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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 10

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 50.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z + 1 \leq -4 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z + 1 \leq 1.0000002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+68}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= (+ z 1.0) -4e+94)
     (* y z)
     (if (<= (+ z 1.0) 1.0)
       t_0
       (if (<= (+ z 1.0) 1.0000002)
         (+ x y)
         (if (<= (+ z 1.0) 5e+68)
           t_0
           (if (<= (+ z 1.0) 5e+256) (* y z) (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if ((z + 1.0) <= -4e+94) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1.0) {
		tmp = t_0;
	} else if ((z + 1.0) <= 1.0000002) {
		tmp = x + y;
	} else if ((z + 1.0) <= 5e+68) {
		tmp = t_0;
	} else if ((z + 1.0) <= 5e+256) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + 1.0d0)
    if ((z + 1.0d0) <= (-4d+94)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 1.0d0) then
        tmp = t_0
    else if ((z + 1.0d0) <= 1.0000002d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 5d+68) then
        tmp = t_0
    else if ((z + 1.0d0) <= 5d+256) 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 t_0 = x * (z + 1.0);
	double tmp;
	if ((z + 1.0) <= -4e+94) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1.0) {
		tmp = t_0;
	} else if ((z + 1.0) <= 1.0000002) {
		tmp = x + y;
	} else if ((z + 1.0) <= 5e+68) {
		tmp = t_0;
	} else if ((z + 1.0) <= 5e+256) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if (z + 1.0) <= -4e+94:
		tmp = y * z
	elif (z + 1.0) <= 1.0:
		tmp = t_0
	elif (z + 1.0) <= 1.0000002:
		tmp = x + y
	elif (z + 1.0) <= 5e+68:
		tmp = t_0
	elif (z + 1.0) <= 5e+256:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (Float64(z + 1.0) <= -4e+94)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 1.0)
		tmp = t_0;
	elseif (Float64(z + 1.0) <= 1.0000002)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 5e+68)
		tmp = t_0;
	elseif (Float64(z + 1.0) <= 5e+256)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if ((z + 1.0) <= -4e+94)
		tmp = y * z;
	elseif ((z + 1.0) <= 1.0)
		tmp = t_0;
	elseif ((z + 1.0) <= 1.0000002)
		tmp = x + y;
	elseif ((z + 1.0) <= 5e+68)
		tmp = t_0;
	elseif ((z + 1.0) <= 5e+256)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z + 1.0), $MachinePrecision], -4e+94], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.0], t$95$0, If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.0000002], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 5e+68], t$95$0, If[LessEqual[N[(z + 1.0), $MachinePrecision], 5e+256], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -4.0000000000000001e94 or 5.0000000000000004e68 < (+.f64 z #s(literal 1 binary64)) < 5.00000000000000015e256

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in x around 0 52.9%

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

   if -4.0000000000000001e94 < (+.f64 z #s(literal 1 binary64)) < 1 or 1.00000019999999989 < (+.f64 z #s(literal 1 binary64)) < 5.0000000000000004e68

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.1%

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

   if 1 < (+.f64 z #s(literal 1 binary64)) < 1.00000019999999989

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 88.7%

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

      1. +-commutative 88.7%

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

   5. Simplified 88.7%

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

   if 5.00000000000000015e256 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 99.8%

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

   4. Taylor expanded in x around inf 66.8%

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

      1. *-commutative 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -4 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z + 1 \leq 1.0000002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z + 1 \leq 5 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+93)
   (* y z)
   (if (<= z -1.0)
     (* x z)
     (if (<= z 4.6e-113)
       y
       (if (<= z 14500000.0) x (if (<= z 4.1e+256) (* y z) (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+93) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 4.6e-113) {
		tmp = y;
	} else if (z <= 14500000.0) {
		tmp = x;
	} else if (z <= 4.1e+256) {
		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 <= (-9.5d+93)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 4.6d-113) then
        tmp = y
    else if (z <= 14500000.0d0) then
        tmp = x
    else if (z <= 4.1d+256) 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 <= -9.5e+93) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 4.6e-113) {
		tmp = y;
	} else if (z <= 14500000.0) {
		tmp = x;
	} else if (z <= 4.1e+256) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e+93:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 4.6e-113:
		tmp = y
	elif z <= 14500000.0:
		tmp = x
	elif z <= 4.1e+256:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+93)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 4.6e-113)
		tmp = y;
	elseif (z <= 14500000.0)
		tmp = x;
	elseif (z <= 4.1e+256)
		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 <= -9.5e+93)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 4.6e-113)
		tmp = y;
	elseif (z <= 14500000.0)
		tmp = x;
	elseif (z <= 4.1e+256)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e+93], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 4.6e-113], y, If[LessEqual[z, 14500000.0], x, If[LessEqual[z, 4.1e+256], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.4999999999999991e93 or 1.45e7 < z < 4.10000000000000006e256

