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

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 8

Speedup: 1.0×

• 21.1% 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. Final simplification 100.0%

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

Alternative 2: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+243}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -195000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+25} \lor \neg \left(z \leq 6.2 \cdot 10^{+236}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= z -4.4e+243)
     (* z (- x))
     (if (<= z -195000000000.0)
       t_0
       (if (<= z 7.3e-9)
         (+ x y)
         (if (or (<= z 1.4e+25) (not (<= z 6.2e+236))) (- x (* x z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (z <= -4.4e+243) {
		tmp = z * -x;
	} else if (z <= -195000000000.0) {
		tmp = t_0;
	} else if (z <= 7.3e-9) {
		tmp = x + y;
	} else if ((z <= 1.4e+25) || !(z <= 6.2e+236)) {
		tmp = x - (x * z);
	} 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 (z <= (-4.4d+243)) then
        tmp = z * -x
    else if (z <= (-195000000000.0d0)) then
        tmp = t_0
    else if (z <= 7.3d-9) then
        tmp = x + y
    else if ((z <= 1.4d+25) .or. (.not. (z <= 6.2d+236))) then
        tmp = x - (x * z)
    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 (z <= -4.4e+243) {
		tmp = z * -x;
	} else if (z <= -195000000000.0) {
		tmp = t_0;
	} else if (z <= 7.3e-9) {
		tmp = x + y;
	} else if ((z <= 1.4e+25) || !(z <= 6.2e+236)) {
		tmp = x - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if z <= -4.4e+243:
		tmp = z * -x
	elif z <= -195000000000.0:
		tmp = t_0
	elif z <= 7.3e-9:
		tmp = x + y
	elif (z <= 1.4e+25) or not (z <= 6.2e+236):
		tmp = x - (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -4.4e+243)
		tmp = Float64(z * Float64(-x));
	elseif (z <= -195000000000.0)
		tmp = t_0;
	elseif (z <= 7.3e-9)
		tmp = Float64(x + y);
	elseif ((z <= 1.4e+25) || !(z <= 6.2e+236))
		tmp = Float64(x - Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (z <= -4.4e+243)
		tmp = z * -x;
	elseif (z <= -195000000000.0)
		tmp = t_0;
	elseif (z <= 7.3e-9)
		tmp = x + y;
	elseif ((z <= 1.4e+25) || ~((z <= 6.2e+236)))
		tmp = x - (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -4.4e+243], N[(z * (-x)), $MachinePrecision], If[LessEqual[z, -195000000000.0], t$95$0, If[LessEqual[z, 7.3e-9], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1.4e+25], N[Not[LessEqual[z, 6.2e+236]], $MachinePrecision]], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.40000000000000018e243

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 91.7%

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

   3. Applied egg-rr 91.7%

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

   4. Taylor expanded in z around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. mul-1-neg 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in y around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

   9. Simplified 83.4%

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

   if -4.40000000000000018e243 < z < -1.95e11 or 1.4000000000000001e25 < z < 6.19999999999999999e236

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.9%

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

      2. mul-1-neg 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.9%

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

      2. neg-mul-1 98.9%

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

   9. Simplified 98.9%

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

   10. Taylor expanded in y around inf 53.2%

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

       1. associate-*r* 53.2%

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

       2. mul-1-neg 53.2%

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

   12. Simplified 53.2%

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

   if -1.95e11 < z < 7.30000000000000002e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.0%

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

   if 7.30000000000000002e-9 < z < 1.4000000000000001e25 or 6.19999999999999999e236 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 49.4%

