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

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 7

Speedup: 1.0×

• 21.5% 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: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+22}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -0.0028:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= z -2.3e+235)
     (* y z)
     (if (<= z -2.6e+67)
       (* x z)
       (if (<= z -4.4e+22)
         (* y z)
         (if (<= z -0.0028)
           t_0
           (if (<= z 9.2e-5) (+ x y) (if (<= z 1.65e+81) t_0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -2.3e+235) {
		tmp = y * z;
	} else if (z <= -2.6e+67) {
		tmp = x * z;
	} else if (z <= -4.4e+22) {
		tmp = y * z;
	} else if (z <= -0.0028) {
		tmp = t_0;
	} else if (z <= 9.2e-5) {
		tmp = x + y;
	} else if (z <= 1.65e+81) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + 1.0d0)
    if (z <= (-2.3d+235)) then
        tmp = y * z
    else if (z <= (-2.6d+67)) then
        tmp = x * z
    else if (z <= (-4.4d+22)) then
        tmp = y * z
    else if (z <= (-0.0028d0)) then
        tmp = t_0
    else if (z <= 9.2d-5) then
        tmp = x + y
    else if (z <= 1.65d+81) then
        tmp = t_0
    else
        tmp = y * z
    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 (z <= -2.3e+235) {
		tmp = y * z;
	} else if (z <= -2.6e+67) {
		tmp = x * z;
	} else if (z <= -4.4e+22) {
		tmp = y * z;
	} else if (z <= -0.0028) {
		tmp = t_0;
	} else if (z <= 9.2e-5) {
		tmp = x + y;
	} else if (z <= 1.65e+81) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if z <= -2.3e+235:
		tmp = y * z
	elif z <= -2.6e+67:
		tmp = x * z
	elif z <= -4.4e+22:
		tmp = y * z
	elif z <= -0.0028:
		tmp = t_0
	elif z <= 9.2e-5:
		tmp = x + y
	elif z <= 1.65e+81:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (z <= -2.3e+235)
		tmp = Float64(y * z);
	elseif (z <= -2.6e+67)
		tmp = Float64(x * z);
	elseif (z <= -4.4e+22)
		tmp = Float64(y * z);
	elseif (z <= -0.0028)
		tmp = t_0;
	elseif (z <= 9.2e-5)
		tmp = Float64(x + y);
	elseif (z <= 1.65e+81)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if (z <= -2.3e+235)
		tmp = y * z;
	elseif (z <= -2.6e+67)
		tmp = x * z;
	elseif (z <= -4.4e+22)
		tmp = y * z;
	elseif (z <= -0.0028)
		tmp = t_0;
	elseif (z <= 9.2e-5)
		tmp = x + y;
	elseif (z <= 1.65e+81)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+235], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.6e+67], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.4e+22], N[(y * z), $MachinePrecision], If[LessEqual[z, -0.0028], t$95$0, If[LessEqual[z, 9.2e-5], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.65e+81], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3e235 or -2.6e67 < z < -4.4e22 or 1.65e81 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

      1. distribute-lft-in 90.8%

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

      2. flip-+ 28.7%

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

   6. Applied egg-rr 28.7%

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

      1. difference-of-squares 29.0%

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

      2. +-commutative 29.0%

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

      3. distribute-lft-in 29.0%

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

      4. associate-/l* 48.6%

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

      5. *-inverses 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x + y}{\frac{1}{z}}} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + y}{\frac{1}{z}}} \]

   9. Taylor expanded in x around 0 49.6%

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

   if -2.3e235 < z < -2.6e67

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 43.7%

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

   if -4.4e22 < z < -0.00279999999999999997 or 9.20000000000000001e-5 < z < 1.65e81

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 70.0%

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

   if -0.00279999999999999997 < z < 9.20000000000000001e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.7%

