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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 10

Speedup: 1.0×

• 20.5% 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, 0.8× speedup

Math

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

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(Float64(x + 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[(N[(x + y), $MachinePrecision] + N[(z * N[(x + y), $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. +-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. Final simplification 100.0%

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

Alternative 2: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-172}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+226} \lor \neg \left(z \leq 1.1 \cdot 10^{+272}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* y z)
   (if (<= z -9e-140)
     y
     (if (<= z -1.35e-195)
       x
       (if (<= z 1.75e-172)
         y
         (if (<= z 2550.0)
           x
           (if (or (<= z 1e+226) (not (<= z 1.1e+272))) (* y z) (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -9e-140) {
		tmp = y;
	} else if (z <= -1.35e-195) {
		tmp = x;
	} else if (z <= 1.75e-172) {
		tmp = y;
	} else if (z <= 2550.0) {
		tmp = x;
	} else if ((z <= 1e+226) || !(z <= 1.1e+272)) {
		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 <= (-1.0d0)) then
        tmp = y * z
    else if (z <= (-9d-140)) then
        tmp = y
    else if (z <= (-1.35d-195)) then
        tmp = x
    else if (z <= 1.75d-172) then
        tmp = y
    else if (z <= 2550.0d0) then
        tmp = x
    else if ((z <= 1d+226) .or. (.not. (z <= 1.1d+272))) 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 <= -1.0) {
		tmp = y * z;
	} else if (z <= -9e-140) {
		tmp = y;
	} else if (z <= -1.35e-195) {
		tmp = x;
	} else if (z <= 1.75e-172) {
		tmp = y;
	} else if (z <= 2550.0) {
		tmp = x;
	} else if ((z <= 1e+226) || !(z <= 1.1e+272)) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= -9e-140:
		tmp = y
	elif z <= -1.35e-195:
		tmp = x
	elif z <= 1.75e-172:
		tmp = y
	elif z <= 2550.0:
		tmp = x
	elif (z <= 1e+226) or not (z <= 1.1e+272):
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= -9e-140)
		tmp = y;
	elseif (z <= -1.35e-195)
		tmp = x;
	elseif (z <= 1.75e-172)
		tmp = y;
	elseif (z <= 2550.0)
		tmp = x;
	elseif ((z <= 1e+226) || !(z <= 1.1e+272))
		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 <= -1.0)
		tmp = y * z;
	elseif (z <= -9e-140)
		tmp = y;
	elseif (z <= -1.35e-195)
		tmp = x;
	elseif (z <= 1.75e-172)
		tmp = y;
	elseif (z <= 2550.0)
		tmp = x;
	elseif ((z <= 1e+226) || ~((z <= 1.1e+272)))
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -9e-140], y, If[LessEqual[z, -1.35e-195], x, If[LessEqual[z, 1.75e-172], y, If[LessEqual[z, 2550.0], x, If[Or[LessEqual[z, 1e+226], N[Not[LessEqual[z, 1.1e+272]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1 or 2550 < z < 9.99999999999999961e225 or 1.10000000000000004e272 < 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 48.9%

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

      1. +-commutative 48.9%

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

      2. distribute-lft-in 48.9%

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

      3. *-rgt-identity 48.9%

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

   5. Applied egg-rr 48.9%

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

   6. Taylor expanded in z around inf 48.0%

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

      1. *-commutative 48.0%

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

   8. Simplified 48.0%

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

   if -1 < z < -9.00000000000000008e-140 or -1.35e-195 < z < 1.75000000000000014e-172

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.7%

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

   4. Taylor expanded in z around 0 53.3%

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

   if -9.00000000000000008e-140 < z < -1.35e-195 or 1.75000000000000014e-172 < z < 2550

