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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 8

Speedup: 1.0×

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. Final simplification 100.0%

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

Alternative 2: 49.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -310:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.7 \cdot 10^{-195}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-231}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-130}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 64:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -310.0)
   (* y z)
   (if (<= z -9.7e-195)
     y
     (if (<= z -2.75e-260)
       x
       (if (<= z 3.9e-231)
         y
         (if (<= z 3.6e-172)
           x
           (if (<= z 1.2e-130) y (if (<= z 64.0) x (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -310.0) {
		tmp = y * z;
	} else if (z <= -9.7e-195) {
		tmp = y;
	} else if (z <= -2.75e-260) {
		tmp = x;
	} else if (z <= 3.9e-231) {
		tmp = y;
	} else if (z <= 3.6e-172) {
		tmp = x;
	} else if (z <= 1.2e-130) {
		tmp = y;
	} else if (z <= 64.0) {
		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 <= (-310.0d0)) then
        tmp = y * z
    else if (z <= (-9.7d-195)) then
        tmp = y
    else if (z <= (-2.75d-260)) then
        tmp = x
    else if (z <= 3.9d-231) then
        tmp = y
    else if (z <= 3.6d-172) then
        tmp = x
    else if (z <= 1.2d-130) then
        tmp = y
    else if (z <= 64.0d0) 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 <= -310.0) {
		tmp = y * z;
	} else if (z <= -9.7e-195) {
		tmp = y;
	} else if (z <= -2.75e-260) {
		tmp = x;
	} else if (z <= 3.9e-231) {
		tmp = y;
	} else if (z <= 3.6e-172) {
		tmp = x;
	} else if (z <= 1.2e-130) {
		tmp = y;
	} else if (z <= 64.0) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -310.0:
		tmp = y * z
	elif z <= -9.7e-195:
		tmp = y
	elif z <= -2.75e-260:
		tmp = x
	elif z <= 3.9e-231:
		tmp = y
	elif z <= 3.6e-172:
		tmp = x
	elif z <= 1.2e-130:
		tmp = y
	elif z <= 64.0:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -310.0)
		tmp = Float64(y * z);
	elseif (z <= -9.7e-195)
		tmp = y;
	elseif (z <= -2.75e-260)
		tmp = x;
	elseif (z <= 3.9e-231)
		tmp = y;
	elseif (z <= 3.6e-172)
		tmp = x;
	elseif (z <= 1.2e-130)
		tmp = y;
	elseif (z <= 64.0)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -310.0)
		tmp = y * z;
	elseif (z <= -9.7e-195)
		tmp = y;
	elseif (z <= -2.75e-260)
		tmp = x;
	elseif (z <= 3.9e-231)
		tmp = y;
	elseif (z <= 3.6e-172)
		tmp = x;
	elseif (z <= 1.2e-130)
		tmp = y;
	elseif (z <= 64.0)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -310.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -9.7e-195], y, If[LessEqual[z, -2.75e-260], x, If[LessEqual[z, 3.9e-231], y, If[LessEqual[z, 3.6e-172], x, If[LessEqual[z, 1.2e-130], y, If[LessEqual[z, 64.0], x, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -310 or 64 < 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 48.4%

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

   5. Taylor expanded in z around inf 46.7%

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

   if -310 < z < -9.70000000000000019e-195 or -2.75000000000000012e-260 < z < 3.8999999999999998e-231 or 3.60000000000000015e-172 < z < 1.19999999999999998e-130

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 50.0%

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

   3. Taylor expanded in z around 0 50.0%

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

   if -9.70000000000000019e-195 < z < -2.75000000000000012e-260 or 3.8999999999999998e-231 < z < 3.60000000000000015e-172 or 1.19999999999999998e-130 < z < 64

