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

Percentage Accurate: 100.0% → 100.0%

Time: 10.7s

Alternatives: 6

Speedup: N/A×

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

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

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(x + Float64(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[(x + N[(y + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]
2. Step-by-step derivation

   1. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(y + z\right)} \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

   3. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + \left(y + z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-64}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= x -1.25e-64) (+ x y) (+ y z)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-64) {
		tmp = x + y;
	} else {
		tmp = y + 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 (x <= (-1.25d-64)) then
        tmp = x + y
    else
        tmp = y + 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 (x <= -1.25e-64) {
		tmp = x + y;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if x <= -1.25e-64:
		tmp = x + y
	else:
		tmp = y + z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e-64)
		tmp = Float64(x + y);
	else
		tmp = Float64(y + 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 (x <= -1.25e-64)
		tmp = x + y;
	else
		tmp = y + 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[x, -1.25e-64], N[(x + y), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000008e-64

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y + z\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 68.2%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 68.2%

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

   if -1.25000000000000008e-64 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y + z\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y + z} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 81.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{z}\right) \]

   7. Simplified 81.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-64}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= x -2.95e-65) (+ x y) z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.95e-65) {
		tmp = x + y;
	} 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 (x <= (-2.95d-65)) then
        tmp = x + y
    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 (x <= -2.95e-65) {
		tmp = x + y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if x <= -2.95e-65:
		tmp = x + y
	else:
		tmp = z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= -2.95e-65)
		tmp = Float64(x + y);
	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 (x <= -2.95e-65)
		tmp = x + y;
	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[x, -2.95e-65], N[(x + y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -2.94999999999999989e-65

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y + z\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 68.7%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 68.7%

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

   if -2.94999999999999989e-65 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y + z\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   6. Step-by-step derivation

   7. Simplified 40.5%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-65}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= x -1.25e-64) x z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-64) {
		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 (x <= (-1.25d-64)) 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 (x <= -1.25e-64) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if x <= -1.25e-64:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e-64)
		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 (x <= -1.25e-64)
		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[x, -1.25e-64], x, z]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000008e-64

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y + z\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 50.4%

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

   if -1.25000000000000008e-64 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

         \[\leadsto x + \color{blue}{\left(y + z\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(y + z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   6. Step-by-step derivation

   7. Simplified 40.3%

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

Alternative 5: 98.5% 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. Step-by-step derivation

   1. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(y + z\right)} \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

   3. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + \left(y + z\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x + z} \]
6. Step-by-step derivation

   1. +-commutative N/A

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

   2. +-lowering-+.f64 65.2%

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{x}\right) \]

7. Simplified 65.2%

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

8. Final simplification 65.2%

   \[\leadsto x + z \]
9. Add Preprocessing

Alternative 6: 49.2% 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. Step-by-step derivation

   1. associate-+l+ N/A

      \[\leadsto x + \color{blue}{\left(y + z\right)} \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + z\right)}\right) \]

   3. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{z}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + \left(y + z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 29.1%

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))