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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 8

Speedup: 1.0×

• 21.3% 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. Final simplification 100.0%

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

Alternative 2: 51.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-214}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* y z)
   (if (<= z -7.8e-197)
     x
     (if (<= z -1.95e-214) y (if (<= z 5e-58) x (if (<= z 1.0) y (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -7.8e-197) {
		tmp = x;
	} else if (z <= -1.95e-214) {
		tmp = y;
	} else if (z <= 5e-58) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = 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 <= (-1.0d0)) then
        tmp = y * z
    else if (z <= (-7.8d-197)) then
        tmp = x
    else if (z <= (-1.95d-214)) then
        tmp = y
    else if (z <= 5d-58) then
        tmp = x
    else if (z <= 1.0d0) then
        tmp = 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 <= -1.0) {
		tmp = y * z;
	} else if (z <= -7.8e-197) {
		tmp = x;
	} else if (z <= -1.95e-214) {
		tmp = y;
	} else if (z <= 5e-58) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= -7.8e-197:
		tmp = x
	elif z <= -1.95e-214:
		tmp = y
	elif z <= 5e-58:
		tmp = x
	elif z <= 1.0:
		tmp = y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= -7.8e-197)
		tmp = x;
	elseif (z <= -1.95e-214)
		tmp = y;
	elseif (z <= 5e-58)
		tmp = x;
	elseif (z <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * 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 <= -7.8e-197)
		tmp = x;
	elseif (z <= -1.95e-214)
		tmp = y;
	elseif (z <= 5e-58)
		tmp = x;
	elseif (z <= 1.0)
		tmp = y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -7.8e-197], x, If[LessEqual[z, -1.95e-214], y, If[LessEqual[z, 5e-58], x, If[LessEqual[z, 1.0], y, N[(y * 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 0 51.9%

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

      1. +-commutative 51.9%

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

      2. distribute-lft-in 51.9%

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

      3. *-rgt-identity 51.9%

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

   5. Applied egg-rr 51.9%

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

   6. Taylor expanded in z around inf 49.9%

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

   if -1 < z < -7.7999999999999998e-197 or -1.95000000000000019e-214 < z < 4.99999999999999977e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.2%

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

   4. Taylor expanded in z around 0 54.2%

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

   if -7.7999999999999998e-197 < z < -1.95000000000000019e-214 or 4.99999999999999977e-58 < z < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 60.9%

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

   4. Taylor expanded in z around 0 57.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-214}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.0165:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= z -1.4e+134)
     (* y z)
     (if (<= z -3.8e+101)
       t_0
       (if (<= z -1.0) (* y z) (if (<= z 0.0165) (+ x y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -1.4e+134) {
		tmp = y * z;
	} else if (z <= -3.8e+101) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 0.0165) {
		tmp = x + y;
	} else {
		tmp = t_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 (z <= (-1.4d+134)) then
        tmp = y * z
    else if (z <= (-3.8d+101)) then
        tmp = t_0
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 0.0165d0) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -1.4e+134) {
		tmp = y * z;
	} else if (z <= -3.8e+101) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 0.0165) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if z <= -1.4e+134:
		tmp = y * z
	elif z <= -3.8e+101:
		tmp = t_0
	elif z <= -1.0:
		tmp = y * z
	elif z <= 0.0165:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (z <= -1.4e+134)
		tmp = Float64(y * z);
	elseif (z <= -3.8e+101)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 0.0165)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if (z <= -1.4e+134)
		tmp = y * z;
	elseif (z <= -3.8e+101)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 0.0165)
		tmp = x + y;
	else
		tmp = t_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[z, -1.4e+134], N[(y * z), $MachinePrecision], If[LessEqual[z, -3.8e+101], t$95$0, If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 0.0165], N[(x + y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999e134 or -3.7999999999999998e101 < z < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. distribute-lft-in 55.5%

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

      3. *-rgt-identity 55.5%

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

   5. Applied egg-rr 55.5%

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

   6. Taylor expanded in z around inf 53.4%

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

   if -1.3999999999999999e134 < z < -3.7999999999999998e101 or 0.016500000000000001 < 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 55.8%

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

   if -1 < z < 0.016500000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.6%

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

      1. +-commutative 98.6%

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

   5. Simplified 98.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 0.0165:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 97.2%

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

      1. +-commutative 97.2%

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

   5. Simplified 97.2%

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

   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 98.6%

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

      1. +-commutative 98.6%

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

   5. Simplified 98.6%

      \[\leadsto \color{blue}{y + x} \]
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: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 880000\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 880000.0))) (* y z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 880000.0)) {
		tmp = y * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 880000.0d0))) then
        tmp = y * z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 880000.0)) {
		tmp = y * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 880000.0):
		tmp = y * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 880000.0))
		tmp = Float64(y * z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 880000.0)))
		tmp = y * 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, 880000.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 8.8e5 < 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 51.5%

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

      1. +-commutative 51.5%

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

      2. distribute-lft-in 51.5%

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

      3. *-rgt-identity 51.5%

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

   5. Applied egg-rr 51.5%

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

   6. Taylor expanded in z around inf 50.4%

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

   if -1 < z < 8.8e5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.8%

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

      1. +-commutative 96.8%

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

   5. Simplified 96.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 880000\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e-90) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-90) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.9d-90)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-90) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e-90:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e-90)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.9e-90)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e-90], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.6%

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

   if -1.9e-90 < 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 57.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 31.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.75e-140) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-140) {
		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 <= (-1.75d-140)) 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 <= -1.75e-140) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e-140:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e-140)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e-140)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e-140], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.7499999999999999e-140

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.4%

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

   4. Taylor expanded in z around 0 41.7%

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

   if -1.7499999999999999e-140 < 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 28.3%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 x around inf 52.4%

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

4. Taylor expanded in z around 0 28.8%

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

5. Final simplification 28.8%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))