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 54.4%

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

   3. Taylor expanded in z around 0 54.1%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -310:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.7 \cdot 10^{-195}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-231}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-172}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-130}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 64:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-58} \lor \neg \left(y \leq 4.5 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.3e-138)
   (* x (+ z 1.0))
   (if (or (<= y 8.2e-58) (not (<= y 4.5e+23))) (* y (+ z 1.0)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.3e-138) {
		tmp = x * (z + 1.0);
	} else if ((y <= 8.2e-58) || !(y <= 4.5e+23)) {
		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 <= 1.3d-138) then
        tmp = x * (z + 1.0d0)
    else if ((y <= 8.2d-58) .or. (.not. (y <= 4.5d+23))) 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 <= 1.3e-138) {
		tmp = x * (z + 1.0);
	} else if ((y <= 8.2e-58) || !(y <= 4.5e+23)) {
		tmp = y * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.3e-138:
		tmp = x * (z + 1.0)
	elif (y <= 8.2e-58) or not (y <= 4.5e+23):
		tmp = y * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.3e-138)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((y <= 8.2e-58) || !(y <= 4.5e+23))
		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 <= 1.3e-138)
		tmp = x * (z + 1.0);
	elseif ((y <= 8.2e-58) || ~((y <= 4.5e+23)))
		tmp = y * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.3e-138], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.2e-58], N[Not[LessEqual[y, 4.5e+23]], $MachinePrecision]], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.3e-138

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.5%

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

   if 1.3e-138 < y < 8.20000000000000056e-58 or 4.49999999999999979e23 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 66.0%

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

   if 8.20000000000000056e-58 < y < 4.49999999999999979e23

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 70.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-58} \lor \neg \left(y \leq 4.5 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16} \lor \neg \left(z \leq 36\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-16) (not (<= z 36.0))) (* y (+ z 1.0)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-16) || !(z <= 36.0)) {
		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 ((z <= (-2.4d-16)) .or. (.not. (z <= 36.0d0))) 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 ((z <= -2.4e-16) || !(z <= 36.0)) {
		tmp = y * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-16) or not (z <= 36.0):
		tmp = y * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e-16) || !(z <= 36.0))
		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 ((z <= -2.4e-16) || ~((z <= 36.0)))
		tmp = y * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e-16], N[Not[LessEqual[z, 36.0]], $MachinePrecision]], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000005e-16 or 36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 48.5%

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

   if -2.40000000000000005e-16 < z < 36

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16} \lor \neg \left(z \leq 36\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 97.8% 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 95.5%

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

   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 99.8%

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

4. Final simplification 97.9%

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

Alternative 6: 32.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3500000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6.5e-52) x (if (<= y 3500000.0) y (if (<= y 6.8e+52) x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.5e-52) {
		tmp = x;
	} else if (y <= 3500000.0) {
		tmp = y;
	} else if (y <= 6.8e+52) {
		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 <= 6.5d-52) then
        tmp = x
    else if (y <= 3500000.0d0) then
        tmp = y
    else if (y <= 6.8d+52) 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 <= 6.5e-52) {
		tmp = x;
	} else if (y <= 3500000.0) {
		tmp = y;
	} else if (y <= 6.8e+52) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.5e-52:
		tmp = x
	elif y <= 3500000.0:
		tmp = y
	elif y <= 6.8e+52:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.5e-52)
		tmp = x;
	elseif (y <= 3500000.0)
		tmp = y;
	elseif (y <= 6.8e+52)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6.5e-52)
		tmp = x;
	elseif (y <= 3500000.0)
		tmp = y;
	elseif (y <= 6.8e+52)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.5e-52], x, If[LessEqual[y, 3500000.0], y, If[LessEqual[y, 6.8e+52], x, y]]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5e-52 or 3.5e6 < y < 6.8e52

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.5%

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

   3. Taylor expanded in z around 0 32.7%

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

   if 6.5e-52 < y < 3.5e6 or 6.8e52 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 68.7%

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

   3. Taylor expanded in z around 0 42.3%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3500000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 115:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* y z) (if (<= z 115.0) (+ x y) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 115.0) {
		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 <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 115.0d0) 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 <= -1.0) {
		tmp = y * z;
	} else if (z <= 115.0) {
		tmp = x + y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= 115.0:
		tmp = x + 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 <= 115.0)
		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 <= -1.0)
		tmp = y * z;
	elseif (z <= 115.0)
		tmp = x + 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, 115.0], N[(x + y), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 115 < 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 48.0%

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

   5. Taylor expanded in z around inf 46.3%

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

   if -1 < z < 115

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 115:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 8: 26.7% 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 54.6%

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

3. Taylor expanded in z around 0 30.2%

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

4. Final simplification 30.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))