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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 9

Speedup: 1.0×

• 20.6% 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: 52.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;1 - z \leq -1 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;1 - z \leq 1.0002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+86} \lor \neg \left(1 - z \leq 4 \cdot 10^{+113}\right) \land \left(1 - z \leq 2 \cdot 10^{+182} \lor \neg \left(1 - z \leq 2 \cdot 10^{+267}\right)\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))) (t_1 (* x (- z))))
   (if (<= (- 1.0 z) -1e+209)
     (* y (- z))
     (if (<= (- 1.0 z) -2e+142)
       t_1
       (if (<= (- 1.0 z) 1.0)
         t_0
         (if (<= (- 1.0 z) 1.0002)
           (+ x y)
           (if (or (<= (- 1.0 z) 5e+86)
                   (and (not (<= (- 1.0 z) 4e+113))
                        (or (<= (- 1.0 z) 2e+182)
                            (not (<= (- 1.0 z) 2e+267)))))
             t_0
             t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double t_1 = x * -z;
	double tmp;
	if ((1.0 - z) <= -1e+209) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -2e+142) {
		tmp = t_1;
	} else if ((1.0 - z) <= 1.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0002) {
		tmp = x + y;
	} else if (((1.0 - z) <= 5e+86) || (!((1.0 - z) <= 4e+113) && (((1.0 - z) <= 2e+182) || !((1.0 - z) <= 2e+267)))) {
		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 = y * (1.0d0 - z)
    t_1 = x * -z
    if ((1.0d0 - z) <= (-1d+209)) then
        tmp = y * -z
    else if ((1.0d0 - z) <= (-2d+142)) then
        tmp = t_1
    else if ((1.0d0 - z) <= 1.0d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.0002d0) then
        tmp = x + y
    else if (((1.0d0 - z) <= 5d+86) .or. (.not. ((1.0d0 - z) <= 4d+113)) .and. ((1.0d0 - z) <= 2d+182) .or. (.not. ((1.0d0 - z) <= 2d+267))) 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 = y * (1.0 - z);
	double t_1 = x * -z;
	double tmp;
	if ((1.0 - z) <= -1e+209) {
		tmp = y * -z;
	} else if ((1.0 - z) <= -2e+142) {
		tmp = t_1;
	} else if ((1.0 - z) <= 1.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.0002) {
		tmp = x + y;
	} else if (((1.0 - z) <= 5e+86) || (!((1.0 - z) <= 4e+113) && (((1.0 - z) <= 2e+182) || !((1.0 - z) <= 2e+267)))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	t_1 = x * -z
	tmp = 0
	if (1.0 - z) <= -1e+209:
		tmp = y * -z
	elif (1.0 - z) <= -2e+142:
		tmp = t_1
	elif (1.0 - z) <= 1.0:
		tmp = t_0
	elif (1.0 - z) <= 1.0002:
		tmp = x + y
	elif ((1.0 - z) <= 5e+86) or (not ((1.0 - z) <= 4e+113) and (((1.0 - z) <= 2e+182) or not ((1.0 - z) <= 2e+267))):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (Float64(1.0 - z) <= -1e+209)
		tmp = Float64(y * Float64(-z));
	elseif (Float64(1.0 - z) <= -2e+142)
		tmp = t_1;
	elseif (Float64(1.0 - z) <= 1.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.0002)
		tmp = Float64(x + y);
	elseif ((Float64(1.0 - z) <= 5e+86) || (!(Float64(1.0 - z) <= 4e+113) && ((Float64(1.0 - z) <= 2e+182) || !(Float64(1.0 - z) <= 2e+267))))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	t_1 = x * -z;
	tmp = 0.0;
	if ((1.0 - z) <= -1e+209)
		tmp = y * -z;
	elseif ((1.0 - z) <= -2e+142)
		tmp = t_1;
	elseif ((1.0 - z) <= 1.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.0002)
		tmp = x + y;
	elseif (((1.0 - z) <= 5e+86) || (~(((1.0 - z) <= 4e+113)) && (((1.0 - z) <= 2e+182) || ~(((1.0 - z) <= 2e+267)))))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+209], N[(y * (-z)), $MachinePrecision], If[LessEqual[N[(1.0 - z), $MachinePrecision], -2e+142], t$95$1, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.0002], N[(x + y), $MachinePrecision], If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], 5e+86], And[N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 4e+113]], $MachinePrecision], Or[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+182], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2e+267]], $MachinePrecision]]]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 z) < -1.0000000000000001e209