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 55.5%

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

   4. Taylor expanded in z around 0 50.2%

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

   if 9.99999999999999961e225 < z < 1.10000000000000004e272

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 13.0%

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

      1. +-commutative 13.0%

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

      2. distribute-lft-in 13.0%

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

      3. *-rgt-identity 13.0%

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

   5. Applied egg-rr 13.0%

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

   6. Taylor expanded in z around inf 13.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-172}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+226} \lor \neg \left(z \leq 1.1 \cdot 10^{+272}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-173}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* x z)
   (if (<= z -7.6e-140)
     y
     (if (<= z -1.06e-196)
       x
       (if (<= z 4.7e-173) y (if (<= z 1.0) x (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -7.6e-140) {
		tmp = y;
	} else if (z <= -1.06e-196) {
		tmp = x;
	} else if (z <= 4.7e-173) {
		tmp = y;
	} else if (z <= 1.0) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = x * z
    else if (z <= (-7.6d-140)) then
        tmp = y
    else if (z <= (-1.06d-196)) then
        tmp = x
    else if (z <= 4.7d-173) then
        tmp = y
    else if (z <= 1.0d0) then
        tmp = x
    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 <= -1.0) {
		tmp = x * z;
	} else if (z <= -7.6e-140) {
		tmp = y;
	} else if (z <= -1.06e-196) {
		tmp = x;
	} else if (z <= 4.7e-173) {
		tmp = y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= -7.6e-140:
		tmp = y
	elif z <= -1.06e-196:
		tmp = x
	elif z <= 4.7e-173:
		tmp = y
	elif z <= 1.0:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= -7.6e-140)
		tmp = y;
	elseif (z <= -1.06e-196)
		tmp = x;
	elseif (z <= 4.7e-173)
		tmp = y;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= -7.6e-140)
		tmp = y;
	elseif (z <= -1.06e-196)
		tmp = x;
	elseif (z <= 4.7e-173)
		tmp = y;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -7.6e-140], y, If[LessEqual[z, -1.06e-196], x, If[LessEqual[z, 4.7e-173], y, If[LessEqual[z, 1.0], x, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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 x around inf 52.4%

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

      1. +-commutative 52.4%

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

      2. distribute-lft-in 52.4%

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

      3. *-rgt-identity 52.4%

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

   5. Applied egg-rr 52.4%

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

   6. Taylor expanded in z around inf 51.3%

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

   if -1 < z < -7.59999999999999997e-140 or -1.05999999999999994e-196 < z < 4.7e-173

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.7%

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

   4. Taylor expanded in z around 0 53.3%

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

   if -7.59999999999999997e-140 < z < -1.05999999999999994e-196 or 4.7e-173 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 54.5%

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

   4. Taylor expanded in z around 0 51.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-140}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-173}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+223} \lor \neg \left(z \leq 1.2 \cdot 10^{+274}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* y z)
   (if (<= z 2550.0)
     (+ x y)
     (if (or (<= z 5.5e+223) (not (<= z 1.2e+274))) (* y z) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 2550.0) {
		tmp = x + y;
	} else if ((z <= 5.5e+223) || !(z <= 1.2e+274)) {
		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 <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 2550.0d0) then
        tmp = x + y
    else if ((z <= 5.5d+223) .or. (.not. (z <= 1.2d+274))) 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 <= -1.0) {
		tmp = y * z;
	} else if (z <= 2550.0) {
		tmp = x + y;
	} else if ((z <= 5.5e+223) || !(z <= 1.2e+274)) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= 2550.0:
		tmp = x + y
	elif (z <= 5.5e+223) or not (z <= 1.2e+274):
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 2550.0)
		tmp = Float64(x + y);
	elseif ((z <= 5.5e+223) || !(z <= 1.2e+274))
		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 <= -1.0)
		tmp = y * z;
	elseif (z <= 2550.0)
		tmp = x + y;
	elseif ((z <= 5.5e+223) || ~((z <= 1.2e+274)))
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 2550.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 5.5e+223], N[Not[LessEqual[z, 1.2e+274]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 2550 < z < 5.4999999999999999e223 or 1.2e274 < 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 48.9%

