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

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Final simplification 100.0%

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

Alternative 2: 72.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-9} \lor \neg \left(x \leq -2.9 \cdot 10^{-40}\right) \land x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e+75)
   1.0
   (if (or (<= x -1.75e-9) (and (not (<= x -2.9e-40)) (<= x 3.1e-97)))
     (/ x y)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e+75) {
		tmp = 1.0;
	} else if ((x <= -1.75e-9) || (!(x <= -2.9e-40) && (x <= 3.1e-97))) {
		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 <= (-7d+75)) then
        tmp = 1.0d0
    else if ((x <= (-1.75d-9)) .or. (.not. (x <= (-2.9d-40))) .and. (x <= 3.1d-97)) 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 <= -7e+75) {
		tmp = 1.0;
	} else if ((x <= -1.75e-9) || (!(x <= -2.9e-40) && (x <= 3.1e-97))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e+75:
		tmp = 1.0
	elif (x <= -1.75e-9) or (not (x <= -2.9e-40) and (x <= 3.1e-97)):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e+75)
		tmp = 1.0;
	elseif ((x <= -1.75e-9) || (!(x <= -2.9e-40) && (x <= 3.1e-97)))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7e+75)
		tmp = 1.0;
	elseif ((x <= -1.75e-9) || (~((x <= -2.9e-40)) && (x <= 3.1e-97)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e+75], 1.0, If[Or[LessEqual[x, -1.75e-9], And[N[Not[LessEqual[x, -2.9e-40]], $MachinePrecision], LessEqual[x, 3.1e-97]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999997e75 or -1.75e-9 < x < -2.8999999999999999e-40 or 3.10000000000000002e-97 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

   if -6.9999999999999997e75 < x < -1.75e-9 or -2.8999999999999999e-40 < x < 3.10000000000000002e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-9} \lor \neg \left(x \leq -2.9 \cdot 10^{-40}\right) \land x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+60}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-9} \lor \neg \left(x \leq -7.2 \cdot 10^{-47}\right) \land x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.25e+60)
   (- 1.0 (/ y x))
   (if (or (<= x -4.9e-9) (and (not (<= x -7.2e-47)) (<= x 3.1e-97)))
     (/ x y)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.25e+60) {
		tmp = 1.0 - (y / x);
	} else if ((x <= -4.9e-9) || (!(x <= -7.2e-47) && (x <= 3.1e-97))) {
		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 <= (-2.25d+60)) then
        tmp = 1.0d0 - (y / x)
    else if ((x <= (-4.9d-9)) .or. (.not. (x <= (-7.2d-47))) .and. (x <= 3.1d-97)) 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 <= -2.25e+60) {
		tmp = 1.0 - (y / x);
	} else if ((x <= -4.9e-9) || (!(x <= -7.2e-47) && (x <= 3.1e-97))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.25e+60:
		tmp = 1.0 - (y / x)
	elif (x <= -4.9e-9) or (not (x <= -7.2e-47) and (x <= 3.1e-97)):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.25e+60)
		tmp = Float64(1.0 - Float64(y / x));
	elseif ((x <= -4.9e-9) || (!(x <= -7.2e-47) && (x <= 3.1e-97)))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.25e+60)
		tmp = 1.0 - (y / x);
	elseif ((x <= -4.9e-9) || (~((x <= -7.2e-47)) && (x <= 3.1e-97)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.25e+60], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -4.9e-9], And[N[Not[LessEqual[x, -7.2e-47]], $MachinePrecision], LessEqual[x, 3.1e-97]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25000000000000006e60

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if -2.25000000000000006e60 < x < -4.90000000000000004e-9 or -7.19999999999999982e-47 < x < 3.10000000000000002e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.4%

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

   if -4.90000000000000004e-9 < x < -7.19999999999999982e-47 or 3.10000000000000002e-97 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+60}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-9} \lor \neg \left(x \leq -7.2 \cdot 10^{-47}\right) \land x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.9% 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%

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

3. Taylor expanded in x around inf 55.4%

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

4. Final simplification 55.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))