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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 8

Speedup: 1.0×

• 20.2% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+222}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{+155}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 14000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+179} \lor \neg \left(z \leq 6 \cdot 10^{+226}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.02e+222)
   (* x z)
   (if (<= z -8.3e+155)
     (* y z)
     (if (<= z -3.7e+62)
       (* x z)
       (if (<= z -1.0)
         (* y z)
         (if (<= z 14000.0)
           (+ x y)
           (if (or (<= z 2e+179) (not (<= z 6e+226)))
             (* y z)
             (* x (+ z 1.0)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.02e+222) {
		tmp = x * z;
	} else if (z <= -8.3e+155) {
		tmp = y * z;
	} else if (z <= -3.7e+62) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 14000.0) {
		tmp = x + y;
	} else if ((z <= 2e+179) || !(z <= 6e+226)) {
		tmp = y * z;
	} else {
		tmp = x * (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 (z <= (-1.02d+222)) then
        tmp = x * z
    else if (z <= (-8.3d+155)) then
        tmp = y * z
    else if (z <= (-3.7d+62)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 14000.0d0) then
        tmp = x + y
    else if ((z <= 2d+179) .or. (.not. (z <= 6d+226))) then
        tmp = y * z
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.02e+222) {
		tmp = x * z;
	} else if (z <= -8.3e+155) {
		tmp = y * z;
	} else if (z <= -3.7e+62) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 14000.0) {
		tmp = x + y;
	} else if ((z <= 2e+179) || !(z <= 6e+226)) {
		tmp = y * z;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.02e+222:
		tmp = x * z
	elif z <= -8.3e+155:
		tmp = y * z
	elif z <= -3.7e+62:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 14000.0:
		tmp = x + y
	elif (z <= 2e+179) or not (z <= 6e+226):
		tmp = y * z
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.02e+222)
		tmp = Float64(x * z);
	elseif (z <= -8.3e+155)
		tmp = Float64(y * z);
	elseif (z <= -3.7e+62)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 14000.0)
		tmp = Float64(x + y);
	elseif ((z <= 2e+179) || !(z <= 6e+226))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.02e+222)
		tmp = x * z;
	elseif (z <= -8.3e+155)
		tmp = y * z;
	elseif (z <= -3.7e+62)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 14000.0)
		tmp = x + y;
	elseif ((z <= 2e+179) || ~((z <= 6e+226)))
		tmp = y * z;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.02e+222], N[(x * z), $MachinePrecision], If[LessEqual[z, -8.3e+155], N[(y * z), $MachinePrecision], If[LessEqual[z, -3.7e+62], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 14000.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 2e+179], N[Not[LessEqual[z, 6e+226]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.01999999999999995e222 or -8.2999999999999998e155 < z < -3.70000000000000014e62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 65.3%

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

   if -1.01999999999999995e222 < z < -8.2999999999999998e155 or -3.70000000000000014e62 < z < -1 or 14000 < z < 1.99999999999999996e179 or 5.9999999999999995e226 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 59.7%

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

   4. Taylor expanded in z around inf 59.7%

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

   if -1 < z < 14000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   if 1.99999999999999996e179 < z < 5.9999999999999995e226