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

      1. +-commutative 48.9%

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

      2. distribute-lft-in 48.9%

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

      3. *-rgt-identity 48.9%

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

   5. Applied egg-rr 48.9%

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

   6. Taylor expanded in z around inf 48.0%

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

      1. *-commutative 48.0%

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

   8. Simplified 48.0%

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

   if -1 < z < 2550

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.9%

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

      1. +-commutative 96.9%

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

   5. Simplified 96.9%

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

   if 5.4999999999999999e223 < z < 1.2e274

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 13.0%

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

      1. +-commutative 13.0%

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

      2. distribute-lft-in 13.0%

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

      3. *-rgt-identity 13.0%

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

   5. Applied egg-rr 13.0%

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

   6. Taylor expanded in z around inf 13.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+223} \lor \neg \left(z \leq 1.2 \cdot 10^{+274}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+75} \lor \neg \left(y \leq 2.65 \cdot 10^{+126}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e-204)
   (* x (+ z 1.0))
   (if (or (<= y 7.1e+75) (not (<= y 2.65e+126))) (* y (+ z 1.0)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-204) {
		tmp = x * (z + 1.0);
	} else if ((y <= 7.1e+75) || !(y <= 2.65e+126)) {
		tmp = y * (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 (y <= 7.5d-204) then
        tmp = x * (z + 1.0d0)
    else if ((y <= 7.1d+75) .or. (.not. (y <= 2.65d+126))) then
        tmp = y * (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 (y <= 7.5e-204) {
		tmp = x * (z + 1.0);
	} else if ((y <= 7.1e+75) || !(y <= 2.65e+126)) {
		tmp = y * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e-204:
		tmp = x * (z + 1.0)
	elif (y <= 7.1e+75) or not (y <= 2.65e+126):
		tmp = y * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e-204)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((y <= 7.1e+75) || !(y <= 2.65e+126))
		tmp = Float64(y * 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 (y <= 7.5e-204)
		tmp = x * (z + 1.0);
	elseif ((y <= 7.1e+75) || ~((y <= 2.65e+126)))
		tmp = y * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e-204], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7.1e+75], N[Not[LessEqual[y, 2.65e+126]], $MachinePrecision]], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.5000000000000003e-204

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 58.8%

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

   if 7.5000000000000003e-204 < y < 7.09999999999999982e75 or 2.65000000000000014e126 < 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 64.0%

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

   if 7.09999999999999982e75 < y < 2.65000000000000014e126

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+75} \lor \neg \left(y \leq 2.65 \cdot 10^{+126}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 2700:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e+27)
   (* y z)
   (if (<= z -4.8e-12) (* x (+ z 1.0)) (if (<= z 2700.0) (+ x y) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e+27) {
		tmp = y * z;
	} else if (z <= -4.8e-12) {
		tmp = x * (z + 1.0);
	} else if (z <= 2700.0) {
		tmp = x + y;
	} 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 (z <= (-1.3d+27)) then
        tmp = y * z
    else if (z <= (-4.8d-12)) then
        tmp = x * (z + 1.0d0)
    else if (z <= 2700.0d0) then
        tmp = x + y
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e+27) {
		tmp = y * z;
	} else if (z <= -4.8e-12) {
		tmp = x * (z + 1.0);
	} else if (z <= 2700.0) {
		tmp = x + y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.3e+27:
		tmp = y * z
	elif z <= -4.8e-12:
		tmp = x * (z + 1.0)
	elif z <= 2700.0:
		tmp = x + y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.3e+27)
		tmp = Float64(y * z);
	elseif (z <= -4.8e-12)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= 2700.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.3e+27)
		tmp = y * z;
	elseif (z <= -4.8e-12)
		tmp = x * (z + 1.0);
	elseif (z <= 2700.0)
		tmp = x + y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.3e+27], N[(y * z), $MachinePrecision], If[LessEqual[z, -4.8e-12], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2700.0], N[(x + y), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000004e27 or 2700 < 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 49.7%

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

      1. +-commutative 49.7%

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

      2. distribute-lft-in 49.7%

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

      3. *-rgt-identity 49.7%

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

   5. Applied egg-rr 49.7%

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

   6. Taylor expanded in z around inf 49.2%

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

      1. *-commutative 49.2%

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

   8. Simplified 49.2%

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

   if -1.30000000000000004e27 < z < -4.79999999999999974e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 39.8%

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

   if -4.79999999999999974e-12 < z < 2700

   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 3 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+27}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 2700:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% 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 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 97.8%

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

Alternative 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. Final simplification 100.0%

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

Alternative 9: 32.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.04e-57) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.04e-57) {
		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 (x <= (-1.04d-57)) 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 (x <= -1.04e-57) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.04e-57:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.04e-57)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.04e-57)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.04e-57], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.04000000000000003e-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 71.9%

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

   4. Taylor expanded in z around 0 37.9%

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

   if -1.04000000000000003e-57 < 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 57.6%

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

   4. Taylor expanded in z around 0 29.3%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 26.2% 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 51.2%

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

4. Taylor expanded in z around 0 25.0%

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

5. Final simplification 25.0%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))