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

Percentage Accurate: 73.4% → 82.2%

Time: 26.4s

Alternatives: 25

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 8.9%

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

   4. Taylor expanded in a around inf 49.4%

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

      1. associate-*r* 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-/l* 51.7%

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

   6. Simplified 51.7%

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

4. Final simplification 86.8%

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

Alternative 2: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;y \leq -0.115:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(i \cdot \frac{t}{x} - c \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= y -1.25e+119)
     (* y (* x (- z (* i (/ j x)))))
     (if (<= y -0.115)
       (* i (- (* t b) (* y j)))
       (if (<= y -1.02e-45)
         (* j (- (* a c) (* y i)))
         (if (<= y 1.95e-299)
           t_1
           (if (<= y 8.8e-197)
             (* b (- (* t i) (* z c)))
             (if (<= y 7.6e-87)
               t_1
               (if (<= y 1.8e-63)
                 (* (* x b) (- (* i (/ t x)) (* c (/ z x))))
                 (if (<= y 1.85e+20) t_1 (* y (- (* x z) (* i j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -1.25e+119) {
		tmp = y * (x * (z - (i * (j / x))));
	} else if (y <= -0.115) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= -1.02e-45) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 1.95e-299) {
		tmp = t_1;
	} else if (y <= 8.8e-197) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 7.6e-87) {
		tmp = t_1;
	} else if (y <= 1.8e-63) {
		tmp = (x * b) * ((i * (t / x)) - (c * (z / x)));
	} else if (y <= 1.85e+20) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (y <= (-1.25d+119)) then
        tmp = y * (x * (z - (i * (j / x))))
    else if (y <= (-0.115d0)) then
        tmp = i * ((t * b) - (y * j))
    else if (y <= (-1.02d-45)) then
        tmp = j * ((a * c) - (y * i))
    else if (y <= 1.95d-299) then
        tmp = t_1
    else if (y <= 8.8d-197) then
        tmp = b * ((t * i) - (z * c))
    else if (y <= 7.6d-87) then
        tmp = t_1
    else if (y <= 1.8d-63) then
        tmp = (x * b) * ((i * (t / x)) - (c * (z / x)))
    else if (y <= 1.85d+20) then
        tmp = t_1
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -1.25e+119) {
		tmp = y * (x * (z - (i * (j / x))));
	} else if (y <= -0.115) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= -1.02e-45) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 1.95e-299) {
		tmp = t_1;
	} else if (y <= 8.8e-197) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 7.6e-87) {
		tmp = t_1;
	} else if (y <= 1.8e-63) {
		tmp = (x * b) * ((i * (t / x)) - (c * (z / x)));
	} else if (y <= 1.85e+20) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= -1.25e+119:
		tmp = y * (x * (z - (i * (j / x))))
	elif y <= -0.115:
		tmp = i * ((t * b) - (y * j))
	elif y <= -1.02e-45:
		tmp = j * ((a * c) - (y * i))
	elif y <= 1.95e-299:
		tmp = t_1
	elif y <= 8.8e-197:
		tmp = b * ((t * i) - (z * c))
	elif y <= 7.6e-87:
		tmp = t_1
	elif y <= 1.8e-63:
		tmp = (x * b) * ((i * (t / x)) - (c * (z / x)))
	elif y <= 1.85e+20:
		tmp = t_1
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= -1.25e+119)
		tmp = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))));
	elseif (y <= -0.115)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (y <= -1.02e-45)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (y <= 1.95e-299)
		tmp = t_1;
	elseif (y <= 8.8e-197)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (y <= 7.6e-87)
		tmp = t_1;
	elseif (y <= 1.8e-63)
		tmp = Float64(Float64(x * b) * Float64(Float64(i * Float64(t / x)) - Float64(c * Float64(z / x))));
	elseif (y <= 1.85e+20)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= -1.25e+119)
		tmp = y * (x * (z - (i * (j / x))));
	elseif (y <= -0.115)
		tmp = i * ((t * b) - (y * j));
	elseif (y <= -1.02e-45)
		tmp = j * ((a * c) - (y * i));
	elseif (y <= 1.95e-299)
		tmp = t_1;
	elseif (y <= 8.8e-197)
		tmp = b * ((t * i) - (z * c));
	elseif (y <= 7.6e-87)
		tmp = t_1;
	elseif (y <= 1.8e-63)
		tmp = (x * b) * ((i * (t / x)) - (c * (z / x)));
	elseif (y <= 1.85e+20)
		tmp = t_1;
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+119], N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.115], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.02e-45], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-299], t$95$1, If[LessEqual[y, 8.8e-197], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-87], t$95$1, If[LessEqual[y, 1.8e-63], N[(N[(x * b), $MachinePrecision] * N[(N[(i * N[(t / x), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+20], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.25e119

   1. Initial program 69.7%

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

   3. Taylor expanded in x around inf 63.0%

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

   4. Taylor expanded in y around inf 73.0%

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

      1. associate-*r* 73.0%

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

      2. *-commutative 73.0%

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

      3. mul-1-neg 73.0%

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

      4. unsub-neg 73.0%

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

      5. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in y around 0 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*r/ 73.0%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   if -1.25e119 < y < -0.115000000000000005

   1. Initial program 77.4%

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

   3. Taylor expanded in i around -inf 56.3%

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

   if -0.115000000000000005 < y < -1.0199999999999999e-45

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 89.0%

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

   4. Taylor expanded in j around -inf 67.4%

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

   if -1.0199999999999999e-45 < y < 1.9499999999999999e-299 or 8.8000000000000001e-197 < y < 7.6e-87 or 1.80000000000000004e-63 < y < 1.85e20

   1. Initial program 80.2%

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

   3. Taylor expanded in a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if 1.9499999999999999e-299 < y < 8.8000000000000001e-197

   1. Initial program 76.4%

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

   3. Taylor expanded in b around inf 83.4%

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

   if 7.6e-87 < y < 1.80000000000000004e-63

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 88.7%

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

   4. Taylor expanded in b around inf 72.0%

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

      1. associate-*r* 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-/l* 72.2%

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

      4. associate-/l* 72.2%

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

   6. Simplified 72.2%

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

   if 1.85e20 < y

   1. Initial program 73.1%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   5. Simplified 69.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;y \leq -0.115:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(i \cdot \frac{t}{x} - c \cdot \frac{z}{x}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;y \leq -380000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= y -3.4e+119)
     (* y (* x (- z (* i (/ j x)))))
     (if (<= y -380000.0)
       (* i (- (* t b) (* y j)))
       (if (<= y -9.5e-44)
         (* j (- (* a c) (* y i)))
         (if (<= y 1.4e-298)
           t_2
           (if (<= y 1e-196)
             t_1
             (if (<= y 2e-88)
               t_2
               (if (<= y 1.2e-63)
                 t_1
                 (if (<= y 1.85e+20) t_2 (* y (- (* x z) (* i j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -3.4e+119) {
		tmp = y * (x * (z - (i * (j / x))));
	} else if (y <= -380000.0) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= -9.5e-44) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 1.4e-298) {
		tmp = t_2;
	} else if (y <= 1e-196) {
		tmp = t_1;
	} else if (y <= 2e-88) {
		tmp = t_2;
	} else if (y <= 1.2e-63) {
		tmp = t_1;
	} else if (y <= 1.85e+20) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (y <= (-3.4d+119)) then
        tmp = y * (x * (z - (i * (j / x))))
    else if (y <= (-380000.0d0)) then
        tmp = i * ((t * b) - (y * j))
    else if (y <= (-9.5d-44)) then
        tmp = j * ((a * c) - (y * i))
    else if (y <= 1.4d-298) then
        tmp = t_2
    else if (y <= 1d-196) then
        tmp = t_1
    else if (y <= 2d-88) then
        tmp = t_2
    else if (y <= 1.2d-63) then
        tmp = t_1
    else if (y <= 1.85d+20) then
        tmp = t_2
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -3.4e+119) {
		tmp = y * (x * (z - (i * (j / x))));
	} else if (y <= -380000.0) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= -9.5e-44) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 1.4e-298) {
		tmp = t_2;
	} else if (y <= 1e-196) {
		tmp = t_1;
	} else if (y <= 2e-88) {
		tmp = t_2;
	} else if (y <= 1.2e-63) {
		tmp = t_1;
	} else if (y <= 1.85e+20) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= -3.4e+119:
		tmp = y * (x * (z - (i * (j / x))))
	elif y <= -380000.0:
		tmp = i * ((t * b) - (y * j))
	elif y <= -9.5e-44:
		tmp = j * ((a * c) - (y * i))
	elif y <= 1.4e-298:
		tmp = t_2
	elif y <= 1e-196:
		tmp = t_1
	elif y <= 2e-88:
		tmp = t_2
	elif y <= 1.2e-63:
		tmp = t_1
	elif y <= 1.85e+20:
		tmp = t_2
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= -3.4e+119)
		tmp = Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x)))));
	elseif (y <= -380000.0)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (y <= -9.5e-44)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (y <= 1.4e-298)
		tmp = t_2;
	elseif (y <= 1e-196)
		tmp = t_1;
	elseif (y <= 2e-88)
		tmp = t_2;
	elseif (y <= 1.2e-63)
		tmp = t_1;
	elseif (y <= 1.85e+20)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= -3.4e+119)
		tmp = y * (x * (z - (i * (j / x))));
	elseif (y <= -380000.0)
		tmp = i * ((t * b) - (y * j));
	elseif (y <= -9.5e-44)
		tmp = j * ((a * c) - (y * i));
	elseif (y <= 1.4e-298)
		tmp = t_2;
	elseif (y <= 1e-196)
		tmp = t_1;
	elseif (y <= 2e-88)
		tmp = t_2;
	elseif (y <= 1.2e-63)
		tmp = t_1;
	elseif (y <= 1.85e+20)
		tmp = t_2;
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+119], N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -380000.0], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-44], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-298], t$95$2, If[LessEqual[y, 1e-196], t$95$1, If[LessEqual[y, 2e-88], t$95$2, If[LessEqual[y, 1.2e-63], t$95$1, If[LessEqual[y, 1.85e+20], t$95$2, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.40000000000000013e119