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+222}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.3 \cdot 10^{+155}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 14000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+179} \lor \neg \left(z \leq 6 \cdot 10^{+226}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+221}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+155}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 14000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+179} \lor \neg \left(z \leq 4.8 \cdot 10^{+230}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e+221)
   (* x z)
   (if (<= z -5.2e+155)
     (* y z)
     (if (<= z -3.1e+62)
       (* x z)
       (if (<= z -1.0)
         (* y z)
         (if (<= z 14000.0)
           (+ x y)
           (if (or (<= z 1.02e+179) (not (<= z 4.8e+230)))
             (* y z)
             (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+221) {
		tmp = x * z;
	} else if (z <= -5.2e+155) {
		tmp = y * z;
	} else if (z <= -3.1e+62) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 14000.0) {
		tmp = x + y;
	} else if ((z <= 1.02e+179) || !(z <= 4.8e+230)) {
		tmp = y * z;
	} else {
		tmp = x * 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 (z <= (-1.5d+221)) then
        tmp = x * z
    else if (z <= (-5.2d+155)) then
        tmp = y * z
    else if (z <= (-3.1d+62)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 14000.0d0) then
        tmp = x + y
    else if ((z <= 1.02d+179) .or. (.not. (z <= 4.8d+230))) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+221) {
		tmp = x * z;
	} else if (z <= -5.2e+155) {
		tmp = y * z;
	} else if (z <= -3.1e+62) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 14000.0) {
		tmp = x + y;
	} else if ((z <= 1.02e+179) || !(z <= 4.8e+230)) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e+221:
		tmp = x * z
	elif z <= -5.2e+155:
		tmp = y * z
	elif z <= -3.1e+62:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 14000.0:
		tmp = x + y
	elif (z <= 1.02e+179) or not (z <= 4.8e+230):
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e+221)
		tmp = Float64(x * z);
	elseif (z <= -5.2e+155)
		tmp = Float64(y * z);
	elseif (z <= -3.1e+62)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 14000.0)
		tmp = Float64(x + y);
	elseif ((z <= 1.02e+179) || !(z <= 4.8e+230))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e+221)
		tmp = x * z;
	elseif (z <= -5.2e+155)
		tmp = y * z;
	elseif (z <= -3.1e+62)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 14000.0)
		tmp = x + y;
	elseif ((z <= 1.02e+179) || ~((z <= 4.8e+230)))
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e+221], N[(x * z), $MachinePrecision], If[LessEqual[z, -5.2e+155], N[(y * z), $MachinePrecision], If[LessEqual[z, -3.1e+62], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 14000.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1.02e+179], N[Not[LessEqual[z, 4.8e+230]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e221 or -5.2000000000000004e155 < z < -3.10000000000000014e62 or 1.0199999999999999e179 < z < 4.79999999999999996e230

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 67.3%

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

   if -1.5000000000000001e221 < z < -5.2000000000000004e155 or -3.10000000000000014e62 < z < -1 or 14000 < z < 1.0199999999999999e179 or 4.79999999999999996e230 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 59.7%

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

   4. Taylor expanded in z around inf 59.7%

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

   if -1 < z < 14000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+221}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+155}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 14000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+179} \lor \neg \left(z \leq 4.8 \cdot 10^{+230}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+221}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+178} \lor \neg \left(z \leq 2.45 \cdot 10^{+228}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e+221)
   (* x z)
   (if (<= z -2.55e+156)
     (* y z)
     (if (<= z -3e+62)
       (* x z)
       (if (<= z -1.0)
         (* y z)
         (if (<= z 5.8e-16)
           y
           (if (or (<= z 7.5e+178) (not (<= z 2.45e+228)))
             (* y z)
             (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e+221) {
		tmp = x * z;
	} else if (z <= -2.55e+156) {
		tmp = y * z;
	} else if (z <= -3e+62) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 5.8e-16) {
		tmp = y;
	} else if ((z <= 7.5e+178) || !(z <= 2.45e+228)) {
		tmp = y * z;
	} else {
		tmp = x * 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 (z <= (-1.15d+221)) then
        tmp = x * z
    else if (z <= (-2.55d+156)) then
        tmp = y * z
    else if (z <= (-3d+62)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 5.8d-16) then
        tmp = y
    else if ((z <= 7.5d+178) .or. (.not. (z <= 2.45d+228))) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e+221) {
		tmp = x * z;
	} else if (z <= -2.55e+156) {
		tmp = y * z;
	} else if (z <= -3e+62) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 5.8e-16) {
		tmp = y;
	} else if ((z <= 7.5e+178) || !(z <= 2.45e+228)) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e+221:
		tmp = x * z
	elif z <= -2.55e+156:
		tmp = y * z
	elif z <= -3e+62:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 5.8e-16:
		tmp = y
	elif (z <= 7.5e+178) or not (z <= 2.45e+228):
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e+221)
		tmp = Float64(x * z);
	elseif (z <= -2.55e+156)
		tmp = Float64(y * z);
	elseif (z <= -3e+62)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 5.8e-16)
		tmp = y;
	elseif ((z <= 7.5e+178) || !(z <= 2.45e+228))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e+221)
		tmp = x * z;
	elseif (z <= -2.55e+156)
		tmp = y * z;
	elseif (z <= -3e+62)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 5.8e-16)
		tmp = y;
	elseif ((z <= 7.5e+178) || ~((z <= 2.45e+228)))
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e+221], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.55e+156], N[(y * z), $MachinePrecision], If[LessEqual[z, -3e+62], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 5.8e-16], y, If[Or[LessEqual[z, 7.5e+178], N[Not[LessEqual[z, 2.45e+228]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999993e221 or -2.55000000000000007e156 < z < -3e62 or 7.4999999999999995e178 < z < 2.4500000000000001e228

