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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 5

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 N/A

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

   4. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 67.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + \left(y + x\right) \leq -1 \cdot 10^{-119}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z (+ y x)) -1e-119) (+ y x) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + (y + x)) <= -1e-119) {
		tmp = y + 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 ((z + (y + x)) <= (-1d-119)) then
        tmp = y + 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 ((z + (y + x)) <= -1e-119) {
		tmp = y + x;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + (y + x)) <= -1e-119:
		tmp = y + x
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + Float64(y + x)) <= -1e-119)
		tmp = Float64(y + x);
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z + (y + x)) <= -1e-119)
		tmp = y + x;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], -1e-119], N[(y + x), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 x y) z) < -1.00000000000000001e-119

   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

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

      2. lower-+.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -1.00000000000000001e-119 < (+.f64 (+.f64 x y) z)

   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. lower-+.f64 73.0

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

   5. Applied rewrites 73.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + \left(y + x\right) \leq -1 \cdot 10^{-119}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 4: 65.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. lower-+.f64 65.7

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

5. Applied rewrites 65.7%

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

Alternative 5: 67.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

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

   2. lower-+.f64 65.7

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

5. Applied rewrites 65.7%

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

Reproduce

herbie shell --seed 2024216 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))