   1. Initial program 69.7%

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

   3. Taylor expanded in x around inf 63.0%

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

   4. Taylor expanded in y around inf 73.0%

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

      1. associate-*r* 73.0%

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

      2. *-commutative 73.0%

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

      3. mul-1-neg 73.0%

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

      4. unsub-neg 73.0%

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

      5. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in y around 0 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*r/ 73.0%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   if -3.40000000000000013e119 < y < -3.8e5

   1. Initial program 77.4%

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

   3. Taylor expanded in i around -inf 56.3%

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

   if -3.8e5 < y < -9.49999999999999924e-44

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 89.0%

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

   4. Taylor expanded in j around -inf 67.4%

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

   if -9.49999999999999924e-44 < y < 1.39999999999999996e-298 or 1e-196 < y < 1.99999999999999987e-88 or 1.2e-63 < y < 1.85e20

   1. Initial program 80.2%

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

   3. Taylor expanded in a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if 1.39999999999999996e-298 < y < 1e-196 or 1.99999999999999987e-88 < y < 1.2e-63

   1. Initial program 83.4%

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

   3. Taylor expanded in b around inf 80.0%

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

   if 1.85e20 < y

   1. Initial program 73.1%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   5. Simplified 69.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right)\\ \mathbf{elif}\;y \leq -380000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-196}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{+227}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* a c)) (* b (- (* t i) (* z c)))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (- t_2 (* i (* y j)))))
   (if (<= x -5.8e+107)
     t_3
     (if (<= x -3.5e-56)
       (+ (* j (- (* a c) (* y i))) (* x (* y z)))
       (if (<= x 6.2e+15)
         t_1
         (if (<= x 6e+52)
           t_3
           (if (<= x 2.25e+128) t_1 (if (<= x 1e+227) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 - (i * (y * j));
	double tmp;
	if (x <= -5.8e+107) {
		tmp = t_3;
	} else if (x <= -3.5e-56) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (x <= 6.2e+15) {
		tmp = t_1;
	} else if (x <= 6e+52) {
		tmp = t_3;
	} else if (x <= 2.25e+128) {
		tmp = t_1;
	} else if (x <= 1e+227) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 - (i * (y * j))
    if (x <= (-5.8d+107)) then
        tmp = t_3
    else if (x <= (-3.5d-56)) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else if (x <= 6.2d+15) then
        tmp = t_1
    else if (x <= 6d+52) then
        tmp = t_3
    else if (x <= 2.25d+128) then
        tmp = t_1
    else if (x <= 1d+227) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 - (i * (y * j));
	double tmp;
	if (x <= -5.8e+107) {
		tmp = t_3;
	} else if (x <= -3.5e-56) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (x <= 6.2e+15) {
		tmp = t_1;
	} else if (x <= 6e+52) {
		tmp = t_3;
	} else if (x <= 2.25e+128) {
		tmp = t_1;
	} else if (x <= 1e+227) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 - (i * (y * j))
	tmp = 0
	if x <= -5.8e+107:
		tmp = t_3
	elif x <= -3.5e-56:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	elif x <= 6.2e+15:
		tmp = t_1
	elif x <= 6e+52:
		tmp = t_3
	elif x <= 2.25e+128:
		tmp = t_1
	elif x <= 1e+227:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 - Float64(i * Float64(y * j)))
	tmp = 0.0
	if (x <= -5.8e+107)
		tmp = t_3;
	elseif (x <= -3.5e-56)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (x <= 6.2e+15)
		tmp = t_1;
	elseif (x <= 6e+52)
		tmp = t_3;
	elseif (x <= 2.25e+128)
		tmp = t_1;
	elseif (x <= 1e+227)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * (a * c)) + (b * ((t * i) - (z * c)));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 - (i * (y * j));
	tmp = 0.0;
	if (x <= -5.8e+107)
		tmp = t_3;
	elseif (x <= -3.5e-56)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	elseif (x <= 6.2e+15)
		tmp = t_1;
	elseif (x <= 6e+52)
		tmp = t_3;
	elseif (x <= 2.25e+128)
		tmp = t_1;
	elseif (x <= 1e+227)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $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[(t$95$2 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+107], t$95$3, If[LessEqual[x, -3.5e-56], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+15], t$95$1, If[LessEqual[x, 6e+52], t$95$3, If[LessEqual[x, 2.25e+128], t$95$1, If[LessEqual[x, 1e+227], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.79999999999999975e107 or 6.2e15 < x < 6e52 or 1.0000000000000001e227 < x

   1. Initial program 77.0%

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

   3. Taylor expanded in b around 0 75.9%

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

   4. Taylor expanded in c around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

   6. Simplified 79.9%

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

   if -5.79999999999999975e107 < x < -3.4999999999999998e-56

   1. Initial program 86.0%

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

   3. Taylor expanded in b around 0 72.5%

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

   4. Taylor expanded in t around 0 67.4%

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

   if -3.4999999999999998e-56 < x < 6.2e15 or 6e52 < x < 2.2500000000000001e128

   1. Initial program 74.3%

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

   3. Taylor expanded in x around 0 77.1%

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

   4. Taylor expanded in a around inf 67.0%

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

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   if 2.2500000000000001e128 < x < 1.0000000000000001e227

