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

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

Alternatives: 8

Speedup: 1.0×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - 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) * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (1.0 - 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 = (1.0d0 - z) * (x + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -y \cdot z\\ \mathbf{if}\;1 - z \leq -2 \cdot 10^{+210}:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;1 - z \leq -400000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 10000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y z))))
   (if (<= (- 1.0 z) -2e+210)
     (- (* x z))
     (if (<= (- 1.0 z) -400000.0)
       t_0
       (if (<= (- 1.0 z) 10000.0) (+ x y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -(y * z);
	double tmp;
	if ((1.0 - z) <= -2e+210) {
		tmp = -(x * z);
	} else if ((1.0 - z) <= -400000.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 10000.0) {
		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 = -(y * z)
    if ((1.0d0 - z) <= (-2d+210)) then
        tmp = -(x * z)
    else if ((1.0d0 - z) <= (-400000.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 10000.0d0) 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 = -(y * z);
	double tmp;
	if ((1.0 - z) <= -2e+210) {
		tmp = -(x * z);
	} else if ((1.0 - z) <= -400000.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 10000.0) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(y * z)
	tmp = 0
	if (1.0 - z) <= -2e+210:
		tmp = -(x * z)
	elif (1.0 - z) <= -400000.0:
		tmp = t_0
	elif (1.0 - z) <= 10000.0:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(y * z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -2e+210)
		tmp = Float64(-Float64(x * z));
	elseif (Float64(1.0 - z) <= -400000.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 10000.0)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(y * z);
	tmp = 0.0;
	if ((1.0 - z) <= -2e+210)
		tmp = -(x * z);
	elseif ((1.0 - z) <= -400000.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 10000.0)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(y * z), $MachinePrecision])}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -2e+210], (-N[(x * z), $MachinePrecision]), If[LessEqual[N[(1.0 - z), $MachinePrecision], -400000.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 10000.0], N[(x + y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -1.99999999999999985e210

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 99.9

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 74.7%

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

   if -1.99999999999999985e210 < (-.f64 #s(literal 1 binary64) z) < -4e5 or 1e4 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 54.2%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y \cdot z\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{z \cdot y}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(y\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(y\right)\right)} \]

      5. neg-lowering-neg.f64 52.8

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

   8. Simplified 52.8%

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

   if -4e5 < (-.f64 #s(literal 1 binary64) z) < 1e4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 98.4

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

   5. Simplified 98.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -2 \cdot 10^{+210}:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;1 - z \leq -400000:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;1 - z \leq 10000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+198}:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;x + y \leq 10^{-277}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -5e+198)
   (- (* x z))
   (if (<= (+ x y) 1e-277) (+ x y) (* y (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -5e+198) {
		tmp = -(x * z);
	} else if ((x + y) <= 1e-277) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - 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 ((x + y) <= (-5d+198)) then
        tmp = -(x * z)
    else if ((x + y) <= 1d-277) then
        tmp = x + y
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -5e+198) {
		tmp = -(x * z);
	} else if ((x + y) <= 1e-277) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -5e+198:
		tmp = -(x * z)
	elif (x + y) <= 1e-277:
		tmp = x + y
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -5e+198)
		tmp = Float64(-Float64(x * z));
	elseif (Float64(x + y) <= 1e-277)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -5e+198)
		tmp = -(x * z);
	elseif ((x + y) <= 1e-277)
		tmp = x + y;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+198], (-N[(x * z), $MachinePrecision]), If[LessEqual[N[(x + y), $MachinePrecision], 1e-277], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5.00000000000000049e198

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 59.3

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

   5. Simplified 59.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 37.1%

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

   if -5.00000000000000049e198 < (+.f64 x y) < 9.99999999999999969e-278

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 60.3

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

   5. Simplified 60.3%

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

   if 9.99999999999999969e-278 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 51.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+198}:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;x + y \leq 10^{-277}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -x \cdot z\\ \mathbf{if}\;1 - z \leq -400000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x z))))
   (if (<= (- 1.0 z) -400000.0) t_0 (if (<= (- 1.0 z) 2.0) (+ x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(x * z);
	double tmp;
	if ((1.0 - z) <= -400000.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		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)
    if ((1.0d0 - z) <= (-400000.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) 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);
	double tmp;
	if ((1.0 - z) <= -400000.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(x * z)
	tmp = 0
	if (1.0 - z) <= -400000.0:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(x * z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -400000.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(x * z);
	tmp = 0.0;
	if ((1.0 - z) <= -400000.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(x * z), $MachinePrecision])}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -400000.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -4e5 or 2 < (-.f64 #s(literal 1 binary64) z)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 97.9

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

   5. Simplified 97.9%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 56.1%

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

   if -4e5 < (-.f64 #s(literal 1 binary64) z) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.0

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

   5. Simplified 99.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -400000:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-257}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -5e-257) (- x (* x z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -5e-257) {
		tmp = x - (x * z);
	} else {
		tmp = y * (1.0 - 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 ((x + y) <= (-5d-257)) then
        tmp = x - (x * z)
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -5e-257) {
		tmp = x - (x * z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -5e-257:
		tmp = x - (x * z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -5e-257)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -5e-257)
		tmp = x - (x * z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-257], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.99999999999999989e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. distribute-lft-out-- N/A

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

      2. *-rgt-identity N/A

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

      3. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 53.0

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

   5. Simplified 53.0%

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

   if -4.99999999999999989e-257 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 51.6%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-257}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 26.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - z\right) \cdot \left(x + y\right) \leq -5 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 z) (+ x y)) -5e-257) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) * (x + y)) <= -5e-257) {
		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 (((1.0d0 - z) * (x + y)) <= (-5d-257)) 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 (((1.0 - z) * (x + y)) <= -5e-257) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) * (x + y)) <= -5e-257:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - z) * Float64(x + y)) <= -5e-257)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) * (x + y)) <= -5e-257)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - z), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision], -5e-257], x, y]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) z)) < -4.99999999999999989e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 51.9

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

   5. Simplified 51.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 25.9%

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

   if -4.99999999999999989e-257 < (*.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) z))

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 56.1

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

   5. Simplified 56.1%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 27.9%

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

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - z\right) \cdot \left(x + y\right) \leq -5 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 54.1

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

5. Simplified 54.1%

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

6. Final simplification 54.1%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 8: 26.5% accurate, 12.0× 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%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 54.1

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

5. Simplified 54.1%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 28.1%

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))