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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 11

Speedup: 1.0×

• 21.0% 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. Step-by-step derivation

   1. distribute-rgt-neg-out 100.0%

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

   2. unsub-neg 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -400:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= (- 1.0 z) -400.0)
     t_0
     (if (<= (- 1.0 z) 2.0)
       (+ x y)
       (if (<= (- 1.0 z) 2e+104) (* y (- 1.0 z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if ((1.0 - z) <= -400.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 2e+104) {
		tmp = y * (1.0 - 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 = x * -z
    if ((1.0d0 - z) <= (-400.0d0)) then
        tmp = t_0
    else if ((1.0d0 - z) <= 2.0d0) then
        tmp = x + y
    else if ((1.0d0 - z) <= 2d+104) then
        tmp = y * (1.0d0 - 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 = x * -z;
	double tmp;
	if ((1.0 - z) <= -400.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 2.0) {
		tmp = x + y;
	} else if ((1.0 - z) <= 2e+104) {
		tmp = y * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if (1.0 - z) <= -400.0:
		tmp = t_0
	elif (1.0 - z) <= 2.0:
		tmp = x + y
	elif (1.0 - z) <= 2e+104:
		tmp = y * (1.0 - z)
	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) <= -400.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 2.0)
		tmp = Float64(x + y);
	elseif (Float64(1.0 - z) <= 2e+104)
		tmp = Float64(y * Float64(1.0 - z));
	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) <= -400.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 2.0)
		tmp = x + y;
	elseif ((1.0 - z) <= 2e+104)
		tmp = y * (1.0 - z);
	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], -400.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+104], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 1 z) < -400 or 2e104 < (-.f64 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 50.9%

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

   6. Taylor expanded in z around inf 50.3%

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

      1. associate-*r* 50.3%

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

      2. neg-mul-1 50.3%

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

   8. Simplified 50.3%

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

   if -400 < (-.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 96.7%

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

      1. +-commutative 96.7%

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

   5. Simplified 96.7%

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

   if 2 < (-.f64 1 z) < 2e104

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 37.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -400:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 2:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -52:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+211} \lor \neg \left(z \leq 2.1 \cdot 10^{+270}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* y (- z))))
   (if (<= z -4e+105)
     t_0
     (if (<= z -52.0)
       t_1
       (if (<= z 1.0)
         (+ x y)
         (if (or (<= z 7.6e+211) (not (<= z 2.1e+270))) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * -z;
	double tmp;
	if (z <= -4e+105) {
		tmp = t_0;
	} else if (z <= -52.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 7.6e+211) || !(z <= 2.1e+270)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = x * -z
    t_1 = y * -z
    if (z <= (-4d+105)) then
        tmp = t_0
    else if (z <= (-52.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 7.6d+211) .or. (.not. (z <= 2.1d+270))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * -z;
	double tmp;
	if (z <= -4e+105) {
		tmp = t_0;
	} else if (z <= -52.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 7.6e+211) || !(z <= 2.1e+270)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = y * -z
	tmp = 0
	if z <= -4e+105:
		tmp = t_0
	elif z <= -52.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 7.6e+211) or not (z <= 2.1e+270):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -4e+105)
		tmp = t_0;
	elseif (z <= -52.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 7.6e+211) || !(z <= 2.1e+270))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = y * -z;
	tmp = 0.0;
	if (z <= -4e+105)
		tmp = t_0;
	elseif (z <= -52.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 7.6e+211) || ~((z <= 2.1e+270)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -4e+105], t$95$0, If[LessEqual[z, -52.0], t$95$1, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 7.6e+211], N[Not[LessEqual[z, 2.1e+270]], $MachinePrecision]], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999998e105 or 1 < z < 7.60000000000000032e211 or 2.1000000000000001e270 < 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 51.8%

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

      1. associate-*r* 51.8%

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

      2. neg-mul-1 51.8%

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

   8. Simplified 51.8%

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

   if -3.9999999999999998e105 < z < -52 or 7.60000000000000032e211 < z < 2.1000000000000001e270

   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 99.9%

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

      3. *-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 46.4%

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

      1. mul-1-neg 46.4%

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

   7. Simplified 46.4%

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

   8. Taylor expanded in z around inf 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

   10. Simplified 45.0%

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

   if -52 < 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 96.7%

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

      1. +-commutative 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -52:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+211} \lor \neg \left(z \leq 2.1 \cdot 10^{+270}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -400 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -400.0) (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) <= -400.0) || !((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) <= (-400.0d0)) .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) <= -400.0) || !((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) <= -400.0) 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) <= -400.0) || !(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) <= -400.0) || ~(((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], -400.0], 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) < -400 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 97.8%

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

      1. mul-1-neg 97.8%

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

      2. *-commutative 97.8%

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

      3. distribute-rgt-neg-out 97.8%

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

      4. +-commutative 97.8%

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

   5. Simplified 97.8%

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

   if -400 < (-.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 96.7%

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

      1. +-commutative 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -400 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-x\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -300000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -300000000000.0) (not (<= z 1.0))) (* x (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -300000000000.0) || !(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 <= (-300000000000.0d0)) .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 <= -300000000000.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -300000000000.0) 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 <= -300000000000.0) || !(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 <= -300000000000.0) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -300000000000.0], 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 < -3e11 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 53.0%

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

   6. Taylor expanded in z around inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

   8. Simplified 52.2%

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

   if -3e11 < 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 95.5%

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

      1. +-commutative 95.5%

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

   5. Simplified 95.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -300000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e-46) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e-46) {
		tmp = x * (1.0 - 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 <= (-4d-46)) then
        tmp = x * (1.0d0 - 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 <= -4e-46) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4e-46:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e-46)
		tmp = Float64(x * Float64(1.0 - 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 <= -4e-46)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e-46], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000009e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -4.00000000000000009e-46 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 62.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.65e-47) (* x (- 1.0 z)) (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e-47) {
		tmp = x * (1.0 - 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 <= (-1.65d-47)) then
        tmp = x * (1.0d0 - 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 <= -1.65e-47) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.65e-47:
		tmp = x * (1.0 - z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.65e-47)
		tmp = Float64(x * Float64(1.0 - 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 <= -1.65e-47)
		tmp = x * (1.0 - z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.65e-47], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000002e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -1.65000000000000002e-47 < x

   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. Step-by-step derivation

      1. distribute-rgt-neg-out 100.0%

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

      2. unsub-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 62.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 9: 31.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.2e-22) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.2e-22) {
		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 <= 1.2d-22) 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 <= 1.2e-22) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.2e-22:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.2e-22)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.2e-22)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.2e-22], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.20000000000000001e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.2%

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

      1. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in z around 0 27.6%

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

   if 1.20000000000000001e-22 < 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 78.0%

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

   4. Taylor expanded in z around 0 44.2%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.3% 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 51.3%

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

   1. +-commutative 51.3%

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

5. Simplified 51.3%

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

6. Final simplification 51.3%

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

Alternative 11: 25.6% 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 47.5%

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

   1. *-commutative 47.5%

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

5. Simplified 47.5%

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

6. Taylor expanded in z around 0 22.7%

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

7. Final simplification 22.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))