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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

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. Add Preprocessing

Alternative 2: 73.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-14} \lor \neg \left(x \leq -6 \cdot 10^{-95}\right) \land \left(x \leq 1.12 \cdot 10^{-56} \lor \neg \left(x \leq 3.4 \cdot 10^{-9}\right) \land x \leq 2.7 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5e+42)
   (- 1.0 (/ y x))
   (if (or (<= x -8e-14)
           (and (not (<= x -6e-95))
                (or (<= x 1.12e-56) (and (not (<= x 3.4e-9)) (<= x 2.7e+22)))))
     (/ x y)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5e+42) {
		tmp = 1.0 - (y / x);
	} else if ((x <= -8e-14) || (!(x <= -6e-95) && ((x <= 1.12e-56) || (!(x <= 3.4e-9) && (x <= 2.7e+22))))) {
		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 <= (-4.5d+42)) then
        tmp = 1.0d0 - (y / x)
    else if ((x <= (-8d-14)) .or. (.not. (x <= (-6d-95))) .and. (x <= 1.12d-56) .or. (.not. (x <= 3.4d-9)) .and. (x <= 2.7d+22)) 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 <= -4.5e+42) {
		tmp = 1.0 - (y / x);
	} else if ((x <= -8e-14) || (!(x <= -6e-95) && ((x <= 1.12e-56) || (!(x <= 3.4e-9) && (x <= 2.7e+22))))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5e+42:
		tmp = 1.0 - (y / x)
	elif (x <= -8e-14) or (not (x <= -6e-95) and ((x <= 1.12e-56) or (not (x <= 3.4e-9) and (x <= 2.7e+22)))):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5e+42)
		tmp = Float64(1.0 - Float64(y / x));
	elseif ((x <= -8e-14) || (!(x <= -6e-95) && ((x <= 1.12e-56) || (!(x <= 3.4e-9) && (x <= 2.7e+22)))))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5e+42)
		tmp = 1.0 - (y / x);
	elseif ((x <= -8e-14) || (~((x <= -6e-95)) && ((x <= 1.12e-56) || (~((x <= 3.4e-9)) && (x <= 2.7e+22)))))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5e+42], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -8e-14], And[N[Not[LessEqual[x, -6e-95]], $MachinePrecision], Or[LessEqual[x, 1.12e-56], And[N[Not[LessEqual[x, 3.4e-9]], $MachinePrecision], LessEqual[x, 2.7e+22]]]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000012e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. unsub-neg 87.1%

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

   5. Simplified 87.1%

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

   if -4.50000000000000012e42 < x < -7.99999999999999999e-14 or -6e-95 < x < 1.12e-56 or 3.3999999999999998e-9 < x < 2.7000000000000002e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.4%

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

   if -7.99999999999999999e-14 < x < -6e-95 or 1.12e-56 < x < 3.3999999999999998e-9 or 2.7000000000000002e22 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-14} \lor \neg \left(x \leq -6 \cdot 10^{-95}\right) \land \left(x \leq 1.12 \cdot 10^{-56} \lor \neg \left(x \leq 3.4 \cdot 10^{-9}\right) \land x \leq 2.7 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-95}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-56} \lor \neg \left(x \leq 1.5 \cdot 10^{-8}\right) \land x \leq 4.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.5e-95)
   1.0
   (if (or (<= x 1.12e-56) (and (not (<= x 1.5e-8)) (<= x 4.6e+23)))
     (/ x y)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.5e-95) {
		tmp = 1.0;
	} else if ((x <= 1.12e-56) || (!(x <= 1.5e-8) && (x <= 4.6e+23))) {
		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 <= (-1.5d-95)) then
        tmp = 1.0d0
    else if ((x <= 1.12d-56) .or. (.not. (x <= 1.5d-8)) .and. (x <= 4.6d+23)) 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 <= -1.5e-95) {
		tmp = 1.0;
	} else if ((x <= 1.12e-56) || (!(x <= 1.5e-8) && (x <= 4.6e+23))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.5e-95:
		tmp = 1.0
	elif (x <= 1.12e-56) or (not (x <= 1.5e-8) and (x <= 4.6e+23)):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.5e-95)
		tmp = 1.0;
	elseif ((x <= 1.12e-56) || (!(x <= 1.5e-8) && (x <= 4.6e+23)))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.5e-95)
		tmp = 1.0;
	elseif ((x <= 1.12e-56) || (~((x <= 1.5e-8)) && (x <= 4.6e+23)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.5e-95], 1.0, If[Or[LessEqual[x, 1.12e-56], And[N[Not[LessEqual[x, 1.5e-8]], $MachinePrecision], LessEqual[x, 4.6e+23]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e-95 or 1.12e-56 < x < 1.49999999999999987e-8 or 4.6000000000000001e23 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.7%

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

   if -1.5e-95 < x < 1.12e-56 or 1.49999999999999987e-8 < x < 4.6000000000000001e23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-95}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-56} \lor \neg \left(x \leq 1.5 \cdot 10^{-8}\right) \land x \leq 4.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% 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 56.2%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024098 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))