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

      1. +-commutative 98.7%

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

   4. Simplified 98.7%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+22}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -0.0028:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+67}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -21 \lor \neg \left(z \leq 1.1 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e+235)
   (* y z)
   (if (<= z -5.1e+67)
     (* x z)
     (if (or (<= z -21.0) (not (<= z 1.1e+23))) (* y z) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e+235) {
		tmp = y * z;
	} else if (z <= -5.1e+67) {
		tmp = x * z;
	} else if ((z <= -21.0) || !(z <= 1.1e+23)) {
		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 <= (-2.3d+235)) then
        tmp = y * z
    else if (z <= (-5.1d+67)) then
        tmp = x * z
    else if ((z <= (-21.0d0)) .or. (.not. (z <= 1.1d+23))) 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 <= -2.3e+235) {
		tmp = y * z;
	} else if (z <= -5.1e+67) {
		tmp = x * z;
	} else if ((z <= -21.0) || !(z <= 1.1e+23)) {
		tmp = y * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.3e+235:
		tmp = y * z
	elif z <= -5.1e+67:
		tmp = x * z
	elif (z <= -21.0) or not (z <= 1.1e+23):
		tmp = y * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.3e+235)
		tmp = Float64(y * z);
	elseif (z <= -5.1e+67)
		tmp = Float64(x * z);
	elseif ((z <= -21.0) || !(z <= 1.1e+23))
		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 <= -2.3e+235)
		tmp = y * z;
	elseif (z <= -5.1e+67)
		tmp = x * z;
	elseif ((z <= -21.0) || ~((z <= 1.1e+23)))
		tmp = y * z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.3e+235], N[(y * z), $MachinePrecision], If[LessEqual[z, -5.1e+67], N[(x * z), $MachinePrecision], If[Or[LessEqual[z, -21.0], N[Not[LessEqual[z, 1.1e+23]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e235 or -5.1000000000000002e67 < z < -21 or 1.10000000000000004e23 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 98.6%

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

      1. +-commutative 98.6%

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

   4. Simplified 98.6%

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

      1. distribute-lft-in 90.4%

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

      2. flip-+ 29.7%

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

   6. Applied egg-rr 29.7%

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

      1. difference-of-squares 30.0%

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

      2. +-commutative 30.0%

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

      3. distribute-lft-in 30.0%

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

      4. associate-/l* 52.7%

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

      5. *-inverses 98.6%

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

      6. *-commutative 98.6%

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

      7. associate-/l* 98.5%

         \[\leadsto \color{blue}{\frac{x + y}{\frac{1}{z}}} \]

   8. Simplified 98.5%

      \[\leadsto \color{blue}{\frac{x + y}{\frac{1}{z}}} \]

   9. Taylor expanded in x around 0 46.5%

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

   if -2.3e235 < z < -5.1000000000000002e67

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 43.7%

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

   if -21 < z < 1.10000000000000004e23

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

   4. Simplified 94.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+235}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+67}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -21 \lor \neg \left(z \leq 1.1 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 98.1% 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 99.9%

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

   2. Taylor expanded in z around inf 98.1%

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

      1. +-commutative 98.1%

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

   4. Simplified 98.1%

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

   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 97.7%

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

      1. +-commutative 97.7%

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

   4. Simplified 97.7%

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

4. Final simplification 97.9%

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

Alternative 5: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e-101) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-101) {
		tmp = x * (z + 1.0);
	} 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) :: tmp
    if (x <= (-1.25d-101)) then
        tmp = x * (z + 1.0d0)
    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 <= -1.25e-101) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e-101:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e-101)
		tmp = Float64(x * Float64(z + 1.0));
	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 <= -1.25e-101)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e-101], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-101

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.9%

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

   if -1.25e-101 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 58.2%

      \[\leadsto \color{blue}{y \cdot \left(1 + z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 6: 32.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 6.8e-121) (* x z) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.8e-121) {
		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 (y <= 6.8d-121) 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 (y <= 6.8e-121) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.8e-121:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.8e-121)
		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 (y <= 6.8e-121)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.8e-121], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.80000000000000003e-121

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 53.1%

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

      1. +-commutative 53.1%

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

   4. Simplified 53.1%

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

   5. Taylor expanded in y around 0 36.2%

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

   if 6.80000000000000003e-121 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 52.8%

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

      1. +-commutative 52.8%

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

   4. Simplified 52.8%

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

      1. distribute-lft-in 46.4%

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

      2. flip-+ 13.9%

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

   6. Applied egg-rr 13.9%

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

      1. difference-of-squares 14.3%

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

      2. +-commutative 14.3%

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

      3. distribute-lft-in 14.3%

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

      4. associate-/l* 28.2%

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

      5. *-inverses 52.8%

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

      6. *-commutative 52.8%

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

      7. associate-/l* 52.7%

         \[\leadsto \color{blue}{\frac{x + y}{\frac{1}{z}}} \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{x + y}{\frac{1}{z}}} \]

   9. Taylor expanded in x around 0 38.6%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 26.9% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in z around inf 53.0%

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

   1. +-commutative 53.0%

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

4. Simplified 53.0%

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

5. Taylor expanded in y around 0 29.2%

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

6. Final simplification 29.2%

   \[\leadsto x \cdot z \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))