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

Percentage Accurate: 100.0% → 100.0%

Time: 1.4s

Alternatives: 6

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]

2. Final simplification 100.0%

   \[\leadsto z + \left(x + y\right) \]

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+62}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e+137)
   (+ x y)
   (if (<= x -3.6e+62) (+ y z) (if (<= x -2.6e+20) x (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+137) {
		tmp = x + y;
	} else if (x <= -3.6e+62) {
		tmp = y + z;
	} else if (x <= -2.6e+20) {
		tmp = x;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Fortran

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 <= (-1.7d+137)) then
        tmp = x + y
    else if (x <= (-3.6d+62)) then
        tmp = y + z
    else if (x <= (-2.6d+20)) then
        tmp = x
    else
        tmp = y + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e+137) {
		tmp = x + y;
	} else if (x <= -3.6e+62) {
		tmp = y + z;
	} else if (x <= -2.6e+20) {
		tmp = x;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.7e+137:
		tmp = x + y
	elif x <= -3.6e+62:
		tmp = y + z
	elif x <= -2.6e+20:
		tmp = x
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e+137)
		tmp = Float64(x + y);
	elseif (x <= -3.6e+62)
		tmp = Float64(y + z);
	elseif (x <= -2.6e+20)
		tmp = x;
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e+137)
		tmp = x + y;
	elseif (x <= -3.6e+62)
		tmp = y + z;
	elseif (x <= -2.6e+20)
		tmp = x;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e+137], N[(x + y), $MachinePrecision], If[LessEqual[x, -3.6e+62], N[(y + z), $MachinePrecision], If[LessEqual[x, -2.6e+20], x, N[(y + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999993e137

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in z around 0 77.5%

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

   if -1.69999999999999993e137 < x < -3.6e62 or -2.6e20 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in x around 0 72.2%

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

   if -3.6e62 < x < -2.6e20

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in x around inf 51.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+62}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]

Alternative 3: 41.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e+136) x (if (<= x -2.2e+61) z (if (<= x -2.6e+20) x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+136) {
		tmp = x;
	} else if (x <= -2.2e+61) {
		tmp = z;
	} else if (x <= -2.6e+20) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

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 <= (-8.2d+136)) then
        tmp = x
    else if (x <= (-2.2d+61)) then
        tmp = z
    else if (x <= (-2.6d+20)) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+136) {
		tmp = x;
	} else if (x <= -2.2e+61) {
		tmp = z;
	} else if (x <= -2.6e+20) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e+136:
		tmp = x
	elif x <= -2.2e+61:
		tmp = z
	elif x <= -2.6e+20:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e+136)
		tmp = x;
	elseif (x <= -2.2e+61)
		tmp = z;
	elseif (x <= -2.6e+20)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e+136)
		tmp = x;
	elseif (x <= -2.2e+61)
		tmp = z;
	elseif (x <= -2.6e+20)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e+136], x, If[LessEqual[x, -2.2e+61], z, If[LessEqual[x, -2.6e+20], x, z]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999995e136 or -2.2e61 < x < -2.6e20

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in x around inf 65.5%

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

   if -8.1999999999999995e136 < x < -2.2e61 or -2.6e20 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in z around inf 38.1%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 47.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.55e+19) (+ x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+19) {
		tmp = x + y;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

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 <= (-1.55d+19)) then
        tmp = x + y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+19) {
		tmp = x + y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+19:
		tmp = x + y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+19)
		tmp = Float64(x + y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.55e+19)
		tmp = x + y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+19], N[(x + y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e19

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in z around 0 74.3%

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

   if -1.55e19 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + z \]

   2. Taylor expanded in z around inf 37.9%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 65.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ x + z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + 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 + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]

2. Taylor expanded in y around 0 70.0%

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

3. Final simplification 70.0%

   \[\leadsto x + z \]

Alternative 6: 34.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + z \]

2. Taylor expanded in x around inf 36.7%

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

3. Final simplification 36.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))