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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 10

Speedup: 1.0×

• 20.7% 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, 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%

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

   1. sub-neg 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -4 \cdot 10^{+149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 0.99:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= (- 1.0 z) -4e+149)
     t_0
     (if (<= (- 1.0 z) 0.99)
       (* y (- 1.0 z))
       (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) <= -4e+149) {
		tmp = t_0;
	} else if ((1.0 - z) <= 0.99) {
		tmp = y * (1.0 - z);
	} 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) <= (-4d+149)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 0.99d0) then
        tmp = y * (1.0d0 - z)
    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) <= -4e+149) {
		tmp = t_0;
	} else if ((1.0 - z) <= 0.99) {
		tmp = y * (1.0 - z);
	} 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) <= -4e+149:
		tmp = t_0
	elif (1.0 - z) <= 0.99:
		tmp = y * (1.0 - z)
	elif (1.0 - z) <= 2.0:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -4e+149)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 0.99)
		tmp = Float64(y * Float64(1.0 - z));
	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) <= -4e+149)
		tmp = t_0;
	elseif ((1.0 - z) <= 0.99)
		tmp = y * (1.0 - z);
	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], -4e+149], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 0.99], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) z) < -4.0000000000000002e149 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 x around inf 61.0%

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

      1. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in z around inf 59.7%

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

      1. neg-mul-1 59.7%

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

   8. Simplified 59.7%

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

   if -4.0000000000000002e149 < (-.f64 #s(literal 1 binary64) z) < 0.98999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 35.5%

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

   if 0.98999999999999999 < (-.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 98.0%

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

      1. +-commutative 98.0%

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

   5. Simplified 98.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 0.99:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-178}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-73)
   (* x (- 1.0 z))
   (if (<= x -1.05e-178) (+ x y) (* y (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-73) {
		tmp = x * (1.0 - z);
	} else if (x <= -1.05e-178) {
		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 <= (-1.4d-73)) then
        tmp = x * (1.0d0 - z)
    else if (x <= (-1.05d-178)) 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 <= -1.4e-73) {
		tmp = x * (1.0 - z);
	} else if (x <= -1.05e-178) {
		tmp = x + y;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-73:
		tmp = x * (1.0 - z)
	elif x <= -1.05e-178:
		tmp = x + y
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-73)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (x <= -1.05e-178)
		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 <= -1.4e-73)
		tmp = x * (1.0 - z);
	elseif (x <= -1.05e-178)
		tmp = x + y;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-73], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e-178], N[(x + y), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000006e-73

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   if -1.40000000000000006e-73 < x < -1.05e-178

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. +-commutative 64.9%

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

   5. Simplified 64.9%

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

   if -1.05e-178 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 61.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-178}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -135 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -135.0) (not (<= z 1.0))) (* x (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -135.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-135.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -135.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -135.0) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -135.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -135.0) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -135.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -135 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in z around inf 60.9%

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

      1. neg-mul-1 60.9%

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

   8. Simplified 60.9%

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

   if -135 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -135 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -210000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -210000000000.0) (not (<= z 1.0))) (* y (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -210000000000.0) || !(z <= 1.0)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-210000000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = y * -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -210000000000.0) || !(z <= 1.0)) {
		tmp = y * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -210000000000.0) or not (z <= 1.0):
		tmp = y * -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -210000000000.0) || !(z <= 1.0))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -210000000000.0) || ~((z <= 1.0)))
		tmp = y * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -210000000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e11 or 1 < 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 98.4%

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

      1. neg-mul-1 61.0%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0 45.2%

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

      1. associate-*r* 45.2%

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

      2. mul-1-neg 45.2%

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

   8. Simplified 45.2%

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

   if -2.1e11 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.4%

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

      1. +-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-220) (- x (* x z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-220) {
		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) <= (-1d-220)) 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) <= -1e-220) {
		tmp = x - (x * z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-220:
		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) <= -1e-220)
		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) <= -1e-220)
		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], -1e-220], 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) < -9.99999999999999992e-221

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. *-commutative 61.2%

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

   7. Applied egg-rr 61.2%

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

   if -9.99999999999999992e-221 < (+.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 57.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 31.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.8e-113) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.8e-113) {
		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 <= 2.8d-113) 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 <= 2.8e-113) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.8e-113:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.8e-113)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.8e-113)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.8e-113], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.8e-113

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 44.2%

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

      1. +-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in y around 0 27.3%

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

   if 2.8e-113 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 58.4%

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

      1. +-commutative 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in y around inf 44.0%

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

Alternative 9: 51.1% accurate, 2.3× 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 49.8%

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

   1. +-commutative 49.8%

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

5. Simplified 49.8%

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

6. Final simplification 49.8%

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

Alternative 10: 26.4% 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%

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

3. Taylor expanded in z around 0 49.8%

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

   1. +-commutative 49.8%

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

5. Simplified 49.8%

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

6. Taylor expanded in y around 0 23.2%

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))