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

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 6

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 2.05 \cdot 10^{+14}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))))
   (if (<= (- 1.0 z) 1.0) t_0 (if (<= (- 1.0 z) 2.05e+14) (+ y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= 1.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.05e+14) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    if ((1.0d0 - z) <= 1.0d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.05d+14) then
        tmp = y + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= 1.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.05e+14) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	tmp = 0
	if (1.0 - z) <= 1.0:
		tmp = t_0
	elif (1.0 - z) <= 2.05e+14:
		tmp = y + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (Float64(1.0 - z) <= 1.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.05e+14)
		tmp = Float64(y + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	tmp = 0.0;
	if ((1.0 - z) <= 1.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.05e+14)
		tmp = y + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.05e+14], N[(y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < 1 or 2.05e14 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1 < (-.f64 #s(literal 1 binary64) z) < 2.05e14

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-79}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.9e-79) (* (- 1.0 z) x) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-79) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = y * (1.0 - 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 <= (-4.9d-79)) then
        tmp = (1.0d0 - z) * x
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-79) {
		tmp = (1.0 - z) * x;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.9e-79:
		tmp = (1.0 - z) * x
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.9e-79)
		tmp = Float64(Float64(1.0 - z) * x);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.9e-79)
		tmp = (1.0 - z) * x;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.9e-79], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9000000000000001e-79

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.9000000000000001e-79 < x

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 31.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 7e-120) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7e-120) {
		tmp = x;
	} else {
		tmp = y;
	}
	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 (y <= 7d-120) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7e-120) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7e-120:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7e-120)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7e-120)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7e-120], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 7e-120

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 7e-120 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 51.2% accurate, 2.3× 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%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 6: 26.7% accurate, 7.0× 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%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in z around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))