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 80.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+128}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 10^{+227}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c\right) + t\_1\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(x \cdot \left(\frac{t \cdot b}{x} - \frac{y \cdot j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* j (* a c)) t_1))
        (t_3 (- (* x (- (* y z) (* t a))) (* i (* y j)))))
   (if (<= x -3.8e+104)
     t_3
     (if (<= x -1.5e-56)
       (+ (* j (- (* a c) (* y i))) (* x (* y z)))
       (if (<= x -5.8e-142)
         t_2
         (if (<= x -9.5e-167)
           (* i (* x (- (/ (* t b) x) (/ (* y j) x))))
           (if (<= x -8.5e-180) t_1 (if (<= x 5.6e+15) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double t_3 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double tmp;
	if (x <= -3.8e+104) {
		tmp = t_3;
	} else if (x <= -1.5e-56) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (x <= -5.8e-142) {
		tmp = t_2;
	} else if (x <= -9.5e-167) {
		tmp = i * (x * (((t * b) / x) - ((y * j) / x)));
	} else if (x <= -8.5e-180) {
		tmp = t_1;
	} else if (x <= 5.6e+15) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (j * (a * c)) + t_1
    t_3 = (x * ((y * z) - (t * a))) - (i * (y * j))
    if (x <= (-3.8d+104)) then
        tmp = t_3
    else if (x <= (-1.5d-56)) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else if (x <= (-5.8d-142)) then
        tmp = t_2
    else if (x <= (-9.5d-167)) then
        tmp = i * (x * (((t * b) / x) - ((y * j) / x)))
    else if (x <= (-8.5d-180)) then
        tmp = t_1
    else if (x <= 5.6d+15) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (j * (a * c)) + t_1;
	double t_3 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double tmp;
	if (x <= -3.8e+104) {
		tmp = t_3;
	} else if (x <= -1.5e-56) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (x <= -5.8e-142) {
		tmp = t_2;
	} else if (x <= -9.5e-167) {
		tmp = i * (x * (((t * b) / x) - ((y * j) / x)));
	} else if (x <= -8.5e-180) {
		tmp = t_1;
	} else if (x <= 5.6e+15) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (j * (a * c)) + t_1
	t_3 = (x * ((y * z) - (t * a))) - (i * (y * j))
	tmp = 0
	if x <= -3.8e+104:
		tmp = t_3
	elif x <= -1.5e-56:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	elif x <= -5.8e-142:
		tmp = t_2
	elif x <= -9.5e-167:
		tmp = i * (x * (((t * b) / x) - ((y * j) / x)))
	elif x <= -8.5e-180:
		tmp = t_1
	elif x <= 5.6e+15:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(j * Float64(a * c)) + t_1)
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)))
	tmp = 0.0
	if (x <= -3.8e+104)
		tmp = t_3;
	elseif (x <= -1.5e-56)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (x <= -5.8e-142)
		tmp = t_2;
	elseif (x <= -9.5e-167)
		tmp = Float64(i * Float64(x * Float64(Float64(Float64(t * b) / x) - Float64(Float64(y * j) / x))));
	elseif (x <= -8.5e-180)
		tmp = t_1;
	elseif (x <= 5.6e+15)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (j * (a * c)) + t_1;
	t_3 = (x * ((y * z) - (t * a))) - (i * (y * j));
	tmp = 0.0;
	if (x <= -3.8e+104)
		tmp = t_3;
	elseif (x <= -1.5e-56)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	elseif (x <= -5.8e-142)
		tmp = t_2;
	elseif (x <= -9.5e-167)
		tmp = i * (x * (((t * b) / x) - ((y * j) / x)));
	elseif (x <= -8.5e-180)
		tmp = t_1;
	elseif (x <= 5.6e+15)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+104], t$95$3, If[LessEqual[x, -1.5e-56], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-142], t$95$2, If[LessEqual[x, -9.5e-167], N[(i * N[(x * N[(N[(N[(t * b), $MachinePrecision] / x), $MachinePrecision] - N[(N[(y * j), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-180], t$95$1, If[LessEqual[x, 5.6e+15], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.79999999999999969e104 or 5.6e15 < x

   1. Initial program 77.7%

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

   3. Taylor expanded in b around 0 77.0%

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

   4. Taylor expanded in c around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   6. Simplified 75.6%

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

   if -3.79999999999999969e104 < x < -1.49999999999999995e-56

   1. Initial program 86.0%

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

   3. Taylor expanded in b around 0 72.5%

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

   4. Taylor expanded in t around 0 67.4%

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

   if -1.49999999999999995e-56 < x < -5.7999999999999998e-142 or -8.4999999999999993e-180 < x < 5.6e15

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in a around inf 69.3%

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

      1. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   if -5.7999999999999998e-142 < x < -9.49999999999999955e-167

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 80.0%

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

   4. Taylor expanded in i around -inf 100.0%

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

   if -9.49999999999999955e-167 < x < -8.4999999999999993e-180

   1. Initial program 41.0%

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

   3. Taylor expanded in b around inf 79.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-142}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(x \cdot \left(\frac{t \cdot b}{x} - \frac{y \cdot j}{x}\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+15}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -7.5e-24)
     t_3
     (if (<= y 9.8e-298)
       t_2
       (if (<= y 3.8e-196)
         t_1
         (if (<= y 3.4e-88)
           t_2
           (if (<= y 1.7e-63) t_1 (if (<= y 1.85e+20) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -7.5e-24) {
		tmp = t_3;
	} else if (y <= 9.8e-298) {
		tmp = t_2;
	} else if (y <= 3.8e-196) {
		tmp = t_1;
	} else if (y <= 3.4e-88) {
		tmp = t_2;
	} else if (y <= 1.7e-63) {
		tmp = t_1;
	} else if (y <= 1.85e+20) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-7.5d-24)) then
        tmp = t_3
    else if (y <= 9.8d-298) then
        tmp = t_2
    else if (y <= 3.8d-196) then
        tmp = t_1
    else if (y <= 3.4d-88) then
        tmp = t_2
    else if (y <= 1.7d-63) then
        tmp = t_1
    else if (y <= 1.85d+20) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -7.5e-24) {
		tmp = t_3;
	} else if (y <= 9.8e-298) {
		tmp = t_2;
	} else if (y <= 3.8e-196) {
		tmp = t_1;
	} else if (y <= 3.4e-88) {
		tmp = t_2;
	} else if (y <= 1.7e-63) {
		tmp = t_1;
	} else if (y <= 1.85e+20) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -7.5e-24:
		tmp = t_3
	elif y <= 9.8e-298:
		tmp = t_2
	elif y <= 3.8e-196:
		tmp = t_1
	elif y <= 3.4e-88:
		tmp = t_2
	elif y <= 1.7e-63:
		tmp = t_1
	elif y <= 1.85e+20:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -7.5e-24)
		tmp = t_3;
	elseif (y <= 9.8e-298)
		tmp = t_2;
	elseif (y <= 3.8e-196)
		tmp = t_1;
	elseif (y <= 3.4e-88)
		tmp = t_2;
	elseif (y <= 1.7e-63)
		tmp = t_1;
	elseif (y <= 1.85e+20)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -7.5e-24)
		tmp = t_3;
	elseif (y <= 9.8e-298)
		tmp = t_2;
	elseif (y <= 3.8e-196)
		tmp = t_1;
	elseif (y <= 3.4e-88)
		tmp = t_2;
	elseif (y <= 1.7e-63)
		tmp = t_1;
	elseif (y <= 1.85e+20)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e-24], t$95$3, If[LessEqual[y, 9.8e-298], t$95$2, If[LessEqual[y, 3.8e-196], t$95$1, If[LessEqual[y, 3.4e-88], t$95$2, If[LessEqual[y, 1.7e-63], t$95$1, If[LessEqual[y, 1.85e+20], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000007e-24 or 1.85e20 < y

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

      5. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if -7.50000000000000007e-24 < y < 9.7999999999999999e-298 or 3.8000000000000001e-196 < y < 3.39999999999999975e-88 or 1.69999999999999999e-63 < y < 1.85e20

   1. Initial program 81.1%

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

   3. Taylor expanded in a around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if 9.7999999999999999e-298 < y < 3.8000000000000001e-196 or 3.39999999999999975e-88 < y < 1.69999999999999999e-63

   1. Initial program 83.4%

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

   3. Taylor expanded in b around inf 80.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-236}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* y z))))
   (if (<= z -5.1e+93)
     t_2
     (if (<= z -4.9e-88)
       t_1
       (if (<= z 1.5e-236)
         (* i (* t b))
         (if (<= z 5.2e-117)
           t_1
           (if (<= z 7.2e-13) (* b (* t i)) (if (<= z 3.4e+61) 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 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -5.1e+93) {
		tmp = t_2;
	} else if (z <= -4.9e-88) {
		tmp = t_1;
	} else if (z <= 1.5e-236) {
		tmp = i * (t * b);
	} else if (z <= 5.2e-117) {
		tmp = t_1;
	} else if (z <= 7.2e-13) {
		tmp = b * (t * i);
	} else if (z <= 3.4e+61) {
		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 = a * (c * j)
    t_2 = x * (y * z)
    if (z <= (-5.1d+93)) then
        tmp = t_2
    else if (z <= (-4.9d-88)) then
        tmp = t_1
    else if (z <= 1.5d-236) then
        tmp = i * (t * b)
    else if (z <= 5.2d-117) then
        tmp = t_1
    else if (z <= 7.2d-13) then
        tmp = b * (t * i)
    else if (z <= 3.4d+61) 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 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -5.1e+93) {
		tmp = t_2;
	} else if (z <= -4.9e-88) {
		tmp = t_1;
	} else if (z <= 1.5e-236) {
		tmp = i * (t * b);
	} else if (z <= 5.2e-117) {
		tmp = t_1;
	} else if (z <= 7.2e-13) {
		tmp = b * (t * i);
	} else if (z <= 3.4e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -5.1e+93:
		tmp = t_2
	elif z <= -4.9e-88:
		tmp = t_1
	elif z <= 1.5e-236:
		tmp = i * (t * b)
	elif z <= 5.2e-117:
		tmp = t_1
	elif z <= 7.2e-13:
		tmp = b * (t * i)
	elif z <= 3.4e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -5.1e+93)
		tmp = t_2;
	elseif (z <= -4.9e-88)
		tmp = t_1;
	elseif (z <= 1.5e-236)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 5.2e-117)
		tmp = t_1;
	elseif (z <= 7.2e-13)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 3.4e+61)
		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 = a * (c * j);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -5.1e+93)
		tmp = t_2;
	elseif (z <= -4.9e-88)
		tmp = t_1;
	elseif (z <= 1.5e-236)
		tmp = i * (t * b);
	elseif (z <= 5.2e-117)
		tmp = t_1;
	elseif (z <= 7.2e-13)
		tmp = b * (t * i);
	elseif (z <= 3.4e+61)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+93], t$95$2, If[LessEqual[z, -4.9e-88], t$95$1, If[LessEqual[z, 1.5e-236], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-117], t$95$1, If[LessEqual[z, 7.2e-13], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+61], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.0999999999999996e93 or 3.40000000000000026e61 < z

