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

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

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

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

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. 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%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \left(x + y\right) + z \cdot \left(x + y\right) \]

Alternative 2: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+191}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+216}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* x z)
   (if (<= z 8.6e-73)
     y
     (if (<= z 1.0)
       x
       (if (<= z 3e+191) (* x z) (if (<= z 7e+216) (* y z) (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 8.6e-73) {
		tmp = y;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 3e+191) {
		tmp = x * z;
	} else if (z <= 7e+216) {
		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 = x * z
    else if (z <= 8.6d-73) then
        tmp = y
    else if (z <= 1.0d0) then
        tmp = x
    else if (z <= 3d+191) then
        tmp = x * z
    else if (z <= 7d+216) 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 = x * z;
	} else if (z <= 8.6e-73) {
		tmp = y;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 3e+191) {
		tmp = x * z;
	} else if (z <= 7e+216) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 8.6e-73:
		tmp = y
	elif z <= 1.0:
		tmp = x
	elif z <= 3e+191:
		tmp = x * z
	elif z <= 7e+216:
		tmp = y * z
	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 <= 8.6e-73)
		tmp = y;
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 3e+191)
		tmp = Float64(x * z);
	elseif (z <= 7e+216)
		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 = x * z;
	elseif (z <= 8.6e-73)
		tmp = y;
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 3e+191)
		tmp = x * z;
	elseif (z <= 7e+216)
		tmp = y * z;
	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, 8.6e-73], y, If[LessEqual[z, 1.0], x, If[LessEqual[z, 3e+191], N[(x * z), $MachinePrecision], If[LessEqual[z, 7e+216], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1 or 1 < z < 2.9999999999999997e191 or 6.99999999999999984e216 < z

   1. Initial program 100.0%

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

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 52.0%

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

   5. Taylor expanded in z around inf 50.7%

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

   if -1 < z < 8.5999999999999998e-73

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 55.8%

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

   3. Taylor expanded in z around 0 54.7%

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

   if 8.5999999999999998e-73 < z < 1

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 38.2%

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

   3. Taylor expanded in z around 0 38.2%

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

   if 2.9999999999999997e191 < z < 6.99999999999999984e216

   1. Initial program 100.0%

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

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 50.2%

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

   5. Taylor expanded in z around inf 50.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+191}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+216}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 31:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+193}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+217}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* x z)
   (if (<= z 31.0)
     (+ x y)
     (if (<= z 2e+193) (* x z) (if (<= z 1.7e+217) (* y z) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 31.0) {
		tmp = x + y;
	} else if (z <= 2e+193) {
		tmp = x * z;
	} else if (z <= 1.7e+217) {
		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 = x * z
    else if (z <= 31.0d0) then
        tmp = x + y
    else if (z <= 2d+193) then
        tmp = x * z
    else if (z <= 1.7d+217) 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 = x * z;
	} else if (z <= 31.0) {
		tmp = x + y;
	} else if (z <= 2e+193) {
		tmp = x * z;
	} else if (z <= 1.7e+217) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 31.0:
		tmp = x + y
	elif z <= 2e+193:
		tmp = x * z
	elif z <= 1.7e+217:
		tmp = y * z
	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 <= 31.0)
		tmp = Float64(x + y);
	elseif (z <= 2e+193)
		tmp = Float64(x * z);
	elseif (z <= 1.7e+217)
		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 = x * z;
	elseif (z <= 31.0)
		tmp = x + y;
	elseif (z <= 2e+193)
		tmp = x * z;
	elseif (z <= 1.7e+217)
		tmp = y * z;
	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, 31.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 2e+193], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.7e+217], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 31 < z < 2.00000000000000013e193 or 1.6999999999999999e217 < z

   1. Initial program 100.0%

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

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 52.0%

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

   5. Taylor expanded in z around inf 50.7%

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

   if -1 < z < 31

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 97.9%

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

   if 2.00000000000000013e193 < z < 1.6999999999999999e217

   1. Initial program 100.0%

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

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 50.2%

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

   5. Taylor expanded in z around inf 50.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 31:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+193}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+217}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 12000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -180.0)
   (* y z)
   (if (<= z 1.4e-73) y (if (<= z 12000000.0) x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -180.0) {
		tmp = y * z;
	} else if (z <= 1.4e-73) {
		tmp = y;
	} else if (z <= 12000000.0) {
		tmp = x;
	} 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 <= (-180.0d0)) then
        tmp = y * z
    else if (z <= 1.4d-73) then
        tmp = y
    else if (z <= 12000000.0d0) then
        tmp = x
    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 <= -180.0) {
		tmp = y * z;
	} else if (z <= 1.4e-73) {
		tmp = y;
	} else if (z <= 12000000.0) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -180.0:
		tmp = y * z
	elif z <= 1.4e-73:
		tmp = y
	elif z <= 12000000.0:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -180.0)
		tmp = Float64(y * z);
	elseif (z <= 1.4e-73)
		tmp = y;
	elseif (z <= 12000000.0)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -180.0)
		tmp = y * z;
	elseif (z <= 1.4e-73)
		tmp = y;
	elseif (z <= 12000000.0)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -180.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.4e-73], y, If[LessEqual[z, 12000000.0], x, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -180 or 1.2e7 < z

   1. Initial program 100.0%

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

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 53.3%

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

   5. Taylor expanded in z around inf 52.4%

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

   if -180 < z < 1.40000000000000006e-73

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 55.7%

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

   3. Taylor expanded in z around 0 53.7%

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

   if 1.40000000000000006e-73 < z < 1.2e7

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 41.2%

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

   3. Taylor expanded in z around 0 37.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -180:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 12000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 97.9% accurate, 0.8× 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. Taylor expanded in z around inf 97.4%

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

   if -1 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in z around 0 97.9%

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

4. Final simplification 97.6%

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

Alternative 6: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.6e-94) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e-94) {
		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 <= 1.6d-94) 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 <= 1.6e-94) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.6e-94:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.6e-94)
		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 <= 1.6e-94)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.6e-94], 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 < 1.59999999999999998e-94

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 56.7%

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

   if 1.59999999999999998e-94 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 76.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

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. Final simplification 100.0%

   \[\leadsto \left(x + y\right) \cdot \left(z + 1\right) \]

Alternative 8: 30.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.1e-170) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.1e-170) {
		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 <= 3.1d-170) 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 <= 3.1e-170) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.1e-170:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.1e-170)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.1e-170)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.1e-170], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.09999999999999986e-170

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around inf 54.9%

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

   3. Taylor expanded in z around 0 28.1%

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

   if 3.09999999999999986e-170 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]

   2. Taylor expanded in x around 0 68.1%

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

   3. Taylor expanded in z around 0 39.6%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 26.9% 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. Taylor expanded in x around inf 48.0%

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

3. Taylor expanded in z around 0 23.8%

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

4. Final simplification 23.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))