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

      1. sub-neg 49.4%

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

      2. +-commutative 49.4%

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

      3. distribute-rgt1-in 49.4%

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

      4. distribute-lft-neg-out 49.4%

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

      5. unsub-neg 49.4%

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

   4. Simplified 49.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+243}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -195000000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+25} \lor \neg \left(z \leq 6.2 \cdot 10^{+236}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+246}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -195000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* y (- z))))
   (if (<= z -6.8e+246)
     t_0
     (if (<= z -195000000000.0)
       t_1
       (if (<= z 1.0) (+ x y) (if (<= z 7.5e+236) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = y * -z;
	double tmp;
	if (z <= -6.8e+246) {
		tmp = t_0;
	} else if (z <= -195000000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if (z <= 7.5e+236) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * -x
    t_1 = y * -z
    if (z <= (-6.8d+246)) then
        tmp = t_0
    else if (z <= (-195000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x + y
    else if (z <= 7.5d+236) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = y * -z;
	double tmp;
	if (z <= -6.8e+246) {
		tmp = t_0;
	} else if (z <= -195000000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if (z <= 7.5e+236) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = y * -z
	tmp = 0
	if z <= -6.8e+246:
		tmp = t_0
	elif z <= -195000000000.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = x + y
	elif z <= 7.5e+236:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -6.8e+246)
		tmp = t_0;
	elseif (z <= -195000000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif (z <= 7.5e+236)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = y * -z;
	tmp = 0.0;
	if (z <= -6.8e+246)
		tmp = t_0;
	elseif (z <= -195000000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif (z <= 7.5e+236)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -6.8e+246], t$95$0, If[LessEqual[z, -195000000000.0], t$95$1, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 7.5e+236], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999977e246 or 7.5e236 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 89.3%

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

   3. Applied egg-rr 89.3%

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

   4. Taylor expanded in z around inf 89.3%

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

      1. associate-*r* 89.3%

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

      2. mul-1-neg 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in y around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. distribute-rgt-neg-in 65.3%

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

   9. Simplified 65.3%

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

   if -6.79999999999999977e246 < z < -1.95e11 or 1 < z < 7.5e236

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.9%

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

      2. mul-1-neg 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in z around inf 98.3%

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

      1. associate-*r* 98.3%

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

      2. neg-mul-1 98.3%

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

   9. Simplified 98.3%

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

   10. Taylor expanded in y around inf 53.5%

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

       1. associate-*r* 53.5%

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

       2. mul-1-neg 53.5%

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

   12. Simplified 53.5%

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

   if -1.95e11 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+246}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -195000000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+236}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 97.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. +-commutative 99.1%

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

      3. distribute-rgt-neg-out 99.1%

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

      4. +-commutative 99.1%

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

   4. Simplified 99.1%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.2%

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

4. Final simplification 98.6%

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

Alternative 5: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -280 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -280.0) (not (<= z 1.0))) (* z (- x)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -280.0) || !(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 <= (-280.0d0)) .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 <= -280.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -280.0) 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 <= -280.0) || !(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 <= -280.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -280.0], 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 < -280 or 1 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 96.7%

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

   3. Applied egg-rr 96.7%

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

   4. Taylor expanded in z around inf 96.7%

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

      1. associate-*r* 96.7%

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

      2. mul-1-neg 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in y around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-rgt-neg-in 53.9%

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

   9. Simplified 53.9%

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

   if -280 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -280 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-34}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e-34) (- x (* x z)) (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e-34) {
		tmp = x - (x * z);
	} else {
		tmp = y - (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 (x <= (-3.2d-34)) then
        tmp = x - (x * z)
    else
        tmp = y - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e-34) {
		tmp = x - (x * z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e-34:
		tmp = x - (x * z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e-34)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(y - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.2e-34)
		tmp = x - (x * z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e-34], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.20000000000000003e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.1%

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

      1. sub-neg 74.1%

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

      2. +-commutative 74.1%

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

      3. distribute-rgt1-in 74.1%

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

      4. distribute-lft-neg-out 74.1%

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

      5. unsub-neg 74.1%

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

   4. Simplified 74.1%

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

   if -3.20000000000000003e-34 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 64.2%

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

      1. sub-neg 64.2%

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

      2. distribute-lft-in 64.2%

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

      3. distribute-rgt-neg-out 64.2%

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

      4. unsub-neg 64.2%

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

      5. *-rgt-identity 64.2%

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

   4. Simplified 64.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-34}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]

Alternative 7: 49.6% 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. Taylor expanded in z around 0 52.6%

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

3. Final simplification 52.6%

   \[\leadsto x + y \]

Alternative 8: 25.6% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-lft-in 98.4%

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

3. Applied egg-rr 98.4%

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

4. Taylor expanded in z around inf 75.7%

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

   1. associate-*r* 75.7%

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

   2. mul-1-neg 75.7%

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

6. Simplified 75.7%

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

7. Taylor expanded in z around 0 30.0%

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

8. Final simplification 30.0%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023278 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))