   1. Initial program 70.3%

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

   3. Taylor expanded in y around inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. *-commutative 59.5%

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

      5. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in z around inf 49.0%

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

   if -5.0999999999999996e93 < z < -4.90000000000000028e-88 or 1.50000000000000007e-236 < z < 5.19999999999999966e-117 or 7.1999999999999996e-13 < z < 3.40000000000000026e61

   1. Initial program 82.1%

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

   3. Taylor expanded in a around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in j around inf 38.2%

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

      1. *-commutative 38.2%

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

   8. Simplified 38.2%

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

   if -4.90000000000000028e-88 < z < 1.50000000000000007e-236

   1. Initial program 85.3%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. distribute-lft-out-- 54.3%

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

      2. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in a around 0 35.4%

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

      1. associate-*r* 32.8%

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

      2. *-commutative 32.8%

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

      3. associate-*r* 38.9%

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

   8. Simplified 38.9%

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

   if 5.19999999999999966e-117 < z < 7.1999999999999996e-13

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around 0 45.3%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-236}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+61}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-240}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= z -3.8e+95)
     (* y (* x z))
     (if (<= z -2.6e-85)
       t_1
       (if (<= z 6.6e-240)
         (* i (* t b))
         (if (<= z 9.2e-120)
           t_1
           (if (<= z 4.3e-13)
             (* b (* t i))
             (if (<= z 6.5e+52) 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 = a * (c * j);
	double tmp;
	if (z <= -3.8e+95) {
		tmp = y * (x * z);
	} else if (z <= -2.6e-85) {
		tmp = t_1;
	} else if (z <= 6.6e-240) {
		tmp = i * (t * b);
	} else if (z <= 9.2e-120) {
		tmp = t_1;
	} else if (z <= 4.3e-13) {
		tmp = b * (t * i);
	} else if (z <= 6.5e+52) {
		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 = a * (c * j)
    if (z <= (-3.8d+95)) then
        tmp = y * (x * z)
    else if (z <= (-2.6d-85)) then
        tmp = t_1
    else if (z <= 6.6d-240) then
        tmp = i * (t * b)
    else if (z <= 9.2d-120) then
        tmp = t_1
    else if (z <= 4.3d-13) then
        tmp = b * (t * i)
    else if (z <= 6.5d+52) 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 = a * (c * j);
	double tmp;
	if (z <= -3.8e+95) {
		tmp = y * (x * z);
	} else if (z <= -2.6e-85) {
		tmp = t_1;
	} else if (z <= 6.6e-240) {
		tmp = i * (t * b);
	} else if (z <= 9.2e-120) {
		tmp = t_1;
	} else if (z <= 4.3e-13) {
		tmp = b * (t * i);
	} else if (z <= 6.5e+52) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if z <= -3.8e+95:
		tmp = y * (x * z)
	elif z <= -2.6e-85:
		tmp = t_1
	elif z <= 6.6e-240:
		tmp = i * (t * b)
	elif z <= 9.2e-120:
		tmp = t_1
	elif z <= 4.3e-13:
		tmp = b * (t * i)
	elif z <= 6.5e+52:
		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(a * Float64(c * j))
	tmp = 0.0
	if (z <= -3.8e+95)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -2.6e-85)
		tmp = t_1;
	elseif (z <= 6.6e-240)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 9.2e-120)
		tmp = t_1;
	elseif (z <= 4.3e-13)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 6.5e+52)
		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 = a * (c * j);
	tmp = 0.0;
	if (z <= -3.8e+95)
		tmp = y * (x * z);
	elseif (z <= -2.6e-85)
		tmp = t_1;
	elseif (z <= 6.6e-240)
		tmp = i * (t * b);
	elseif (z <= 9.2e-120)
		tmp = t_1;
	elseif (z <= 4.3e-13)
		tmp = b * (t * i);
	elseif (z <= 6.5e+52)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+95], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-85], t$95$1, If[LessEqual[z, 6.6e-240], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-120], t$95$1, If[LessEqual[z, 4.3e-13], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+52], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.7999999999999999e95

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

      5. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 48.5%

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

   if -3.7999999999999999e95 < z < -2.60000000000000011e-85 or 6.6000000000000003e-240 < z < 9.19999999999999946e-120 or 4.2999999999999999e-13 < z < 6.49999999999999996e52

   1. Initial program 82.1%

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

   3. Taylor expanded in a around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in j around inf 38.2%

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

      1. *-commutative 38.2%

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

   8. Simplified 38.2%

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

   if -2.60000000000000011e-85 < z < 6.6000000000000003e-240

   1. Initial program 85.3%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. distribute-lft-out-- 54.3%

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

      2. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in a around 0 35.4%

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

      1. associate-*r* 32.8%

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

      2. *-commutative 32.8%

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

      3. associate-*r* 38.9%

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

   8. Simplified 38.9%

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

   if 9.19999999999999946e-120 < z < 4.2999999999999999e-13

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around 0 45.3%

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

   if 6.49999999999999996e52 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in z around inf 54.6%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-240}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-120}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-234}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= z -2e+94)
     (* y (* x z))
     (if (<= z -4.2e-85)
       t_1
       (if (<= z 1.15e-234)
         (* i (* t b))
         (if (<= z 1.12e-118)
           (* a (* c j))
           (if (<= z 1.95e-13)
             (* b (* t i))
             (if (<= z 6.8e+53) 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 = j * (a * c);
	double tmp;
	if (z <= -2e+94) {
		tmp = y * (x * z);
	} else if (z <= -4.2e-85) {
		tmp = t_1;
	} else if (z <= 1.15e-234) {
		tmp = i * (t * b);
	} else if (z <= 1.12e-118) {
		tmp = a * (c * j);
	} else if (z <= 1.95e-13) {
		tmp = b * (t * i);
	} else if (z <= 6.8e+53) {
		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 = j * (a * c)
    if (z <= (-2d+94)) then
        tmp = y * (x * z)
    else if (z <= (-4.2d-85)) then
        tmp = t_1
    else if (z <= 1.15d-234) then
        tmp = i * (t * b)
    else if (z <= 1.12d-118) then
        tmp = a * (c * j)
    else if (z <= 1.95d-13) then
        tmp = b * (t * i)
    else if (z <= 6.8d+53) 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 = j * (a * c);
	double tmp;
	if (z <= -2e+94) {
		tmp = y * (x * z);
	} else if (z <= -4.2e-85) {
		tmp = t_1;
	} else if (z <= 1.15e-234) {
		tmp = i * (t * b);
	} else if (z <= 1.12e-118) {
		tmp = a * (c * j);
	} else if (z <= 1.95e-13) {
		tmp = b * (t * i);
	} else if (z <= 6.8e+53) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if z <= -2e+94:
		tmp = y * (x * z)
	elif z <= -4.2e-85:
		tmp = t_1
	elif z <= 1.15e-234:
		tmp = i * (t * b)
	elif z <= 1.12e-118:
		tmp = a * (c * j)
	elif z <= 1.95e-13:
		tmp = b * (t * i)
	elif z <= 6.8e+53:
		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(j * Float64(a * c))
	tmp = 0.0
	if (z <= -2e+94)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -4.2e-85)
		tmp = t_1;
	elseif (z <= 1.15e-234)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 1.12e-118)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1.95e-13)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 6.8e+53)
		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 = j * (a * c);
	tmp = 0.0;
	if (z <= -2e+94)
		tmp = y * (x * z);
	elseif (z <= -4.2e-85)
		tmp = t_1;
	elseif (z <= 1.15e-234)
		tmp = i * (t * b);
	elseif (z <= 1.12e-118)
		tmp = a * (c * j);
	elseif (z <= 1.95e-13)
		tmp = b * (t * i);
	elseif (z <= 6.8e+53)
		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[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+94], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-85], t$95$1, If[LessEqual[z, 1.15e-234], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-118], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-13], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+53], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2e94

