AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 2.3s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

double code(double x, double y) {
	return x / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (x + y)
end function

Java

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (x + y);
end

Wolfram

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

double code(double x, double y) {
	return x / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (x + y)
end function

Java

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (x + y);
end

Wolfram

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

double code(double x, double y) {
	return x / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (x + y)
end function

Java

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (x + y);
end

Wolfram

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x}{x + y} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x}{x + y} \]

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+135} \lor \neg \left(y \leq -4.1 \cdot 10^{+128}\right) \land \left(y \leq -2.3 \cdot 10^{+47} \lor \neg \left(y \leq 3.7 \cdot 10^{+32}\right)\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.9e+135)
         (and (not (<= y -4.1e+128))
              (or (<= y -2.3e+47) (not (<= y 3.7e+32)))))
   (/ x y)
   (- 1.0 (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.9e+135) || (!(y <= -4.1e+128) && ((y <= -2.3e+47) || !(y <= 3.7e+32)))) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4.9d+135)) .or. (.not. (y <= (-4.1d+128))) .and. (y <= (-2.3d+47)) .or. (.not. (y <= 3.7d+32))) then
        tmp = x / y
    else
        tmp = 1.0d0 - (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.9e+135) || (!(y <= -4.1e+128) && ((y <= -2.3e+47) || !(y <= 3.7e+32)))) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.9e+135) or (not (y <= -4.1e+128) and ((y <= -2.3e+47) or not (y <= 3.7e+32))):
		tmp = x / y
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.9e+135) || (!(y <= -4.1e+128) && ((y <= -2.3e+47) || !(y <= 3.7e+32))))
		tmp = Float64(x / y);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.9e+135) || (~((y <= -4.1e+128)) && ((y <= -2.3e+47) || ~((y <= 3.7e+32)))))
		tmp = x / y;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.9e+135], And[N[Not[LessEqual[y, -4.1e+128]], $MachinePrecision], Or[LessEqual[y, -2.3e+47], N[Not[LessEqual[y, 3.7e+32]], $MachinePrecision]]]], N[(x / y), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9000000000000001e135 or -4.10000000000000012e128 < y < -2.2999999999999999e47 or 3.7e32 < y

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if -4.9000000000000001e135 < y < -4.10000000000000012e128 or -2.2999999999999999e47 < y < 3.7e32

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around inf 76.7%

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y}{x}} \]
   3. Step-by-step derivation

      1. mul-1-neg 76.7%

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

      2. unsub-neg 76.7%

         \[\leadsto \color{blue}{1 - \frac{y}{x}} \]

   4. Simplified 76.7%

      \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+135} \lor \neg \left(y \leq -4.1 \cdot 10^{+128}\right) \land \left(y \leq -2.3 \cdot 10^{+47} \lor \neg \left(y \leq 3.7 \cdot 10^{+32}\right)\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 3: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+135} \lor \neg \left(y \leq -4 \cdot 10^{+128}\right) \land \left(y \leq -2.1 \cdot 10^{+46} \lor \neg \left(y \leq 2.95 \cdot 10^{+31}\right)\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.2e+135)
         (and (not (<= y -4e+128)) (or (<= y -2.1e+46) (not (<= y 2.95e+31)))))
   (/ x y)
   1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.2e+135) || (!(y <= -4e+128) && ((y <= -2.1e+46) || !(y <= 2.95e+31)))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3.2d+135)) .or. (.not. (y <= (-4d+128))) .and. (y <= (-2.1d+46)) .or. (.not. (y <= 2.95d+31))) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.2e+135) || (!(y <= -4e+128) && ((y <= -2.1e+46) || !(y <= 2.95e+31)))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.2e+135) or (not (y <= -4e+128) and ((y <= -2.1e+46) or not (y <= 2.95e+31))):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.2e+135) || (!(y <= -4e+128) && ((y <= -2.1e+46) || !(y <= 2.95e+31))))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.2e+135) || (~((y <= -4e+128)) && ((y <= -2.1e+46) || ~((y <= 2.95e+31)))))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.2e+135], And[N[Not[LessEqual[y, -4e+128]], $MachinePrecision], Or[LessEqual[y, -2.1e+46], N[Not[LessEqual[y, 2.95e+31]], $MachinePrecision]]]], N[(x / y), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999975e135 or -4.0000000000000003e128 < y < -2.1e46 or 2.9500000000000002e31 < y

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if -3.19999999999999975e135 < y < -4.0000000000000003e128 or -2.1e46 < y < 2.9500000000000002e31

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around inf 76.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+135} \lor \neg \left(y \leq -4 \cdot 10^{+128}\right) \land \left(y \leq -2.1 \cdot 10^{+46} \lor \neg \left(y \leq 2.95 \cdot 10^{+31}\right)\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 50.0% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x}{x + y} \]

2. Taylor expanded in x around inf 56.1%

   \[\leadsto \color{blue}{1} \]

3. Final simplification 56.1%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))