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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 4

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

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

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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) + z \leq -5 \cdot 10^{-168}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ (+ x y) z) -5e-168) (+ x y) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x + y) + z) <= -5e-168) {
		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 + y) + z) <= (-5d-168)) 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 + y) + z) <= -5e-168) {
		tmp = x + y;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x + y) + z) <= -5e-168:
		tmp = x + y
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x + y) + z) <= -5e-168)
		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 + y) + z) <= -5e-168)
		tmp = x + y;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], -5e-168], N[(x + y), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 x y) z) < -5.00000000000000001e-168

   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 67.1

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

   5. Applied rewrites 67.1%

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

   if -5.00000000000000001e-168 < (+.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 68.6

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

   5. Applied rewrites 68.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + z \leq -5 \cdot 10^{-168}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-168}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= (+ x y) -5e-168) (+ x z) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -5e-168) {
		tmp = x + z;
	} 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 + y) <= (-5d-168)) then
        tmp = x + z
    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 + y) <= -5e-168) {
		tmp = x + z;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -5e-168:
		tmp = x + z
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -5e-168)
		tmp = Float64(x + z);
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -5e-168)
		tmp = x + z;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-168], N[(x + z), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.00000000000000001e-168

   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 66.0

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

   5. Applied rewrites 66.0%

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

   if -5.00000000000000001e-168 < (+.f64 x y)

   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 69.9

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

   5. Applied rewrites 69.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-168}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + y), $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 65.4

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

5. Applied rewrites 65.4%

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

6. Final simplification 65.4%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))