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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 8

Speedup: 1.0×

• 20.5% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq -5 \cdot 10^{+117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 0.99995 \lor \neg \left(1 - z \leq 10000000000\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))))
   (if (<= (- 1.0 z) -5e+117)
     t_0
     (if (<= (- 1.0 z) -1e+64)
       (* z (- x))
       (if (or (<= (- 1.0 z) 0.99995) (not (<= (- 1.0 z) 10000000000.0)))
         t_0
         (+ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= -5e+117) {
		tmp = t_0;
	} else if ((1.0 - z) <= -1e+64) {
		tmp = z * -x;
	} else if (((1.0 - z) <= 0.99995) || !((1.0 - z) <= 10000000000.0)) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    if ((1.0d0 - z) <= (-5d+117)) then
        tmp = t_0
    else if ((1.0d0 - z) <= (-1d+64)) then
        tmp = z * -x
    else if (((1.0d0 - z) <= 0.99995d0) .or. (.not. ((1.0d0 - z) <= 10000000000.0d0))) then
        tmp = t_0
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= -5e+117) {
		tmp = t_0;
	} else if ((1.0 - z) <= -1e+64) {
		tmp = z * -x;
	} else if (((1.0 - z) <= 0.99995) || !((1.0 - z) <= 10000000000.0)) {
		tmp = t_0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	tmp = 0
	if (1.0 - z) <= -5e+117:
		tmp = t_0
	elif (1.0 - z) <= -1e+64:
		tmp = z * -x
	elif ((1.0 - z) <= 0.99995) or not ((1.0 - z) <= 10000000000.0):
		tmp = t_0
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -5e+117)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= -1e+64)
		tmp = Float64(z * Float64(-x));
	elseif ((Float64(1.0 - z) <= 0.99995) || !(Float64(1.0 - z) <= 10000000000.0))
		tmp = t_0;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	tmp = 0.0;
	if ((1.0 - z) <= -5e+117)
		tmp = t_0;
	elseif ((1.0 - z) <= -1e+64)
		tmp = z * -x;
	elseif (((1.0 - z) <= 0.99995) || ~(((1.0 - z) <= 10000000000.0)))
		tmp = t_0;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -5e+117], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+64], N[(z * (-x)), $MachinePrecision], If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 0.99995], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 10000000000.0]], $MachinePrecision]], t$95$0, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 1 z) < -4.99999999999999983e117 or -1.00000000000000002e64 < (-.f64 1 z) < 0.999950000000000006 or 1e10 < (-.f64 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 0 46.7%

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

   if -4.99999999999999983e117 < (-.f64 1 z) < -1.00000000000000002e64

   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. Taylor expanded in y around 0 42.1%

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

   6. Taylor expanded in z around inf 42.1%

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

      1. associate-*r* 42.1%

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

      2. neg-mul-1 42.1%

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

   8. Simplified 42.1%

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

   if 0.999950000000000006 < (-.f64 1 z) < 1e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.3%

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

      1. +-commutative 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq -1 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;1 - z \leq 0.99995 \lor \neg \left(1 - z \leq 10000000000\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+75} \lor \neg \left(y \leq 5.6 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e-204)
   (* x (- 1.0 z))
   (if (or (<= y 7e+75) (not (<= y 5.6e+125))) (* y (- 1.0 z)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e-204) {
		tmp = x * (1.0 - z);
	} else if ((y <= 7e+75) || !(y <= 5.6e+125)) {
		tmp = y * (1.0 - 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 (y <= 7.5d-204) then
        tmp = x * (1.0d0 - z)
    else if ((y <= 7d+75) .or. (.not. (y <= 5.6d+125))) then
        tmp = y * (1.0d0 - 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 (y <= 7.5e-204) {
		tmp = x * (1.0 - z);
	} else if ((y <= 7e+75) || !(y <= 5.6e+125)) {
		tmp = y * (1.0 - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7.5e-204:
		tmp = x * (1.0 - z)
	elif (y <= 7e+75) or not (y <= 5.6e+125):
		tmp = y * (1.0 - z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e-204)
		tmp = Float64(x * Float64(1.0 - z));
	elseif ((y <= 7e+75) || !(y <= 5.6e+125))
		tmp = Float64(y * Float64(1.0 - z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.5e-204)
		tmp = x * (1.0 - z);
	elseif ((y <= 7e+75) || ~((y <= 5.6e+125)))
		tmp = y * (1.0 - z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e-204], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7e+75], N[Not[LessEqual[y, 5.6e+125]], $MachinePrecision]], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.5000000000000003e-204

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if 7.5000000000000003e-204 < y < 6.9999999999999997e75 or 5.6000000000000002e125 < 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 64.0%

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

   if 6.9999999999999997e75 < y < 5.6000000000000002e125

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

      1. +-commutative 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+75} \lor \neg \left(y \leq 5.6 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -2000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -2000.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- x) y))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -2000.0) || !((1.0 - z) <= 2.0)) {
		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 (((1.0d0 - z) <= (-2000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) 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 (((1.0 - z) <= -2000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-x - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -2000.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-x - y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -2000.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-x) - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -2000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-x - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -2000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -2e3 or 2 < (-.f64 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 98.0%

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

      1. associate-*r* 98.0%

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

      2. neg-mul-1 98.0%

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

      3. *-commutative 98.0%

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

      4. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   if -2e3 < (-.f64 1 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 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -2000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19.5 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -19.5) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -19.5) || !(z <= 1.0)) {
		tmp = z * -x;
	} 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 <= (-19.5d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    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 <= -19.5) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -19.5) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -19.5) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -19.5) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -19.5], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -19.5 or 1 < z

   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. Taylor expanded in y around 0 52.4%

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

   6. Taylor expanded in z around inf 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

   8. Simplified 51.3%

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

   if -19.5 < 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 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19.5 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 32.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -2.5e-53) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e-53) {
		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 (x <= (-2.5d-53)) 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 (x <= -2.5e-53) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e-53:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e-53)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e-53)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e-53], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.5%

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

      1. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in z around 0 38.8%

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

   if -2.5e-53 < 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 57.3%

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

   4. Taylor expanded in z around 0 29.2%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.7% 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 49.2%

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

   1. +-commutative 49.2%

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

5. Simplified 49.2%

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

6. Final simplification 49.2%

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

Alternative 8: 26.2% 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 x around inf 51.2%

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

   1. *-commutative 51.2%

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

5. Simplified 51.2%

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

6. Taylor expanded in z around 0 25.1%

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

7. Final simplification 25.1%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))