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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

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: 73.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-47} \lor \neg \left(x \leq -4 \cdot 10^{-111}\right) \land x \leq 35000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8e+61)
   1.0
   (if (or (<= x -1.08e-47) (and (not (<= x -4e-111)) (<= x 35000000.0)))
     (/ x y)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8e+61) {
		tmp = 1.0;
	} else if ((x <= -1.08e-47) || (!(x <= -4e-111) && (x <= 35000000.0))) {
		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 <= (-8d+61)) then
        tmp = 1.0d0
    else if ((x <= (-1.08d-47)) .or. (.not. (x <= (-4d-111))) .and. (x <= 35000000.0d0)) 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 <= -8e+61) {
		tmp = 1.0;
	} else if ((x <= -1.08e-47) || (!(x <= -4e-111) && (x <= 35000000.0))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8e+61:
		tmp = 1.0
	elif (x <= -1.08e-47) or (not (x <= -4e-111) and (x <= 35000000.0)):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8e+61)
		tmp = 1.0;
	elseif ((x <= -1.08e-47) || (!(x <= -4e-111) && (x <= 35000000.0)))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8e+61)
		tmp = 1.0;
	elseif ((x <= -1.08e-47) || (~((x <= -4e-111)) && (x <= 35000000.0)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8e+61], 1.0, If[Or[LessEqual[x, -1.08e-47], And[N[Not[LessEqual[x, -4e-111]], $MachinePrecision], LessEqual[x, 35000000.0]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -7.9999999999999996e61 or -1.08000000000000005e-47 < x < -4.00000000000000035e-111 or 3.5e7 < 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 -7.9999999999999996e61 < x < -1.08000000000000005e-47 or -4.00000000000000035e-111 < x < 3.5e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-47} \lor \neg \left(x \leq -4 \cdot 10^{-111}\right) \land x \leq 35000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{x}\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y x))))
   (if (<= x -3.3e+59)
     t_0
     (if (<= x -1.7e-47)
       (/ x y)
       (if (<= x -4e-111) t_0 (if (<= x 35000000.0) (/ x y) 1.0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (y / x);
	double tmp;
	if (x <= -3.3e+59) {
		tmp = t_0;
	} else if (x <= -1.7e-47) {
		tmp = x / y;
	} else if (x <= -4e-111) {
		tmp = t_0;
	} else if (x <= 35000000.0) {
		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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / x)
    if (x <= (-3.3d+59)) then
        tmp = t_0
    else if (x <= (-1.7d-47)) then
        tmp = x / y
    else if (x <= (-4d-111)) then
        tmp = t_0
    else if (x <= 35000000.0d0) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (y / x);
	double tmp;
	if (x <= -3.3e+59) {
		tmp = t_0;
	} else if (x <= -1.7e-47) {
		tmp = x / y;
	} else if (x <= -4e-111) {
		tmp = t_0;
	} else if (x <= 35000000.0) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (y / x)
	tmp = 0
	if x <= -3.3e+59:
		tmp = t_0
	elif x <= -1.7e-47:
		tmp = x / y
	elif x <= -4e-111:
		tmp = t_0
	elif x <= 35000000.0:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(y / x))
	tmp = 0.0
	if (x <= -3.3e+59)
		tmp = t_0;
	elseif (x <= -1.7e-47)
		tmp = Float64(x / y);
	elseif (x <= -4e-111)
		tmp = t_0;
	elseif (x <= 35000000.0)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (y / x);
	tmp = 0.0;
	if (x <= -3.3e+59)
		tmp = t_0;
	elseif (x <= -1.7e-47)
		tmp = x / y;
	elseif (x <= -4e-111)
		tmp = t_0;
	elseif (x <= 35000000.0)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+59], t$95$0, If[LessEqual[x, -1.7e-47], N[(x / y), $MachinePrecision], If[LessEqual[x, -4e-111], t$95$0, If[LessEqual[x, 35000000.0], N[(x / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2999999999999999e59 or -1.7000000000000001e-47 < x < -4.00000000000000035e-111

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

   5. Simplified 82.9%

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

   if -3.2999999999999999e59 < x < -1.7000000000000001e-47 or -4.00000000000000035e-111 < x < 3.5e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.5%

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

   if 3.5e7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-111}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.6% 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%

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

3. Taylor expanded in x around inf 51.1%

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

4. Final simplification 51.1%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))