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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

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: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160} \lor \neg \left(y \leq 2.05 \cdot 10^{-87}\right) \land y \leq 6.5 \cdot 10^{+78}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.2e-63)
   (/ x y)
   (if (or (<= y 1.6e-160) (and (not (<= y 2.05e-87)) (<= y 6.5e+78)))
     (- 1.0 (/ y x))
     (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.2e-63) {
		tmp = x / y;
	} else if ((y <= 1.6e-160) || (!(y <= 2.05e-87) && (y <= 6.5e+78))) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.2d-63)) then
        tmp = x / y
    else if ((y <= 1.6d-160) .or. (.not. (y <= 2.05d-87)) .and. (y <= 6.5d+78)) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.2e-63) {
		tmp = x / y;
	} else if ((y <= 1.6e-160) || (!(y <= 2.05e-87) && (y <= 6.5e+78))) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.2e-63:
		tmp = x / y
	elif (y <= 1.6e-160) or (not (y <= 2.05e-87) and (y <= 6.5e+78)):
		tmp = 1.0 - (y / x)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.2e-63)
		tmp = Float64(x / y);
	elseif ((y <= 1.6e-160) || (!(y <= 2.05e-87) && (y <= 6.5e+78)))
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.2e-63)
		tmp = x / y;
	elseif ((y <= 1.6e-160) || (~((y <= 2.05e-87)) && (y <= 6.5e+78)))
		tmp = 1.0 - (y / x);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.2e-63], N[(x / y), $MachinePrecision], If[Or[LessEqual[y, 1.6e-160], And[N[Not[LessEqual[y, 2.05e-87]], $MachinePrecision], LessEqual[y, 6.5e+78]]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e-63 or 1.60000000000000004e-160 < y < 2.05000000000000016e-87 or 6.50000000000000036e78 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.7%

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

   if -2.2e-63 < y < 1.60000000000000004e-160 or 2.05000000000000016e-87 < y < 6.50000000000000036e78

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

   4. Simplified 79.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160} \lor \neg \left(y \leq 2.05 \cdot 10^{-87}\right) \land y \leq 6.5 \cdot 10^{+78}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.3e-63)
   (/ x y)
   (if (<= y 1.6e-160)
     1.0
     (if (<= y 7.6e-88) (/ x y) (if (<= y 5.8e+78) 1.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.3e-63) {
		tmp = x / y;
	} else if (y <= 1.6e-160) {
		tmp = 1.0;
	} else if (y <= 7.6e-88) {
		tmp = x / y;
	} else if (y <= 5.8e+78) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.3d-63)) then
        tmp = x / y
    else if (y <= 1.6d-160) then
        tmp = 1.0d0
    else if (y <= 7.6d-88) then
        tmp = x / y
    else if (y <= 5.8d+78) then
        tmp = 1.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.3e-63) {
		tmp = x / y;
	} else if (y <= 1.6e-160) {
		tmp = 1.0;
	} else if (y <= 7.6e-88) {
		tmp = x / y;
	} else if (y <= 5.8e+78) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.3e-63:
		tmp = x / y
	elif y <= 1.6e-160:
		tmp = 1.0
	elif y <= 7.6e-88:
		tmp = x / y
	elif y <= 5.8e+78:
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.3e-63)
		tmp = Float64(x / y);
	elseif (y <= 1.6e-160)
		tmp = 1.0;
	elseif (y <= 7.6e-88)
		tmp = Float64(x / y);
	elseif (y <= 5.8e+78)
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.3e-63)
		tmp = x / y;
	elseif (y <= 1.6e-160)
		tmp = 1.0;
	elseif (y <= 7.6e-88)
		tmp = x / y;
	elseif (y <= 5.8e+78)
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.3e-63], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.6e-160], 1.0, If[LessEqual[y, 7.6e-88], N[(x / y), $MachinePrecision], If[LessEqual[y, 5.8e+78], 1.0, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999994e-63 or 1.60000000000000004e-160 < y < 7.60000000000000022e-88 or 5.80000000000000034e78 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.7%

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

   if -3.29999999999999994e-63 < y < 1.60000000000000004e-160 or 7.60000000000000022e-88 < y < 5.80000000000000034e78

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 50.7% 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 48.8%

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

3. Final simplification 48.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))