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. mul-1-neg 55.1%

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

   7. Simplified 55.1%

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

   if -1.0000000000000001e209 < (-.f64 1 z) < -2.0000000000000001e142 or 4.9999999999999998e86 < (-.f64 1 z) < 4e113 or 2.0000000000000001e182 < (-.f64 1 z) < 1.9999999999999999e267

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 53.2%

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

      1. *-commutative 53.2%

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

   4. Simplified 53.2%

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

   5. Taylor expanded in z around inf 53.2%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 53.2%

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

   if -2.0000000000000001e142 < (-.f64 1 z) < 1 or 1.0002 < (-.f64 1 z) < 4.9999999999999998e86 or 4e113 < (-.f64 1 z) < 2.0000000000000001e182 or 1.9999999999999999e267 < (-.f64 1 z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 54.0%

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

   if 1 < (-.f64 1 z) < 1.0002

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.6%

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

      1. +-commutative 86.6%

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

   4. Simplified 86.6%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -1 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq -2 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;1 - z \leq 1:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 1.0002:\\ \;\;\;\;x + y\\ \mathbf{elif}\;1 - z \leq 5 \cdot 10^{+86} \lor \neg \left(1 - z \leq 4 \cdot 10^{+113}\right) \land \left(1 - z \leq 2 \cdot 10^{+182} \lor \neg \left(1 - z \leq 2 \cdot 10^{+267}\right)\right):\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+269}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -19:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+138} \lor \neg \left(z \leq 1.95 \cdot 10^{+208}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))) (t_1 (* x (- z))))
   (if (<= z -2.15e+269)
     t_0
     (if (<= z -3e+184)
       t_1
       (if (<= z -5.2e+113)
         t_0
         (if (<= z -8.2e+89)
           t_1
           (if (<= z -19.0)
             t_0
             (if (<= z 1.0)
               (+ x y)
               (if (or (<= z 8e+138) (not (<= z 1.95e+208))) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double t_1 = x * -z;
	double tmp;
	if (z <= -2.15e+269) {
		tmp = t_0;
	} else if (z <= -3e+184) {
		tmp = t_1;
	} else if (z <= -5.2e+113) {
		tmp = t_0;
	} else if (z <= -8.2e+89) {
		tmp = t_1;
	} else if (z <= -19.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 8e+138) || !(z <= 1.95e+208)) {
		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 = y * -z
    t_1 = x * -z
    if (z <= (-2.15d+269)) then
        tmp = t_0
    else if (z <= (-3d+184)) then
        tmp = t_1
    else if (z <= (-5.2d+113)) then
        tmp = t_0
    else if (z <= (-8.2d+89)) then
        tmp = t_1
    else if (z <= (-19.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else if ((z <= 8d+138) .or. (.not. (z <= 1.95d+208))) 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 = y * -z;
	double t_1 = x * -z;
	double tmp;
	if (z <= -2.15e+269) {
		tmp = t_0;
	} else if (z <= -3e+184) {
		tmp = t_1;
	} else if (z <= -5.2e+113) {
		tmp = t_0;
	} else if (z <= -8.2e+89) {
		tmp = t_1;
	} else if (z <= -19.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else if ((z <= 8e+138) || !(z <= 1.95e+208)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	t_1 = x * -z
	tmp = 0
	if z <= -2.15e+269:
		tmp = t_0
	elif z <= -3e+184:
		tmp = t_1
	elif z <= -5.2e+113:
		tmp = t_0
	elif z <= -8.2e+89:
		tmp = t_1
	elif z <= -19.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	elif (z <= 8e+138) or not (z <= 1.95e+208):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -2.15e+269)
		tmp = t_0;
	elseif (z <= -3e+184)
		tmp = t_1;
	elseif (z <= -5.2e+113)
		tmp = t_0;
	elseif (z <= -8.2e+89)
		tmp = t_1;
	elseif (z <= -19.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	elseif ((z <= 8e+138) || !(z <= 1.95e+208))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	t_1 = x * -z;
	tmp = 0.0;
	if (z <= -2.15e+269)
		tmp = t_0;
	elseif (z <= -3e+184)
		tmp = t_1;
	elseif (z <= -5.2e+113)
		tmp = t_0;
	elseif (z <= -8.2e+89)
		tmp = t_1;
	elseif (z <= -19.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	elseif ((z <= 8e+138) || ~((z <= 1.95e+208)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.15e+269], t$95$0, If[LessEqual[z, -3e+184], t$95$1, If[LessEqual[z, -5.2e+113], t$95$0, If[LessEqual[z, -8.2e+89], t$95$1, If[LessEqual[z, -19.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 8e+138], N[Not[LessEqual[z, 1.95e+208]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.14999999999999992e269 or -2.99999999999999986e184 < z < -5.1999999999999998e113 or -8.1999999999999997e89 < z < -19 or 1 < z < 8.0000000000000003e138 or 1.95e208 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 96.2%