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.6%

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

   4. Taylor expanded in x around 0 52.4%

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

   if -9.4999999999999991e93 < z < -1 or 4.10000000000000006e256 < 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 96.1%

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

   4. Taylor expanded in x around inf 45.0%

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

      1. *-commutative 45.0%

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

   6. Simplified 45.0%

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

   if -1 < z < 4.60000000000000016e-113

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.7%

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

      1. +-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around inf 46.3%

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

   if 4.60000000000000016e-113 < z < 1.45e7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 90.9%

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

      1. +-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in y around 0 32.6%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-113}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+94)
   (* y z)
   (if (<= z -1.0)
     (* x z)
     (if (<= z 14500000.0) (+ x y) (if (<= z 7e+256) (* y z) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+94) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 14500000.0) {
		tmp = x + y;
	} else if (z <= 7e+256) {
		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 <= (-1.1d+94)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 14500000.0d0) then
        tmp = x + y
    else if (z <= 7d+256) 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 <= -1.1e+94) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 14500000.0) {
		tmp = x + y;
	} else if (z <= 7e+256) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+94:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 14500000.0:
		tmp = x + y
	elif z <= 7e+256:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+94)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 14500000.0)
		tmp = Float64(x + y);
	elseif (z <= 7e+256)
		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 <= -1.1e+94)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 14500000.0)
		tmp = x + y;
	elseif (z <= 7e+256)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+94], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 14500000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 7e+256], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000006e94 or 1.45e7 < z < 6.9999999999999995e256

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.6%

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

   4. Taylor expanded in x around 0 52.4%

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

   if -1.10000000000000006e94 < z < -1 or 6.9999999999999995e256 < 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 96.1%

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

   4. Taylor expanded in x around inf 45.0%

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

      1. *-commutative 45.0%

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

   6. Simplified 45.0%

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

   if -1 < z < 1.45e7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.3%

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

      1. +-commutative 96.3%

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

   5. Simplified 96.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+94}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+256}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-112}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e-16)
   (* y z)
   (if (<= z 2e-112) y (if (<= z 14500000.0) x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e-16) {
		tmp = y * z;
	} else if (z <= 2e-112) {
		tmp = y;
	} else if (z <= 14500000.0) {
		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 <= (-1.6d-16)) then
        tmp = y * z
    else if (z <= 2d-112) then
        tmp = y
    else if (z <= 14500000.0d0) 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 <= -1.6e-16) {
		tmp = y * z;
	} else if (z <= 2e-112) {
		tmp = y;
	} else if (z <= 14500000.0) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e-16:
		tmp = y * z
	elif z <= 2e-112:
		tmp = y
	elif z <= 14500000.0:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e-16)
		tmp = Float64(y * z);
	elseif (z <= 2e-112)
		tmp = y;
	elseif (z <= 14500000.0)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.6e-16)
		tmp = y * z;
	elseif (z <= 2e-112)
		tmp = y;
	elseif (z <= 14500000.0)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e-16], N[(y * z), $MachinePrecision], If[LessEqual[z, 2e-112], y, If[LessEqual[z, 14500000.0], x, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000011e-16 or 1.45e7 < 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 95.3%

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

   4. Taylor expanded in x around 0 51.8%

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

   if -1.60000000000000011e-16 < z < 1.9999999999999999e-112

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 47.4%

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

   if 1.9999999999999999e-112 < z < 1.45e7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 90.9%

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

      1. +-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in y around 0 32.6%

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

Alternative 6: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-287}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-287) (+ x (* x z)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-287) {
		tmp = x + (x * z);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x + y) <= (-1d-287)) then
        tmp = x + (x * z)
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-287) {
		tmp = x + (x * z);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-287:
		tmp = x + (x * z)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-287)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-287)
		tmp = x + (x * z);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-287], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000002e-287

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 52.5%

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

      1. distribute-lft-in 52.5%

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

      2. *-rgt-identity 52.5%

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

   5. Applied egg-rr 52.5%

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

   if -1.00000000000000002e-287 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 51.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-287}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-287) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-287) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x + y) <= (-1d-287)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-287) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-287:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-287)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-287)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-287], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000002e-287

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 52.5%

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

   if -1.00000000000000002e-287 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 51.7%

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

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 9: 31.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.6e-19) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e-19) {
		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 <= 3.6d-19) 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 <= 3.6e-19) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.6e-19:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.6e-19)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.6e-19)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.6e-19], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.6000000000000001e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 47.4%

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

      1. +-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in y around 0 28.4%

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

   if 3.6000000000000001e-19 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 46.8%

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

      1. +-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around inf 35.7%

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

Alternative 10: 24.9% 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. Add Preprocessing

3. Taylor expanded in z around 0 47.3%

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

   1. +-commutative 47.3%

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

5. Simplified 47.3%

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

6. Taylor expanded in y around 0 24.1%

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

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))