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

      5. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 48.5%

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

   if -2e94 < z < -4.2e-85 or 1.95000000000000002e-13 < z < 6.79999999999999995e53

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in j around inf 43.4%

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

      1. associate-*r* 44.9%

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

   8. Simplified 44.9%

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

   if -4.2e-85 < z < 1.14999999999999995e-234

   1. Initial program 85.3%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. distribute-lft-out-- 54.3%

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

      2. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in a around 0 35.4%

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

      1. associate-*r* 32.8%

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

      2. *-commutative 32.8%

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

      3. associate-*r* 38.9%

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

   8. Simplified 38.9%

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

   if 1.14999999999999995e-234 < z < 1.12e-118

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

      4. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in j around inf 27.9%

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

      1. *-commutative 27.9%

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

   8. Simplified 27.9%

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

   if 1.12e-118 < z < 1.95000000000000002e-13

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around 0 45.3%

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

   if 6.79999999999999995e53 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in z around inf 54.6%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-234}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-215}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (* y z))))
        (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.06e+157)
     t_2
     (if (<= t -1.15e-291)
       t_1
       (if (<= t 1.7e-215)
         (* z (- (* x y) (* b c)))
         (if (<= t 9.2e+136) 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 * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.06e+157) {
		tmp = t_2;
	} else if (t <= -1.15e-291) {
		tmp = t_1;
	} else if (t <= 1.7e-215) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9.2e+136) {
		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 * ((a * c) - (y * i))) + (x * (y * z))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.06d+157)) then
        tmp = t_2
    else if (t <= (-1.15d-291)) then
        tmp = t_1
    else if (t <= 1.7d-215) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 9.2d+136) 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 * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.06e+157) {
		tmp = t_2;
	} else if (t <= -1.15e-291) {
		tmp = t_1;
	} else if (t <= 1.7e-215) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9.2e+136) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.06e+157:
		tmp = t_2
	elif t <= -1.15e-291:
		tmp = t_1
	elif t <= 1.7e-215:
		tmp = z * ((x * y) - (b * c))
	elif t <= 9.2e+136:
		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(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.06e+157)
		tmp = t_2;
	elseif (t <= -1.15e-291)
		tmp = t_1;
	elseif (t <= 1.7e-215)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 9.2e+136)
		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 * ((a * c) - (y * i))) + (x * (y * z));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.06e+157)
		tmp = t_2;
	elseif (t <= -1.15e-291)
		tmp = t_1;
	elseif (t <= 1.7e-215)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 9.2e+136)
		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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e+157], t$95$2, If[LessEqual[t, -1.15e-291], t$95$1, If[LessEqual[t, 1.7e-215], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+136], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.06e157 or 9.2e136 < t

   1. Initial program 59.8%

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

   3. Taylor expanded in t around inf 74.1%

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

      1. distribute-lft-out-- 74.1%

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

      2. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   if -1.06e157 < t < -1.15e-291 or 1.70000000000000001e-215 < t < 9.2e136

   1. Initial program 84.8%

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

   3. Taylor expanded in b around 0 72.4%

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

   4. Taylor expanded in t around 0 65.5%

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

   if -1.15e-291 < t < 1.70000000000000001e-215

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. *-commutative 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-215}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= x -1.05e-41)
     (+ t_1 (* x (- (* y z) (* t a))))
     (if (<= x 1.1e-108)
       (- (* b (- (* t i) (* z c))) (* j (- (* y i) (* a c))))
       (+ t_1 (- (* i (* t b)) (* x (- (* t a) (* 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 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -1.05e-41) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (x <= 1.1e-108) {
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	} else {
		tmp = t_1 + ((i * (t * b)) - (x * ((t * a) - (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 = j * ((a * c) - (y * i))
    if (x <= (-1.05d-41)) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (x <= 1.1d-108) then
        tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)))
    else
        tmp = t_1 + ((i * (t * b)) - (x * ((t * a) - (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 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -1.05e-41) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (x <= 1.1e-108) {
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	} else {
		tmp = t_1 + ((i * (t * b)) - (x * ((t * a) - (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if x <= -1.05e-41:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif x <= 1.1e-108:
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)))
	else:
		tmp = t_1 + ((i * (t * b)) - (x * ((t * a) - (y * z))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -1.05e-41)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (x <= 1.1e-108)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	else
		tmp = Float64(t_1 + Float64(Float64(i * Float64(t * b)) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -1.05e-41)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (x <= 1.1e-108)
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	else
		tmp = t_1 + ((i * (t * b)) - (x * ((t * a) - (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-41], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-108], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05000000000000006e-41

   1. Initial program 79.9%

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

   3. Taylor expanded in b around 0 73.8%

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

   if -1.05000000000000006e-41 < x < 1.1000000000000001e-108

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 81.2%

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

   if 1.1000000000000001e-108 < x

   1. Initial program 75.6%

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

   3. Taylor expanded in c around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. associate-*r* 78.1%

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

      3. distribute-rgt-neg-in 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-*l* 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= z -3e+96)
     (* y (* x z))
     (if (<= z -5.1e-210)
       t_1
       (if (<= z 2.25e-253)
         (* i (* t b))
         (if (<= z 9e-179)
           (* j (* y (- i)))
           (if (<= z 1.2e+62) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -3e+96) {
		tmp = y * (x * z);
	} else if (z <= -5.1e-210) {
		tmp = t_1;
	} else if (z <= 2.25e-253) {
		tmp = i * (t * b);
	} else if (z <= 9e-179) {
		tmp = j * (y * -i);
	} else if (z <= 1.2e+62) {
		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 = a * ((c * j) - (x * t))
    if (z <= (-3d+96)) then
        tmp = y * (x * z)
    else if (z <= (-5.1d-210)) then
        tmp = t_1
    else if (z <= 2.25d-253) then
        tmp = i * (t * b)
    else if (z <= 9d-179) then
        tmp = j * (y * -i)
    else if (z <= 1.2d+62) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -3e+96) {
		tmp = y * (x * z);
	} else if (z <= -5.1e-210) {
		tmp = t_1;
	} else if (z <= 2.25e-253) {
		tmp = i * (t * b);
	} else if (z <= 9e-179) {
		tmp = j * (y * -i);
	} else if (z <= 1.2e+62) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if z <= -3e+96:
		tmp = y * (x * z)
	elif z <= -5.1e-210:
		tmp = t_1
	elif z <= 2.25e-253:
		tmp = i * (t * b)
	elif z <= 9e-179:
		tmp = j * (y * -i)
	elif z <= 1.2e+62:
		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(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (z <= -3e+96)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -5.1e-210)
		tmp = t_1;
	elseif (z <= 2.25e-253)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 9e-179)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (z <= 1.2e+62)
		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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (z <= -3e+96)
		tmp = y * (x * z);
	elseif (z <= -5.1e-210)
		tmp = t_1;
	elseif (z <= 2.25e-253)
		tmp = i * (t * b);
	elseif (z <= 9e-179)
		tmp = j * (y * -i);
	elseif (z <= 1.2e+62)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+96], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-210], t$95$1, If[LessEqual[z, 2.25e-253], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-179], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+62], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3e96

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

      5. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 48.5%

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

   if -3e96 < z < -5.09999999999999995e-210 or 8.99999999999999984e-179 < z < 1.2e62

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

      4. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   if -5.09999999999999995e-210 < z < 2.25000000000000014e-253

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around 0 49.2%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 52.4%

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

   8. Simplified 52.4%

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

   if 2.25000000000000014e-253 < z < 8.99999999999999984e-179

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

      5. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in z around 0 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

