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

Percentage Accurate: 100.0% → 100.0%

Time: 1.6s

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: 46.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.8e+142)
   (+ x y)
   (if (<= x -3e+132) z (if (<= x -6e+84) (+ x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e+142) {
		tmp = x + y;
	} else if (x <= -3e+132) {
		tmp = z;
	} else if (x <= -6e+84) {
		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 <= (-8.8d+142)) then
        tmp = x + y
    else if (x <= (-3d+132)) then
        tmp = z
    else if (x <= (-6d+84)) 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 <= -8.8e+142) {
		tmp = x + y;
	} else if (x <= -3e+132) {
		tmp = z;
	} else if (x <= -6e+84) {
		tmp = x + y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.8e+142:
		tmp = x + y
	elif x <= -3e+132:
		tmp = z
	elif x <= -6e+84:
		tmp = x + y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.8e+142)
		tmp = Float64(x + y);
	elseif (x <= -3e+132)
		tmp = z;
	elseif (x <= -6e+84)
		tmp = Float64(x + y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.8e+142)
		tmp = x + y;
	elseif (x <= -3e+132)
		tmp = z;
	elseif (x <= -6e+84)
		tmp = x + y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.8e+142], N[(x + y), $MachinePrecision], If[LessEqual[x, -3e+132], z, If[LessEqual[x, -6e+84], N[(x + y), $MachinePrecision], z]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999947e142 or -2.9999999999999998e132 < x < -5.99999999999999992e84

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 91.6%

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

   if -8.79999999999999947e142 < x < -2.9999999999999998e132 or -5.99999999999999992e84 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 34.4%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.8e+142)
   (+ x y)
   (if (<= x -1.22e+132) z (if (<= x -7e+84) (+ x y) (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e+142) {
		tmp = x + y;
	} else if (x <= -1.22e+132) {
		tmp = z;
	} else if (x <= -7e+84) {
		tmp = x + y;
	} 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 <= (-8.8d+142)) then
        tmp = x + y
    else if (x <= (-1.22d+132)) then
        tmp = z
    else if (x <= (-7d+84)) then
        tmp = x + y
    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 <= -8.8e+142) {
		tmp = x + y;
	} else if (x <= -1.22e+132) {
		tmp = z;
	} else if (x <= -7e+84) {
		tmp = x + y;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.8e+142:
		tmp = x + y
	elif x <= -1.22e+132:
		tmp = z
	elif x <= -7e+84:
		tmp = x + y
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.8e+142)
		tmp = Float64(x + y);
	elseif (x <= -1.22e+132)
		tmp = z;
	elseif (x <= -7e+84)
		tmp = Float64(x + y);
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.8e+142)
		tmp = x + y;
	elseif (x <= -1.22e+132)
		tmp = z;
	elseif (x <= -7e+84)
		tmp = x + y;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.8e+142], N[(x + y), $MachinePrecision], If[LessEqual[x, -1.22e+132], z, If[LessEqual[x, -7e+84], N[(x + y), $MachinePrecision], N[(y + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.79999999999999947e142 or -1.22e132 < x < -6.9999999999999998e84

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 91.6%

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

   if -8.79999999999999947e142 < x < -1.22e132

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 2.8%

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

   if -6.9999999999999998e84 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 71.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+84}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]

Alternative 4: 44.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.8e+142) x (if (<= x -3.2e+132) z (if (<= x -6.2e+86) x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e+142) {
		tmp = x;
	} else if (x <= -3.2e+132) {
		tmp = z;
	} else if (x <= -6.2e+86) {
		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 <= (-8.8d+142)) then
        tmp = x
    else if (x <= (-3.2d+132)) then
        tmp = z
    else if (x <= (-6.2d+86)) 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 <= -8.8e+142) {
		tmp = x;
	} else if (x <= -3.2e+132) {
		tmp = z;
	} else if (x <= -6.2e+86) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.8e+142:
		tmp = x
	elif x <= -3.2e+132:
		tmp = z
	elif x <= -6.2e+86:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.8e+142)
		tmp = x;
	elseif (x <= -3.2e+132)
		tmp = z;
	elseif (x <= -6.2e+86)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.8e+142)
		tmp = x;
	elseif (x <= -3.2e+132)
		tmp = z;
	elseif (x <= -6.2e+86)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.8e+142], x, If[LessEqual[x, -3.2e+132], z, If[LessEqual[x, -6.2e+86], x, z]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999947e142 or -3.1999999999999997e132 < x < -6.2000000000000004e86

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.2%

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

   if -8.79999999999999947e142 < x < -3.1999999999999997e132 or -6.2000000000000004e86 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 34.7%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+132}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 66.9% 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 67.2%

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

3. Final simplification 67.2%

   \[\leadsto x + z \]

Alternative 6: 33.7% 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 39.2%

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

3. Final simplification 39.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))