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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 10

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (z + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (z + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $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. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -0.5:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -2e+46)
   (* x z)
   (if (<= (+ z 1.0) -0.5)
     (* y z)
     (if (<= (+ z 1.0) 4e+21) (+ x y) (* x (+ z 1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -2e+46) {
		tmp = x * z;
	} else if ((z + 1.0) <= -0.5) {
		tmp = y * z;
	} else if ((z + 1.0) <= 4e+21) {
		tmp = x + y;
	} 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 + 1.0d0) <= (-2d+46)) then
        tmp = x * z
    else if ((z + 1.0d0) <= (-0.5d0)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 4d+21) then
        tmp = x + y
    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 + 1.0) <= -2e+46) {
		tmp = x * z;
	} else if ((z + 1.0) <= -0.5) {
		tmp = y * z;
	} else if ((z + 1.0) <= 4e+21) {
		tmp = x + y;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -2e+46:
		tmp = x * z
	elif (z + 1.0) <= -0.5:
		tmp = y * z
	elif (z + 1.0) <= 4e+21:
		tmp = x + y
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -2e+46)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= -0.5)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 4e+21)
		tmp = Float64(x + y);
	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 + 1.0) <= -2e+46)
		tmp = x * z;
	elseif ((z + 1.0) <= -0.5)
		tmp = y * z;
	elseif ((z + 1.0) <= 4e+21)
		tmp = x + y;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -2e+46], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -0.5], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 4e+21], N[(x + y), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -2e46

   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%

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

   4. Taylor expanded in x around inf 52.1%

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

      1. *-commutative 52.1%

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

   6. Simplified 52.1%

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

   if -2e46 < (+.f64 z #s(literal 1 binary64)) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.8%

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

   4. Taylor expanded in x around 0 52.7%

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

   if -0.5 < (+.f64 z #s(literal 1 binary64)) < 4e21

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.9%

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

      1. +-commutative 94.9%

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

   5. Simplified 94.9%

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

   if 4e21 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -0.5:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 4 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e+45)
   (* x z)
   (if (<= z -1.0) (* y z) (if (<= z 2.4e+21) (+ x y) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e+45) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 2.4e+21) {
		tmp = x + 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 <= (-2.8d+45)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 2.4d+21) then
        tmp = x + 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 <= -2.8e+45) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 2.4e+21) {
		tmp = x + y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.8e+45:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 2.4e+21:
		tmp = x + y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.8e+45)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 2.4e+21)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.8e+45)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 2.4e+21)
		tmp = x + y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.8e+45], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.4e+21], N[(x + y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e45 or 2.4e21 < 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 100.0%

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

   4. Taylor expanded in x around inf 52.9%

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

      1. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   if -2.7999999999999999e45 < 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 inf 89.8%

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

   4. Taylor expanded in x around 0 52.7%

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

   if -1 < z < 2.4e21

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.9%

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

      1. +-commutative 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e+45)
   (* x z)
   (if (<= z -4.8e-5) (* y z) (if (<= z 2.4e+21) y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+45) {
		tmp = x * z;
	} else if (z <= -4.8e-5) {
		tmp = y * z;
	} else if (z <= 2.4e+21) {
		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 <= (-7.5d+45)) then
        tmp = x * z
    else if (z <= (-4.8d-5)) then
        tmp = y * z
    else if (z <= 2.4d+21) 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 <= -7.5e+45) {
		tmp = x * z;
	} else if (z <= -4.8e-5) {
		tmp = y * z;
	} else if (z <= 2.4e+21) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e+45:
		tmp = x * z
	elif z <= -4.8e-5:
		tmp = y * z
	elif z <= 2.4e+21:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e+45)
		tmp = Float64(x * z);
	elseif (z <= -4.8e-5)
		tmp = Float64(y * z);
	elseif (z <= 2.4e+21)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e+45)
		tmp = x * z;
	elseif (z <= -4.8e-5)
		tmp = y * z;
	elseif (z <= 2.4e+21)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e+45], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.8e-5], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.4e+21], y, N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000058e45 or 2.4e21 < 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 100.0%

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

   4. Taylor expanded in x around inf 52.9%

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

      1. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   if -7.50000000000000058e45 < z < -4.8000000000000001e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.7%

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

   4. Taylor expanded in x around 0 48.0%

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

   if -4.8000000000000001e-5 < z < 2.4e21

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.4%

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

      1. +-commutative 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in y around inf 52.4%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-5} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-5) (not (<= z 1.0))) (* y z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-5) || !(z <= 1.0)) {
		tmp = y * 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 <= (-4.8d-5)) .or. (.not. (z <= 1.0d0))) then
        tmp = y * 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 <= -4.8e-5) || !(z <= 1.0)) {
		tmp = y * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-5) or not (z <= 1.0):
		tmp = y * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-5) || !(z <= 1.0))
		tmp = Float64(y * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-5) || ~((z <= 1.0)))
		tmp = y * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-5], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000001e-5 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 98.2%

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

   4. Taylor expanded in x around 0 52.5%

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

   if -4.8000000000000001e-5 < 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 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%

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

   6. Taylor expanded in y around inf 54.2%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-5} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-299) (* x (+ z 1.0)) (+ y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-299) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (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 ((x + y) <= (-1d-299)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-299) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-299:
		tmp = x * (z + 1.0)
	else:
		tmp = y + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-299)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-299)
		tmp = x * (z + 1.0);
	else
		tmp = y + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-299], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999992e-300

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 50.5%

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

   if -9.99999999999999992e-300 < (+.f64 x 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 53.8%

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

      1. distribute-lft-in 53.8%

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

      2. *-rgt-identity 53.8%

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

   5. Applied egg-rr 53.8%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-299) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-299) {
		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 + y) <= (-1d-299)) 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 + y) <= -1e-299) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-299:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-299)
		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 + y) <= -1e-299)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-299], 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 (+.f64 x y) < -9.99999999999999992e-300

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 50.5%

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

   if -9.99999999999999992e-300 < (+.f64 x 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 53.8%

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

Alternative 8: 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 9: 32.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.1e-110) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.1e-110) {
		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 <= 2.1d-110) 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 <= 2.1e-110) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.1e-110:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.1e-110)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.1e-110)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.1e-110], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.10000000000000002e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 44.7%

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

      1. +-commutative 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in y around 0 26.9%

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

   if 2.10000000000000002e-110 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 50.5%

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

      1. +-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in y around inf 36.7%

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

Alternative 10: 26.3% 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 z around 0 46.8%

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

   1. +-commutative 46.8%

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

5. Simplified 46.8%

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

6. Taylor expanded in y around 0 22.9%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024181 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))