-209)
		tmp = t_1;
	elseif (i <= -1.3e-299)
		tmp = c * (t * j);
	elseif (i <= 1.7e+48)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.55e-9], t$95$2, If[LessEqual[i, -2.15e-209], t$95$1, If[LessEqual[i, -1.3e-299], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e+48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.55000000000000002e-9 or 1.7000000000000002e48 < i

   1. Initial program 64.8%

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

   3. Taylor expanded in b around inf 49.7%

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

      1. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in i around inf 40.7%

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

   if -1.55000000000000002e-9 < i < -2.15000000000000003e-209 or -1.2999999999999999e-299 < i < 1.7000000000000002e48

   1. Initial program 77.5%

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

   3. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

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

   8. Simplified 35.4%

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

   if -2.15000000000000003e-209 < i < -1.2999999999999999e-299

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 52.8%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -7.8e+105)
   (* i (* a b))
   (if (<= a 5.3e-73) (* c (* t j)) (* b (* a 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 (a <= -7.8e+105) {
		tmp = i * (a * b);
	} else if (a <= 5.3e-73) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 (a <= (-7.8d+105)) then
        tmp = i * (a * b)
    else if (a <= 5.3d-73) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 (a <= -7.8e+105) {
		tmp = i * (a * b);
	} else if (a <= 5.3e-73) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -7.8e+105:
		tmp = i * (a * b)
	elif a <= 5.3e-73:
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -7.8e+105)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= 5.3e-73)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -7.8e+105)
		tmp = i * (a * b);
	elseif (a <= 5.3e-73)
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -7.8e+105], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e-73], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.79999999999999957e105

   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 i around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in b around inf 38.1%

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

      1. +-commutative 38.1%

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

      2. *-commutative 38.1%

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

      3. mul-1-neg 38.1%

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

      4. unsub-neg 38.1%

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

      5. *-commutative 38.1%

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

      6. associate-/l* 44.3%

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

      7. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   9. Taylor expanded in b around inf 44.8%

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

       1. associate-*r* 44.8%

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

       2. *-commutative 44.8%

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

   11. Simplified 44.8%

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

   if -7.79999999999999957e105 < a < 5.29999999999999972e-73

   1. Initial program 75.8%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. +-commutative 40.8%

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

      2. mul-1-neg 40.8%

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

      3. unsub-neg 40.8%

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

      4. *-commutative 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in j around inf 32.3%

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

   if 5.29999999999999972e-73 < a

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 49.0%

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

      1. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in i around inf 40.4%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -7.2e+105)
   (* a (* b i))
   (if (<= a 2.3e-74) (* c (* t j)) (* b (* a 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 (a <= -7.2e+105) {
		tmp = a * (b * i);
	} else if (a <= 2.3e-74) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 (a <= (-7.2d+105)) then
        tmp = a * (b * i)
    else if (a <= 2.3d-74) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 (a <= -7.2e+105) {
		tmp = a * (b * i);
	} else if (a <= 2.3e-74) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -7.2e+105:
		tmp = a * (b * i)
	elif a <= 2.3e-74:
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -7.2e+105)
		tmp = Float64(a * Float64(b * i));
	elseif (a <= 2.3e-74)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -7.2e+105)
		tmp = a * (b * i);
	elseif (a <= 2.3e-74)
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -7.2e+105], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-74], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.1999999999999998e105

   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 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in i around inf 44.8%

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

   if -7.1999999999999998e105 < a < 2.2999999999999998e-74

   1. Initial program 75.8%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. +-commutative 40.8%

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

      2. mul-1-neg 40.8%

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

      3. unsub-neg 40.8%

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

      4. *-commutative 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in j around inf 32.3%

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

   if 2.2999999999999998e-74 < a

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 49.0%

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

      1. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in i around inf 40.4%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.3% 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 73.1%

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

3. Taylor expanded in b around inf 41.0%

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

   1. *-commutative 41.0%

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

5. Simplified 41.0%

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

6. Taylor expanded in i around inf 24.0%

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

Developer target: 69.3% 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 2024101 
(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)))))