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

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -2.1e-19) (+ x y) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-19) {
		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 <= (-2.1d-19)) 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 <= -2.1e-19) {
		tmp = x + y;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-19:
		tmp = x + y
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-19)
		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 <= -2.1e-19)
		tmp = x + y;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-19], N[(x + y), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.2%

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

   5. Simplified 81.2%

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

   if -2.0999999999999999e-19 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 72.1%

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

   5. Simplified 72.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.6 \cdot 10^{+74}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 2.6e+74) (+ x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.6e+74) {
		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 (z <= 2.6d+74) 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 (z <= 2.6e+74) {
		tmp = x + y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.6e+74:
		tmp = x + y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.6e+74)
		tmp = Float64(x + y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.6e+74)
		tmp = x + y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.6e+74], N[(x + y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if z < 2.6000000000000001e74

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.1%

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

   5. Simplified 76.1%

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

   if 2.6000000000000001e74 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 68.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.6 \cdot 10^{+74}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -2.1e-19) x z))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-19) {
		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-19)) 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-19) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-19:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-19)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e-19)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-19], x, z]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 63.0%

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

   if -2.0999999999999999e-19 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 36.4%

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

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. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 69.2%

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

5. Simplified 69.2%

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

6. Final simplification 69.2%

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

Alternative 6: 34.7% 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. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 39.7%

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

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))