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 67.3%

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

   if -1.14999999999999993e221 < z < -2.55000000000000007e156 or -3e62 < z < -1 or 5.7999999999999996e-16 < z < 7.4999999999999995e178 or 2.4500000000000001e228 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 58.8%

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

   4. Taylor expanded in z around inf 57.8%

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

   if -1 < z < 5.7999999999999996e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 58.3%

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

   4. Taylor expanded in z around 0 58.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+221}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+62}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+178} \lor \neg \left(z \leq 2.45 \cdot 10^{+228}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{-62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= x -2.25e-62)
     t_0
     (if (<= x -4.5e-138) (+ x y) (if (<= x -2.9e-148) 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 (x <= -2.25e-62) {
		tmp = t_0;
	} else if (x <= -4.5e-138) {
		tmp = x + y;
	} else if (x <= -2.9e-148) {
		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 (x <= (-2.25d-62)) then
        tmp = t_0
    else if (x <= (-4.5d-138)) then
        tmp = x + y
    else if (x <= (-2.9d-148)) 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 (x <= -2.25e-62) {
		tmp = t_0;
	} else if (x <= -4.5e-138) {
		tmp = x + y;
	} else if (x <= -2.9e-148) {
		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 x <= -2.25e-62:
		tmp = t_0
	elif x <= -4.5e-138:
		tmp = x + y
	elif x <= -2.9e-148:
		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 (x <= -2.25e-62)
		tmp = t_0;
	elseif (x <= -4.5e-138)
		tmp = Float64(x + y);
	elseif (x <= -2.9e-148)
		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 (x <= -2.25e-62)
		tmp = t_0;
	elseif (x <= -4.5e-138)
		tmp = x + y;
	elseif (x <= -2.9e-148)
		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[x, -2.25e-62], t$95$0, If[LessEqual[x, -4.5e-138], N[(x + y), $MachinePrecision], If[LessEqual[x, -2.9e-148], t$95$0, N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25000000000000009e-62 or -4.50000000000000008e-138 < x < -2.8999999999999998e-148

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.8%

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

   if -2.25000000000000009e-62 < x < -4.50000000000000008e-138

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 60.9%

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

      1. +-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -2.8999999999999998e-148 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-138}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.5× 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. Add Preprocessing

   3. Taylor expanded in z around inf 97.3%

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

      1. +-commutative 97.3%

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

   5. Simplified 97.3%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 98.4%

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

Alternative 7: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.8 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 5.8e-16))) (* x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 5.8e-16)) {
		tmp = x * z;
	} 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 ((z <= (-1.0d0)) .or. (.not. (z <= 5.8d-16))) then
        tmp = x * z
    else
        tmp = 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 <= 5.8e-16)) {
		tmp = x * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 5.8e-16):
		tmp = x * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 5.8e-16))
		tmp = Float64(x * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 5.8e-16)))
		tmp = x * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 5.8e-16]], $MachinePrecision]], N[(x * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5.7999999999999996e-16 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.6%

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

      1. +-commutative 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in y around 0 51.9%

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

   if -1 < z < 5.7999999999999996e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 58.3%

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

   4. Taylor expanded in z around 0 58.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.8 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 26.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 54.2%

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

4. Taylor expanded in z around 0 28.9%

   \[\leadsto \color{blue}{y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))