Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) + z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) + z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \left(x + y\right) + z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (+ (+ x y) z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (x + y) + z;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) + z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return (x + y) + z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (x + y) + z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(x + y) + z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (x + y) + z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-284}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -5.1e-284) x (if (<= y 1.45e-153) z (if (<= y 3.8e-143) x z))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e-284) {
		tmp = x;
	} else if (y <= 1.45e-153) {
		tmp = z;
	} else if (y <= 3.8e-143) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.1d-284)) then
        tmp = x
    else if (y <= 1.45d-153) then
        tmp = z
    else if (y <= 3.8d-143) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e-284) {
		tmp = x;
	} else if (y <= 1.45e-153) {
		tmp = z;
	} else if (y <= 3.8e-143) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -5.1e-284:
		tmp = x
	elif y <= 1.45e-153:
		tmp = z
	elif y <= 3.8e-143:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -5.1e-284)
		tmp = x;
	elseif (y <= 1.45e-153)
		tmp = z;
	elseif (y <= 3.8e-143)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.1e-284)
		tmp = x;
	elseif (y <= 1.45e-153)
		tmp = z;
	elseif (y <= 3.8e-143)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -5.1e-284], x, If[LessEqual[y, 1.45e-153], z, If[LessEqual[y, 3.8e-143], x, z]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1000000000000002e-284 or 1.45000000000000001e-153 < y < 3.79999999999999981e-143

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{x} + z \]

   4. Taylor expanded in x around inf 34.9%

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

   if -5.1000000000000002e-284 < y < 1.45000000000000001e-153 or 3.79999999999999981e-143 < y

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 32.6%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x + z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (+ x z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x + z;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return x + z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x + z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(x + z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x + z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(x + z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 63.4%

   \[\leadsto \color{blue}{x} + z \]
4. Add Preprocessing

Alternative 4: 49.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 63.4%

   \[\leadsto \color{blue}{x} + z \]

4. Taylor expanded in x around inf 32.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))