   8. Simplified 51.3%

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

   9. Taylor expanded in i around 0 51.3%

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

       1. mul-1-neg 51.3%

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

       2. *-commutative 51.3%

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

       3. associate-*r* 57.1%

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

       4. distribute-rgt-neg-in 57.1%

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

   11. Simplified 57.1%

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

   if 1.2e62 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in z around inf 54.6%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-222}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= x -1.5e+229)
     t_1
     (if (<= x -1.3e+163)
       (* x (* y z))
       (if (<= x -3.6e+138)
         t_1
         (if (<= x 2.55e-222)
           (* j (* a c))
           (if (<= x 2.1e+80) (* i (* t b)) (* y (* x 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 = x * (t * -a);
	double tmp;
	if (x <= -1.5e+229) {
		tmp = t_1;
	} else if (x <= -1.3e+163) {
		tmp = x * (y * z);
	} else if (x <= -3.6e+138) {
		tmp = t_1;
	} else if (x <= 2.55e-222) {
		tmp = j * (a * c);
	} else if (x <= 2.1e+80) {
		tmp = i * (t * b);
	} else {
		tmp = y * (x * 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 = x * (t * -a)
    if (x <= (-1.5d+229)) then
        tmp = t_1
    else if (x <= (-1.3d+163)) then
        tmp = x * (y * z)
    else if (x <= (-3.6d+138)) then
        tmp = t_1
    else if (x <= 2.55d-222) then
        tmp = j * (a * c)
    else if (x <= 2.1d+80) then
        tmp = i * (t * b)
    else
        tmp = y * (x * 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 = x * (t * -a);
	double tmp;
	if (x <= -1.5e+229) {
		tmp = t_1;
	} else if (x <= -1.3e+163) {
		tmp = x * (y * z);
	} else if (x <= -3.6e+138) {
		tmp = t_1;
	} else if (x <= 2.55e-222) {
		tmp = j * (a * c);
	} else if (x <= 2.1e+80) {
		tmp = i * (t * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if x <= -1.5e+229:
		tmp = t_1
	elif x <= -1.3e+163:
		tmp = x * (y * z)
	elif x <= -3.6e+138:
		tmp = t_1
	elif x <= 2.55e-222:
		tmp = j * (a * c)
	elif x <= 2.1e+80:
		tmp = i * (t * b)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (x <= -1.5e+229)
		tmp = t_1;
	elseif (x <= -1.3e+163)
		tmp = Float64(x * Float64(y * z));
	elseif (x <= -3.6e+138)
		tmp = t_1;
	elseif (x <= 2.55e-222)
		tmp = Float64(j * Float64(a * c));
	elseif (x <= 2.1e+80)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (x <= -1.5e+229)
		tmp = t_1;
	elseif (x <= -1.3e+163)
		tmp = x * (y * z);
	elseif (x <= -3.6e+138)
		tmp = t_1;
	elseif (x <= 2.55e-222)
		tmp = j * (a * c);
	elseif (x <= 2.1e+80)
		tmp = i * (t * b);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+229], t$95$1, If[LessEqual[x, -1.3e+163], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e+138], t$95$1, If[LessEqual[x, 2.55e-222], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+80], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.49999999999999999e229 or -1.3000000000000001e163 < x < -3.6000000000000001e138

   1. Initial program 71.3%

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

   3. Taylor expanded in x around inf 68.6%

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

   4. Taylor expanded in y around 0 64.1%

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

      1. neg-mul-1 64.1%

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

      2. distribute-lft-neg-in 64.1%

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

      3. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   if -1.49999999999999999e229 < x < -1.3000000000000001e163

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

      4. *-commutative 57.8%

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

      5. *-commutative 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in z around inf 46.7%

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

   if -3.6000000000000001e138 < x < 2.5500000000000001e-222

   1. Initial program 77.5%

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

   3. Taylor expanded in a around inf 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

      4. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in j around inf 32.0%

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

      1. associate-*r* 32.8%

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

   8. Simplified 32.8%

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

   if 2.5500000000000001e-222 < x < 2.10000000000000001e80

   1. Initial program 74.6%

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

   3. Taylor expanded in t around inf 40.6%

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

      1. distribute-lft-out-- 40.6%

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

      2. *-commutative 40.6%

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

   5. Simplified 40.6%

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

   6. Taylor expanded in a around 0 33.8%

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

      1. associate-*r* 33.0%

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

      2. *-commutative 33.0%

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

      3. associate-*r* 37.5%

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

   8. Simplified 37.5%

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

   if 2.10000000000000001e80 < x

   1. Initial program 81.2%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in z around inf 59.7%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-222}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.65 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -3.65e+102)
     t_1
     (if (<= x -2.4e-55)
       (+ (* j (- (* a c) (* y i))) (* x (* y z)))
       (if (<= x 2.4e+127) (+ (* j (* a c)) (* b (- (* t i) (* z c)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.65e+102) {
		tmp = t_1;
	} else if (x <= -2.4e-55) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (x <= 2.4e+127) {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-3.65d+102)) then
        tmp = t_1
    else if (x <= (-2.4d-55)) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else if (x <= 2.4d+127) then
        tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.65e+102) {
		tmp = t_1;
	} else if (x <= -2.4e-55) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else if (x <= 2.4e+127) {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.65e+102:
		tmp = t_1
	elif x <= -2.4e-55:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	elif x <= 2.4e+127:
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.65e+102)
		tmp = t_1;
	elseif (x <= -2.4e-55)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (x <= 2.4e+127)
		tmp = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.65e+102)
		tmp = t_1;
	elseif (x <= -2.4e-55)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	elseif (x <= 2.4e+127)
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.65e+102], t$95$1, If[LessEqual[x, -2.4e-55], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+127], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.64999999999999995e102 or 2.4000000000000002e127 < x

   1. Initial program 79.1%

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

   3. Taylor expanded in x around inf 74.4%

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

   if -3.64999999999999995e102 < x < -2.39999999999999991e-55

   1. Initial program 86.0%

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

   3. Taylor expanded in b around 0 72.5%

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

   4. Taylor expanded in t around 0 67.4%

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

   if -2.39999999999999991e-55 < x < 2.4000000000000002e127

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 75.2%

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

   4. Taylor expanded in a around inf 63.9%

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

      1. *-commutative 63.9%

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

   6. Simplified 63.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-8} \lor \neg \left(b \leq 2.5 \cdot 10^{+99}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -8.6e+119)
     t_1
     (if (<= b -7.5e+74)
       (* a (- (* c j) (* x t)))
       (if (or (<= b -4.5e-8) (not (<= b 2.5e+99)))
         t_1
         (* j (- (* a 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 t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8.6e+119) {
		tmp = t_1;
	} else if (b <= -7.5e+74) {
		tmp = a * ((c * j) - (x * t));
	} else if ((b <= -4.5e-8) || !(b <= 2.5e+99)) {
		tmp = t_1;
	} else {
		tmp = j * ((a * 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) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-8.6d+119)) then
        tmp = t_1
    else if (b <= (-7.5d+74)) then
        tmp = a * ((c * j) - (x * t))
    else if ((b <= (-4.5d-8)) .or. (.not. (b <= 2.5d+99))) then
        tmp = t_1
    else
        tmp = j * ((a * 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 t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8.6e+119) {
		tmp = t_1;
	} else if (b <= -7.5e+74) {
		tmp = a * ((c * j) - (x * t));
	} else if ((b <= -4.5e-8) || !(b <= 2.5e+99)) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -8.6e+119:
		tmp = t_1
	elif b <= -7.5e+74:
		tmp = a * ((c * j) - (x * t))
	elif (b <= -4.5e-8) or not (b <= 2.5e+99):
		tmp = t_1
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8.6e+119)
		tmp = t_1;
	elseif (b <= -7.5e+74)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif ((b <= -4.5e-8) || !(b <= 2.5e+99))
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -8.6e+119)
		tmp = t_1;
	elseif (b <= -7.5e+74)
		tmp = a * ((c * j) - (x * t));
	elseif ((b <= -4.5e-8) || ~((b <= 2.5e+99)))
		tmp = t_1;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.6e+119], t$95$1, If[LessEqual[b, -7.5e+74], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -4.5e-8], N[Not[LessEqual[b, 2.5e+99]], $MachinePrecision]], t$95$1, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.60000000000000063e119 or -7.5e74 < b < -4.49999999999999993e-8 or 2.50000000000000004e99 < b

   1. Initial program 75.9%

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

   3. Taylor expanded in b around inf 63.9%

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

   if -8.60000000000000063e119 < b < -7.5e74

   1. Initial program 64.2%

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

   3. Taylor expanded in a around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -4.49999999999999993e-8 < b < 2.50000000000000004e99

