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

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{x}{x + y} \]
4. Add Preprocessing

Alternative 2: 73.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-35} \lor \neg \left(x \leq 1.15 \cdot 10^{-10}\right) \land x \leq 1.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e+71)
   1.0
   (if (or (<= x 1.4e-35) (and (not (<= x 1.15e-10)) (<= x 1.1e+78)))
     (/ x y)
     (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e+71) {
		tmp = 1.0;
	} else if ((x <= 1.4e-35) || (!(x <= 1.15e-10) && (x <= 1.1e+78))) {
		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 (x <= (-2.4d+71)) then
        tmp = 1.0d0
    else if ((x <= 1.4d-35) .or. (.not. (x <= 1.15d-10)) .and. (x <= 1.1d+78)) 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 (x <= -2.4e+71) {
		tmp = 1.0;
	} else if ((x <= 1.4e-35) || (!(x <= 1.15e-10) && (x <= 1.1e+78))) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e+71:
		tmp = 1.0
	elif (x <= 1.4e-35) or (not (x <= 1.15e-10) and (x <= 1.1e+78)):
		tmp = x / y
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e+71)
		tmp = 1.0;
	elseif ((x <= 1.4e-35) || (!(x <= 1.15e-10) && (x <= 1.1e+78)))
		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 (x <= -2.4e+71)
		tmp = 1.0;
	elseif ((x <= 1.4e-35) || (~((x <= 1.15e-10)) && (x <= 1.1e+78)))
		tmp = x / y;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e+71], 1.0, If[Or[LessEqual[x, 1.4e-35], And[N[Not[LessEqual[x, 1.15e-10]], $MachinePrecision], LessEqual[x, 1.1e+78]]], N[(x / y), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.39999999999999981e71

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.7%

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

   if -2.39999999999999981e71 < x < 1.4e-35 or 1.15000000000000004e-10 < x < 1.10000000000000007e78

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

   if 1.4e-35 < x < 1.15000000000000004e-10 or 1.10000000000000007e78 < x

   1. Initial program 99.9%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

   5. Simplified 94.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-35} \lor \neg \left(x \leq 1.15 \cdot 10^{-10}\right) \land x \leq 1.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-40} \lor \neg \left(x \leq 3.6 \cdot 10^{-10}\right) \land x \leq 2.55 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6e+72)
   1.0
   (if (or (<= x 1.36e-40) (and (not (<= x 3.6e-10)) (<= x 2.55e+75)))
     (/ x y)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6e+72) {
		tmp = 1.0;
	} else if ((x <= 1.36e-40) || (!(x <= 3.6e-10) && (x <= 2.55e+75))) {
		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 (x <= (-6d+72)) then
        tmp = 1.0d0
    else if ((x <= 1.36d-40) .or. (.not. (x <= 3.6d-10)) .and. (x <= 2.55d+75)) 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 (x <= -6e+72) {
		tmp = 1.0;
	} else if ((x <= 1.36e-40) || (!(x <= 3.6e-10) && (x <= 2.55e+75))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6e+72:
		tmp = 1.0
	elif (x <= 1.36e-40) or (not (x <= 3.6e-10) and (x <= 2.55e+75)):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6e+72)
		tmp = 1.0;
	elseif ((x <= 1.36e-40) || (!(x <= 3.6e-10) && (x <= 2.55e+75)))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6e+72)
		tmp = 1.0;
	elseif ((x <= 1.36e-40) || (~((x <= 3.6e-10)) && (x <= 2.55e+75)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6e+72], 1.0, If[Or[LessEqual[x, 1.36e-40], And[N[Not[LessEqual[x, 3.6e-10]], $MachinePrecision], LessEqual[x, 2.55e+75]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000006e72 or 1.3599999999999999e-40 < x < 3.6e-10 or 2.55000000000000018e75 < x

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 85.8%

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

   if -6.00000000000000006e72 < x < 1.3599999999999999e-40 or 3.6e-10 < x < 2.55000000000000018e75

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-40} \lor \neg \left(x \leq 3.6 \cdot 10^{-10}\right) \land x \leq 2.55 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% 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. Add Preprocessing

3. Taylor expanded in x around inf 50.2%

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

4. Final simplification 50.2%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024047 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))