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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 7

Speedup: 1.0×

• 20.7% 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: 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 99.2%

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

      1. +-commutative 99.2%

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

   4. Simplified 99.2%

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

   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 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 99.1%

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

Alternative 3: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-125}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-39)
   (* x (+ z 1.0))
   (if (<= x -1.08e-125) (+ x y) (* y (+ z 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-39) {
		tmp = x * (z + 1.0);
	} else if (x <= -1.08e-125) {
		tmp = x + y;
	} 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) :: tmp
    if (x <= (-7.2d-39)) then
        tmp = x * (z + 1.0d0)
    else if (x <= (-1.08d-125)) then
        tmp = x + y
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-39) {
		tmp = x * (z + 1.0);
	} else if (x <= -1.08e-125) {
		tmp = x + y;
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-39:
		tmp = x * (z + 1.0)
	elif x <= -1.08e-125:
		tmp = x + y
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-39)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (x <= -1.08e-125)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-39)
		tmp = x * (z + 1.0);
	elseif (x <= -1.08e-125)
		tmp = x + y;
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-39], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.08e-125], N[(x + y), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2000000000000001e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.4%

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

   if -7.2000000000000001e-39 < x < -1.07999999999999998e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 65.2%

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

      1. +-commutative 65.2%

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

   4. Simplified 65.2%

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

   if -1.07999999999999998e-125 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 56.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-125}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 4: 51.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 99.2%

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

      1. +-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around 0 52.7%

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

   if -1 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 52.3%

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

   5. Taylor expanded in z around 0 52.1%

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

4. Final simplification 52.4%

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

Alternative 5: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.06\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.06))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.06)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	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 <= 0.06d0))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.06)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.06):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.06))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.06)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.06]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.059999999999999998 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 95.8%

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

   3. Applied egg-rr 95.8%

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

   4. Taylor expanded in z around inf 95.3%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

   7. Simplified 51.7%

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

   if -1 < z < 0.059999999999999998

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 52.3%

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

   5. Taylor expanded in z around 0 52.1%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.06\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 31000\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 31000.0))) (* y z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 31000.0)) {
		tmp = y * z;
	} 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 <= 31000.0d0))) then
        tmp = y * z
    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 <= 31000.0)) {
		tmp = y * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 31000.0):
		tmp = y * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 31000.0))
		tmp = Float64(y * z);
	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 <= 31000.0)))
		tmp = y * z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 31000.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 31000 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 95.8%

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

   3. Applied egg-rr 95.8%

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

   4. Taylor expanded in z around inf 95.3%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

   7. Simplified 51.7%

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

   if -1 < z < 31000

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 31000\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 26.4% 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. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-lft-in 98.0%

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

3. Applied egg-rr 98.0%

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

4. Taylor expanded in z around inf 72.4%

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

5. Taylor expanded in z around 0 28.9%

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

6. Final simplification 28.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))