   1. Initial program 80.2%

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

   3. Taylor expanded in x around inf 74.4%

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

   4. Taylor expanded in j around -inf 51.4%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-8} \lor \neg \left(b \leq 2.5 \cdot 10^{+99}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.25e-43)
     t_2
     (if (<= a -4.6e-181)
       t_1
       (if (<= a -1e-261) (* x (* y z)) (if (<= a 7.5e+40) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.25e-43) {
		tmp = t_2;
	} else if (a <= -4.6e-181) {
		tmp = t_1;
	} else if (a <= -1e-261) {
		tmp = x * (y * z);
	} else if (a <= 7.5e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.25d-43)) then
        tmp = t_2
    else if (a <= (-4.6d-181)) then
        tmp = t_1
    else if (a <= (-1d-261)) then
        tmp = x * (y * z)
    else if (a <= 7.5d+40) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.25e-43) {
		tmp = t_2;
	} else if (a <= -4.6e-181) {
		tmp = t_1;
	} else if (a <= -1e-261) {
		tmp = x * (y * z);
	} else if (a <= 7.5e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.25e-43:
		tmp = t_2
	elif a <= -4.6e-181:
		tmp = t_1
	elif a <= -1e-261:
		tmp = x * (y * z)
	elif a <= 7.5e+40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.25e-43)
		tmp = t_2;
	elseif (a <= -4.6e-181)
		tmp = t_1;
	elseif (a <= -1e-261)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 7.5e+40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.25e-43)
		tmp = t_2;
	elseif (a <= -4.6e-181)
		tmp = t_1;
	elseif (a <= -1e-261)
		tmp = x * (y * z);
	elseif (a <= 7.5e+40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.25e-43], t$95$2, If[LessEqual[a, -4.6e-181], t$95$1, If[LessEqual[a, -1e-261], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+40], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.25000000000000012e-43 or 7.4999999999999996e40 < a

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   if -2.25000000000000012e-43 < a < -4.59999999999999982e-181 or -9.99999999999999984e-262 < a < 7.4999999999999996e40

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 47.2%

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

   if -4.59999999999999982e-181 < a < -9.99999999999999984e-262

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around inf 52.1%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-181}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{-50} \lor \neg \left(c \leq 5.6 \cdot 10^{+138}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.7e-50) (not (<= c 5.6e+138)))
   (+ (* j (* a c)) (* b (- (* t i) (* z c))))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.7e-50) || !(c <= 5.6e+138)) {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.7d-50)) .or. (.not. (c <= 5.6d+138))) then
        tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.7e-50) || !(c <= 5.6e+138)) {
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.7e-50) or not (c <= 5.6e+138):
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.7e-50) || !(c <= 5.6e+138))
		tmp = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.7e-50) || ~((c <= 5.6e+138)))
		tmp = (j * (a * c)) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.7e-50], N[Not[LessEqual[c, 5.6e+138]], $MachinePrecision]], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.7000000000000001e-50 or 5.6000000000000002e138 < c

   1. Initial program 67.7%

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

   3. Taylor expanded in x around 0 67.1%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   if -3.7000000000000001e-50 < c < 5.6000000000000002e138

   1. Initial program 84.1%

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

   3. Taylor expanded in b around 0 71.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{-50} \lor \neg \left(c \leq 5.6 \cdot 10^{+138}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-53} \lor \neg \left(x \leq 2 \cdot 10^{+80}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -1.9e-53) (not (<= x 2e+80)))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
   (- (* b (- (* t i) (* z c))) (* j (- (* y i) (* a 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 ((x <= -1.9e-53) || !(x <= 2e+80)) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * 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 ((x <= (-1.9d-53)) .or. (.not. (x <= 2d+80))) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * 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 ((x <= -1.9e-53) || !(x <= 2e+80)) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -1.9e-53) or not (x <= 2e+80):
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -1.9e-53) || !(x <= 2e+80))
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -1.9e-53) || ~((x <= 2e+80)))
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (b * ((t * i) - (z * c))) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -1.9e-53], N[Not[LessEqual[x, 2e+80]], $MachinePrecision]], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e-53 or 2e80 < x

   1. Initial program 80.3%

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

   3. Taylor expanded in b around 0 77.0%

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

   if -1.8999999999999999e-53 < x < 2e80

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 76.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-53} \lor \neg \left(x \leq 2 \cdot 10^{+80}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= a -1.35e+140)
     t_1
     (if (<= a -4.4e-284)
       (* y (* x z))
       (if (<= a 1.45e-164)
         (* y (- (* i j)))
         (if (<= a 2.15e+45) (* i (* t b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (a <= -1.35e+140) {
		tmp = t_1;
	} else if (a <= -4.4e-284) {
		tmp = y * (x * z);
	} else if (a <= 1.45e-164) {
		tmp = y * -(i * j);
	} else if (a <= 2.15e+45) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t * -a)
    if (a <= (-1.35d+140)) then
        tmp = t_1
    else if (a <= (-4.4d-284)) then
        tmp = y * (x * z)
    else if (a <= 1.45d-164) then
        tmp = y * -(i * j)
    else if (a <= 2.15d+45) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (a <= -1.35e+140) {
		tmp = t_1;
	} else if (a <= -4.4e-284) {
		tmp = y * (x * z);
	} else if (a <= 1.45e-164) {
		tmp = y * -(i * j);
	} else if (a <= 2.15e+45) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if a <= -1.35e+140:
		tmp = t_1
	elif a <= -4.4e-284:
		tmp = y * (x * z)
	elif a <= 1.45e-164:
		tmp = y * -(i * j)
	elif a <= 2.15e+45:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (a <= -1.35e+140)
		tmp = t_1;
	elseif (a <= -4.4e-284)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.45e-164)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (a <= 2.15e+45)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (a <= -1.35e+140)
		tmp = t_1;
	elseif (a <= -4.4e-284)
		tmp = y * (x * z);
	elseif (a <= 1.45e-164)
		tmp = y * -(i * j);
	elseif (a <= 2.15e+45)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+140], t$95$1, If[LessEqual[a, -4.4e-284], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-164], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 2.15e+45], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.35000000000000009e140 or 2.1500000000000002e45 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in x around inf 59.2%

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

   4. Taylor expanded in y around 0 53.0%

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

      1. neg-mul-1 53.0%

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

      2. distribute-lft-neg-in 53.0%

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

      3. *-commutative 53.0%

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

   6. Simplified 53.0%

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

   if -1.35000000000000009e140 < a < -4.4000000000000001e-284

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in z around inf 33.7%

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

   if -4.4000000000000001e-284 < a < 1.45e-164

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

      5. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. distribute-rgt-neg-in 38.9%

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

   8. Simplified 38.9%

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

   if 1.45e-164 < a < 2.1500000000000002e45

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 39.3%

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

      1. distribute-lft-out-- 39.3%

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

      2. *-commutative 39.3%

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

   5. Simplified 39.3%

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

   6. Taylor expanded in a around 0 37.4%

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

      1. associate-*r* 34.3%

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

      2. *-commutative 34.3%

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

      3. associate-*r* 37.5%

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

   8. Simplified 37.5%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= a -1.75e+140)
     t_1
     (if (<= a -8.5e-284)
       (* y (* x z))
       (if (<= a 4.6e-164)
         (* i (* y (- j)))
         (if (<= a 2.7e+45) (* i (* t b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (a <= -1.75e+140) {
		tmp = t_1;
	} else if (a <= -8.5e-284) {
		tmp = y * (x * z);
	} else if (a <= 4.6e-164) {
		tmp = i * (y * -j);
	} else if (a <= 2.7e+45) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t * -a)
    if (a <= (-1.75d+140)) then
        tmp = t_1
    else if (a <= (-8.5d-284)) then
        tmp = y * (x * z)
    else if (a <= 4.6d-164) then
        tmp = i * (y * -j)
    else if (a <= 2.7d+45) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double tmp;
	if (a <= -1.75e+140) {
		tmp = t_1;
	} else if (a <= -8.5e-284) {
		tmp = y * (x * z);
	} else if (a <= 4.6e-164) {
		tmp = i * (y * -j);
	} else if (a <= 2.7e+45) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if a <= -1.75e+140:
		tmp = t_1
	elif a <= -8.5e-284:
		tmp = y * (x * z)
	elif a <= 4.6e-164:
		tmp = i * (y * -j)
	elif a <= 2.7e+45:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (a <= -1.75e+140)
		tmp = t_1;
	elseif (a <= -8.5e-284)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 4.6e-164)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 2.7e+45)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (a <= -1.75e+140)
		tmp = t_1;
	elseif (a <= -8.5e-284)
		tmp = y * (x * z);
	elseif (a <= 4.6e-164)
		tmp = i * (y * -j);
	elseif (a <= 2.7e+45)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+140], t$95$1, If[LessEqual[a, -8.5e-284], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-164], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+45], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.74999999999999995e140 or 2.69999999999999984e45 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in x around inf 59.2%