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

      1. mul-1-neg 96.2%

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

      2. *-commutative 96.2%

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

      3. distribute-rgt-neg-out 96.2%

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

      4. +-commutative 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in y around inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. mul-1-neg 48.0%

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

   7. Simplified 48.0%

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

   if -2.14999999999999992e269 < z < -2.99999999999999986e184 or -5.1999999999999998e113 < z < -8.1999999999999997e89 or 8.0000000000000003e138 < z < 1.95e208

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 53.2%

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

      1. *-commutative 53.2%

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

   4. Simplified 53.2%

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

   5. Taylor expanded in z around inf 53.2%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 53.2%

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

   if -19 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.5%

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

      1. +-commutative 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+269}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -19:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+138} \lor \neg \left(z \leq 1.95 \cdot 10^{+208}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -5000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -5000.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- y) x))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -5000.0) || !((1.0 - z) <= 2.0)) {
		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 (((1.0d0 - z) <= (-5000.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) 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 (((1.0 - z) <= -5000.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -5000.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-y - x)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -5000.0) || !(Float64(1.0 - z) <= 2.0))
		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 (((1.0 - z) <= -5000.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-y - x);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -5000.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -5e3 or 2 < (-.f64 1 z)

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.6%

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

      1. mul-1-neg 97.6%

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

      2. *-commutative 97.6%

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

      3. distribute-rgt-neg-out 97.6%

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

      4. +-commutative 97.6%

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

   4. Simplified 97.6%

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

   if -5e3 < (-.f64 1 z) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.5%

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

      1. +-commutative 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -5000 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12600 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -12600.0) (not (<= z 1.0))) (* x (- z)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -12600.0) || !(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 <= (-12600.0d0)) .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 <= -12600.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -12600.0) 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 <= -12600.0) || !(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 <= -12600.0) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -12600.0], 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 < -12600 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 55.1%

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

      1. *-commutative 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in z around inf 55.1%

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

      1. associate-*r* 98.3%

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

      2. mul-1-neg 98.3%

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

   7. Simplified 55.1%

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

   if -12600 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.2%

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

      1. +-commutative 96.2%

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

   4. Simplified 96.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12600 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.45e-127) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.45e-127) {
		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 (y <= 1.45d-127) 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 (y <= 1.45e-127) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.45e-127:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.45e-127)
		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 (y <= 1.45e-127)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.45e-127], 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 y < 1.45e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.2%

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

      1. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   if 1.45e-127 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.9%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7: 31.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.9e-97) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.9e-97) {
		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 <= 3.9d-97) 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 <= 3.9e-97) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.9e-97:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.9e-97)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.9e-97)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.9e-97], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.8999999999999998e-97

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in z around 0 29.1%

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

   if 3.8999999999999998e-97 < y

   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 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-*r* 86.8%

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

      2. mul-1-neg 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in z around 0 36.1%

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

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 50.5% 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 51.6%

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

   1. +-commutative 51.6%

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

4. Simplified 51.6%

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

5. Final simplification 51.6%

   \[\leadsto x + y \]

Alternative 9: 26.0% 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. Taylor expanded in x around inf 50.1%

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

   1. *-commutative 50.1%

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

4. Simplified 50.1%

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

5. Taylor expanded in z around 0 24.4%

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

6. Final simplification 24.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))