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: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+75}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+118)
   (+ x y)
   (if (<= x -8e+75) (+ y z) (if (<= x -2.4e+53) x (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+118) {
		tmp = x + y;
	} else if (x <= -8e+75) {
		tmp = y + z;
	} else if (x <= -2.4e+53) {
		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 <= (-1d+118)) then
        tmp = x + y
    else if (x <= (-8d+75)) then
        tmp = y + z
    else if (x <= (-2.4d+53)) 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 <= -1e+118) {
		tmp = x + y;
	} else if (x <= -8e+75) {
		tmp = y + z;
	} else if (x <= -2.4e+53) {
		tmp = x;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+118:
		tmp = x + y
	elif x <= -8e+75:
		tmp = y + z
	elif x <= -2.4e+53:
		tmp = x
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+118)
		tmp = Float64(x + y);
	elseif (x <= -8e+75)
		tmp = Float64(y + z);
	elseif (x <= -2.4e+53)
		tmp = x;
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+118)
		tmp = x + y;
	elseif (x <= -8e+75)
		tmp = y + z;
	elseif (x <= -2.4e+53)
		tmp = x;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+118], N[(x + y), $MachinePrecision], If[LessEqual[x, -8e+75], N[(y + z), $MachinePrecision], If[LessEqual[x, -2.4e+53], x, N[(y + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999967e117

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.7%

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

   if -9.99999999999999967e117 < x < -7.99999999999999941e75 or -2.4e53 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.4%

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

   if -7.99999999999999941e75 < x < -2.4e53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+75}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]

Alternative 3: 43.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e+117) x (if (<= x -3.8e+76) z (if (<= x -4.2e+52) x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e+117) {
		tmp = x;
	} else if (x <= -3.8e+76) {
		tmp = z;
	} else if (x <= -4.2e+52) {
		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 <= (-4d+117)) then
        tmp = x
    else if (x <= (-3.8d+76)) then
        tmp = z
    else if (x <= (-4.2d+52)) 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 <= -4e+117) {
		tmp = x;
	} else if (x <= -3.8e+76) {
		tmp = z;
	} else if (x <= -4.2e+52) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4e+117:
		tmp = x
	elif x <= -3.8e+76:
		tmp = z
	elif x <= -4.2e+52:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e+117)
		tmp = x;
	elseif (x <= -3.8e+76)
		tmp = z;
	elseif (x <= -4.2e+52)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4e+117)
		tmp = x;
	elseif (x <= -3.8e+76)
		tmp = z;
	elseif (x <= -4.2e+52)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e+117], x, If[LessEqual[x, -3.8e+76], z, If[LessEqual[x, -4.2e+52], x, z]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000002e117 or -3.80000000000000024e76 < x < -4.2e52

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.2%

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

   if -4.0000000000000002e117 < x < -3.80000000000000024e76 or -4.2e52 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 33.0%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 45.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+117)
   (+ x y)
   (if (<= x -1.3e+76) z (if (<= x -1.42e+53) x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+117) {
		tmp = x + y;
	} else if (x <= -1.3e+76) {
		tmp = z;
	} else if (x <= -1.42e+53) {
		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 <= (-2.1d+117)) then
        tmp = x + y
    else if (x <= (-1.3d+76)) then
        tmp = z
    else if (x <= (-1.42d+53)) 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 <= -2.1e+117) {
		tmp = x + y;
	} else if (x <= -1.3e+76) {
		tmp = z;
	} else if (x <= -1.42e+53) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+117:
		tmp = x + y
	elif x <= -1.3e+76:
		tmp = z
	elif x <= -1.42e+53:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+117)
		tmp = Float64(x + y);
	elseif (x <= -1.3e+76)
		tmp = z;
	elseif (x <= -1.42e+53)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+117)
		tmp = x + y;
	elseif (x <= -1.3e+76)
		tmp = z;
	elseif (x <= -1.42e+53)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+117], N[(x + y), $MachinePrecision], If[LessEqual[x, -1.3e+76], z, If[LessEqual[x, -1.42e+53], x, z]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1000000000000001e117

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.7%

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

   if -2.1000000000000001e117 < x < -1.3e76 or -1.41999999999999999e53 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 33.0%

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

   if -1.3e76 < x < -1.41999999999999999e53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+76}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 66.7% 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 64.7%

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

3. Final simplification 64.7%

   \[\leadsto x + z \]

Alternative 6: 34.0% 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 35.7%

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

3. Final simplification 35.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))