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

   4. Taylor expanded in y around 0 53.0%

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

      1. neg-mul-1 53.0%

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

      2. distribute-lft-neg-in 53.0%

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

      3. *-commutative 53.0%

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

   6. Simplified 53.0%

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

   if -1.74999999999999995e140 < a < -8.4999999999999995e-284

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in z around inf 33.7%

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

   if -8.4999999999999995e-284 < a < 4.59999999999999971e-164

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

      5. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around 0 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   8. Simplified 41.2%

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

   if 4.59999999999999971e-164 < a < 2.69999999999999984e45

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 39.3%

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

      1. distribute-lft-out-- 39.3%

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

      2. *-commutative 39.3%

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

   5. Simplified 39.3%

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

   6. Taylor expanded in a around 0 37.4%

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

      1. associate-*r* 34.3%

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

      2. *-commutative 34.3%

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

      3. associate-*r* 37.5%

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

   8. Simplified 37.5%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-165}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.65e+75)
   (* t (* x (- a)))
   (if (<= a -1.6e-284)
     (* y (* x z))
     (if (<= a 3e-165)
       (* i (* y (- j)))
       (if (<= a 1.35e+45) (* i (* t b)) (* x (* t (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.65e+75) {
		tmp = t * (x * -a);
	} else if (a <= -1.6e-284) {
		tmp = y * (x * z);
	} else if (a <= 3e-165) {
		tmp = i * (y * -j);
	} else if (a <= 1.35e+45) {
		tmp = i * (t * b);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.65d+75)) then
        tmp = t * (x * -a)
    else if (a <= (-1.6d-284)) then
        tmp = y * (x * z)
    else if (a <= 3d-165) then
        tmp = i * (y * -j)
    else if (a <= 1.35d+45) then
        tmp = i * (t * b)
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.65e+75) {
		tmp = t * (x * -a);
	} else if (a <= -1.6e-284) {
		tmp = y * (x * z);
	} else if (a <= 3e-165) {
		tmp = i * (y * -j);
	} else if (a <= 1.35e+45) {
		tmp = i * (t * b);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.65e+75:
		tmp = t * (x * -a)
	elif a <= -1.6e-284:
		tmp = y * (x * z)
	elif a <= 3e-165:
		tmp = i * (y * -j)
	elif a <= 1.35e+45:
		tmp = i * (t * b)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.65e+75)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -1.6e-284)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 3e-165)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 1.35e+45)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.65e+75)
		tmp = t * (x * -a);
	elseif (a <= -1.6e-284)
		tmp = y * (x * z);
	elseif (a <= 3e-165)
		tmp = i * (y * -j);
	elseif (a <= 1.35e+45)
		tmp = i * (t * b);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.65e+75], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-284], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-165], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+45], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.64999999999999999e75

   1. Initial program 59.2%

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

   3. Taylor expanded in t around inf 49.3%

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

      1. distribute-lft-out-- 49.3%

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

      2. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in a around inf 47.6%

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

   if -1.64999999999999999e75 < a < -1.60000000000000012e-284

   1. Initial program 85.5%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

      4. *-commutative 48.9%

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

      5. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in z around inf 35.6%

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

   if -1.60000000000000012e-284 < a < 2.99999999999999979e-165

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

      5. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around 0 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   8. Simplified 41.2%

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

   if 2.99999999999999979e-165 < a < 1.34999999999999992e45

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 39.3%

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

      1. distribute-lft-out-- 39.3%

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

      2. *-commutative 39.3%

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

   5. Simplified 39.3%

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

   6. Taylor expanded in a around 0 37.4%

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

      1. associate-*r* 34.3%

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

      2. *-commutative 34.3%

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

      3. associate-*r* 37.5%

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

   8. Simplified 37.5%

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

   if 1.34999999999999992e45 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf 58.8%

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

   4. Taylor expanded in y around 0 49.8%

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

      1. neg-mul-1 49.8%

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

      2. distribute-lft-neg-in 49.8%

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

      3. *-commutative 49.8%

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

   6. Simplified 49.8%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-165}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 13500000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.65e+110)
     t_1
     (if (<= x 1.8e-213)
       (* c (- (* a j) (* z b)))
       (if (<= x 13500000.0) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.65e+110) {
		tmp = t_1;
	} else if (x <= 1.8e-213) {
		tmp = c * ((a * j) - (z * b));
	} else if (x <= 13500000.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.65d+110)) then
        tmp = t_1
    else if (x <= 1.8d-213) then
        tmp = c * ((a * j) - (z * b))
    else if (x <= 13500000.0d0) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.65e+110) {
		tmp = t_1;
	} else if (x <= 1.8e-213) {
		tmp = c * ((a * j) - (z * b));
	} else if (x <= 13500000.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.65e+110:
		tmp = t_1
	elif x <= 1.8e-213:
		tmp = c * ((a * j) - (z * b))
	elif x <= 13500000.0:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.65e+110)
		tmp = t_1;
	elseif (x <= 1.8e-213)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (x <= 13500000.0)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.65e+110)
		tmp = t_1;
	elseif (x <= 1.8e-213)
		tmp = c * ((a * j) - (z * b));
	elseif (x <= 13500000.0)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+110], t$95$1, If[LessEqual[x, 1.8e-213], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 13500000.0], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.64999999999999986e110 or 1.35e7 < x

   1. Initial program 77.8%

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

   3. Taylor expanded in x around inf 68.3%

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

   if -1.64999999999999986e110 < x < 1.8e-213

   1. Initial program 77.6%

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

   3. Taylor expanded in c around inf 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   if 1.8e-213 < x < 1.35e7

   1. Initial program 77.9%

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

   3. Taylor expanded in b around inf 58.1%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 13500000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{+43} \lor \neg \left(j \leq 3.8 \cdot 10^{-76}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.05e+43) (not (<= j 3.8e-76))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.05e+43) || !(j <= 3.8e-76)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.05d+43)) .or. (.not. (j <= 3.8d-76))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.05e+43) || !(j <= 3.8e-76)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.05e+43) or not (j <= 3.8e-76):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.05e+43) || !(j <= 3.8e-76))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.05e+43) || ~((j <= 3.8e-76)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.05e+43], N[Not[LessEqual[j, 3.8e-76]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.05e43 or 3.8000000000000002e-76 < j

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

      4. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in j around inf 37.0%

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

      1. *-commutative 37.0%

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

   8. Simplified 37.0%

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

   if -2.05e43 < j < 3.8000000000000002e-76

   1. Initial program 76.3%

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

   3. Taylor expanded in t around inf 42.8%

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

      1. distribute-lft-out-- 42.8%

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

      2. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in a around 0 25.9%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{+43} \lor \neg \left(j \leq 3.8 \cdot 10^{-76}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+43} \lor \neg \left(j \leq 7 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.95e+43) (not (<= j 7e-63))) (* a (* c j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.95e+43) || !(j <= 7e-63)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.95d+43)) .or. (.not. (j <= 7d-63))) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.95e+43) || !(j <= 7e-63)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.95e+43) or not (j <= 7e-63):
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.95e+43) || !(j <= 7e-63))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.95e+43) || ~((j <= 7e-63)))
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.95e+43], N[Not[LessEqual[j, 7e-63]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.95e43 or 7.00000000000000006e-63 < j

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in j around inf 37.3%

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

      1. *-commutative 37.3%

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

   8. Simplified 37.3%

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

   if -1.95e43 < j < 7.00000000000000006e-63

   1. Initial program 75.5%

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

   3. Taylor expanded in t around inf 43.0%

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

      1. distribute-lft-out-- 43.0%

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

      2. *-commutative 43.0%

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

   5. Simplified 43.0%

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

   6. Taylor expanded in a around 0 25.2%

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

      1. associate-*r* 25.0%

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

      2. *-commutative 25.0%

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

      3. associate-*r* 29.0%

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

   8. Simplified 29.0%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+43} \lor \neg \left(j \leq 7 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.8%

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

3. Taylor expanded in a around inf 41.1%

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

   1. +-commutative 41.1%

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

   2. mul-1-neg 41.1%

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

   3. unsub-neg 41.1%

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

   4. *-commutative 41.1%

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

5. Simplified 41.1%

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

6. Taylor expanded in j around inf 22.2%

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

   1. *-commutative 22.2%

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

8. Simplified 22.2%

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

9. Final simplification 22.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))