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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 9

Speedup: 1.0×

• 20.6% 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, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. distribute-rgt-in 100.0%

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

   2. *-un-lft-identity 100.0%

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

   3. +-commutative 100.0%

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

   4. associate-+r+ 100.0%

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

   5. *-commutative 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto x + \left(y + z \cdot \left(x + y\right)\right) \]
6. Add Preprocessing

Alternative 2: 50.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+17}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-275}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.7e+17)
   (* x z)
   (if (<= z 1.4e-307)
     x
     (if (<= z 3.3e-275) y (if (<= z 1.4e-127) x (if (<= z 0.5) y (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.7e+17) {
		tmp = x * z;
	} else if (z <= 1.4e-307) {
		tmp = x;
	} else if (z <= 3.3e-275) {
		tmp = y;
	} else if (z <= 1.4e-127) {
		tmp = x;
	} else if (z <= 0.5) {
		tmp = y;
	} 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 <= (-4.7d+17)) then
        tmp = x * z
    else if (z <= 1.4d-307) then
        tmp = x
    else if (z <= 3.3d-275) then
        tmp = y
    else if (z <= 1.4d-127) then
        tmp = x
    else if (z <= 0.5d0) then
        tmp = y
    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 <= -4.7e+17) {
		tmp = x * z;
	} else if (z <= 1.4e-307) {
		tmp = x;
	} else if (z <= 3.3e-275) {
		tmp = y;
	} else if (z <= 1.4e-127) {
		tmp = x;
	} else if (z <= 0.5) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.7e+17:
		tmp = x * z
	elif z <= 1.4e-307:
		tmp = x
	elif z <= 3.3e-275:
		tmp = y
	elif z <= 1.4e-127:
		tmp = x
	elif z <= 0.5:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.7e+17)
		tmp = Float64(x * z);
	elseif (z <= 1.4e-307)
		tmp = x;
	elseif (z <= 3.3e-275)
		tmp = y;
	elseif (z <= 1.4e-127)
		tmp = x;
	elseif (z <= 0.5)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.7e+17)
		tmp = x * z;
	elseif (z <= 1.4e-307)
		tmp = x;
	elseif (z <= 3.3e-275)
		tmp = y;
	elseif (z <= 1.4e-127)
		tmp = x;
	elseif (z <= 0.5)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.7e+17], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.4e-307], x, If[LessEqual[z, 3.3e-275], y, If[LessEqual[z, 1.4e-127], x, If[LessEqual[z, 0.5], y, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7e17 or 0.5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 49.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.0%

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

      2. distribute-lft-in 49.0%

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

      3. *-rgt-identity 49.0%

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

   5. Applied egg-rr 49.0%

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

   6. Taylor expanded in z around inf 48.0%

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

   if -4.7e17 < z < 1.4e-307 or 3.3e-275 < z < 1.4e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.8%

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

   4. Taylor expanded in z around 0 45.8%

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

   if 1.4e-307 < z < 3.3e-275 or 1.4e-127 < z < 0.5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 53.2%

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

   4. Taylor expanded in z around 0 51.6%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+17}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-275}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.38 \lor \neg \left(z \leq 1.42 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.38) (not (<= z 1.42e-8))) (* x (+ z 1.0)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.38) || !(z <= 1.42e-8)) {
		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 <= (-0.38d0)) .or. (.not. (z <= 1.42d-8))) 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 <= -0.38) || !(z <= 1.42e-8)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.38) or not (z <= 1.42e-8):
		tmp = x * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.38) || !(z <= 1.42e-8))
		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 <= -0.38) || ~((z <= 1.42e-8)))
		tmp = x * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.38], N[Not[LessEqual[z, 1.42e-8]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.38 or 1.41999999999999998e-8 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 49.4%

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

   if -0.38 < z < 1.41999999999999998e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.38 \lor \neg \left(z \leq 1.42 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% 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 98.0%

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

      1. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   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 97.9%

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

      1. +-commutative 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 5: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 400000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 400000.0))) (* x z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 400000.0)) {
		tmp = x * 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 <= 400000.0d0))) then
        tmp = x * 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 <= 400000.0)) {
		tmp = x * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 400000.0):
		tmp = x * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 400000.0))
		tmp = Float64(x * 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 <= 400000.0)))
		tmp = x * 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, 400000.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 4e5 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.5%

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

      2. distribute-lft-in 48.5%

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

      3. *-rgt-identity 48.5%

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

   5. Applied egg-rr 48.5%

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

   6. Taylor expanded in z around inf 47.8%

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

   if -1 < z < 4e5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.6%

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

      1. +-commutative 96.6%

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

   5. Simplified 96.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 400000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.45e-57) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.45e-57) {
		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 (y <= 1.45d-57) 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 (y <= 1.45e-57) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.45e-57:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.45e-57)
		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 (y <= 1.45e-57)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.45e-57], 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 y < 1.45000000000000013e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.4%

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

   if 1.45000000000000013e-57 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 68.5%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Final simplification 100.0%

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

Alternative 8: 31.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.1e-112) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.1e-112) {
		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 <= 1.1d-112) 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 <= 1.1e-112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.1e-112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.1e-112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.1e-112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.1e-112], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.10000000000000011e-112

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.1%

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

   4. Taylor expanded in z around 0 26.6%

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

   if 1.10000000000000011e-112 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.5%

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

   4. Taylor expanded in z around 0 33.1%

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

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 25.8% 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. Add Preprocessing

3. Taylor expanded in x around inf 48.7%

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

4. Taylor expanded in z around 0 24.6%

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

5. Final simplification 24.6%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))