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

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 7

Speedup: 1.0×

• 22.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]

2. Final simplification 100.0%

   \[\leadsto \left(x + y\right) \cdot \left(z + 1\right) \]

Alternative 2: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= y 1e-59)
     t_0
     (if (<= y 9.5e+26) (+ x y) (if (<= y 8.5e+43) t_0 (* y (+ z 1.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (y <= 1e-59) {
		tmp = t_0;
	} else if (y <= 9.5e+26) {
		tmp = x + y;
	} else if (y <= 8.5e+43) {
		tmp = t_0;
	} else {
		tmp = y * (z + 1.0);
	}
	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 = x * (z + 1.0d0)
    if (y <= 1d-59) then
        tmp = t_0
    else if (y <= 9.5d+26) then
        tmp = x + y
    else if (y <= 8.5d+43) then
        tmp = t_0
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (y <= 1e-59) {
		tmp = t_0;
	} else if (y <= 9.5e+26) {
		tmp = x + y;
	} else if (y <= 8.5e+43) {
		tmp = t_0;
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if y <= 1e-59:
		tmp = t_0
	elif y <= 9.5e+26:
		tmp = x + y
	elif y <= 8.5e+43:
		tmp = t_0
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= 1e-59)
		tmp = t_0;
	elseif (y <= 9.5e+26)
		tmp = Float64(x + y);
	elseif (y <= 8.5e+43)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= 1e-59)
		tmp = t_0;
	elseif (y <= 9.5e+26)
		tmp = x + y;
	elseif (y <= 8.5e+43)
		tmp = t_0;
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1e-59], t$95$0, If[LessEqual[y, 9.5e+26], N[(x + y), $MachinePrecision], If[LessEqual[y, 8.5e+43], t$95$0, N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1e-59 or 9.50000000000000054e26 < y < 8.5e43

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 59.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]

   if 1e-59 < y < 9.50000000000000054e26

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 65.5%

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

      1. +-commutative 65.5%

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

   4. Simplified 65.5%

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

   if 8.5e43 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{y \cdot \left(1 + z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{-59}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-12} \lor \neg \left(z \leq 80000000000000\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-12) (not (<= z 80000000000000.0)))
   (* x (+ z 1.0))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-12) || !(z <= 80000000000000.0)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + 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 ((z <= (-5.3d-12)) .or. (.not. (z <= 80000000000000.0d0))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-12) || !(z <= 80000000000000.0)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.3e-12) or not (z <= 80000000000000.0):
		tmp = x * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.3e-12) || !(z <= 80000000000000.0))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.3e-12) || ~((z <= 80000000000000.0)))
		tmp = x * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.3e-12], N[Not[LessEqual[z, 80000000000000.0]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.29999999999999963e-12 or 8e13 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 55.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]

   if -5.29999999999999963e-12 < z < 8e13

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 97.8%

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

      1. +-commutative 97.8%

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

   4. Simplified 97.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-12} \lor \neg \left(z \leq 80000000000000\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 97.9% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* z (+ x y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x + y);
	} else {
		tmp = x + 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 ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x + y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x + y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * (x + y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(x + y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * (x + y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{z \cdot \left(x + y\right)} \]
   3. Step-by-step derivation

      1. +-commutative 99.1%

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

   4. Simplified 99.1%

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

   if -1 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 98.0%

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

      1. +-commutative 98.0%

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

   4. Simplified 98.0%

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

4. Final simplification 98.5%

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

Alternative 5: 32.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.25e-54) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-54) {
		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 <= 1.25d-54) 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 <= 1.25e-54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.25e-54:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.25e-54)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.25e-54)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.25e-54], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.25000000000000004e-54

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 59.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]

   3. Taylor expanded in z around 0 29.9%

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

   if 1.25000000000000004e-54 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 70.6%

      \[\leadsto \color{blue}{y \cdot \left(1 + z\right)} \]

   3. Taylor expanded in z around 0 36.8%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 51.6% accurate, 2.3× 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%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]

2. Taylor expanded in z around 0 53.0%

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

   1. +-commutative 53.0%

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

4. Simplified 53.0%

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

5. Final simplification 53.0%

   \[\leadsto x + y \]

Alternative 7: 26.8% 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%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]

2. Taylor expanded in x around inf 51.7%

   \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]

3. Taylor expanded in z around 0 26.6%

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

4. Final simplification 26.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))