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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Alternatives: 7

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(z + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

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 + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(z + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

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 + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(z + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

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 + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+268}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+184}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+114}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+89}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5600:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+140} \lor \neg \left(z \leq 4.9 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.6e+268)
   (* y z)
   (if (<= z -1.15e+184)
     (* x z)
     (if (<= z -7.5e+114)
       (* y z)
       (if (<= z -9e+89)
         (* x z)
         (if (<= z -1.0)
           (* y z)
           (if (<= z 5600.0)
             (+ x y)
             (if (or (<= z 2.7e+140) (not (<= z 4.9e+204)))
               (* y z)
               (* x (+ z 1.0))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e+268) {
		tmp = y * z;
	} else if (z <= -1.15e+184) {
		tmp = x * z;
	} else if (z <= -7.5e+114) {
		tmp = y * z;
	} else if (z <= -9e+89) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 5600.0) {
		tmp = x + y;
	} else if ((z <= 2.7e+140) || !(z <= 4.9e+204)) {
		tmp = y * z;
	} else {
		tmp = x * (z + 1.0);
	}
	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) :: tmp
    if (z <= (-4.6d+268)) then
        tmp = y * z
    else if (z <= (-1.15d+184)) then
        tmp = x * z
    else if (z <= (-7.5d+114)) then
        tmp = y * z
    else if (z <= (-9d+89)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 5600.0d0) then
        tmp = x + y
    else if ((z <= 2.7d+140) .or. (.not. (z <= 4.9d+204))) then
        tmp = y * z
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e+268) {
		tmp = y * z;
	} else if (z <= -1.15e+184) {
		tmp = x * z;
	} else if (z <= -7.5e+114) {
		tmp = y * z;
	} else if (z <= -9e+89) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 5600.0) {
		tmp = x + y;
	} else if ((z <= 2.7e+140) || !(z <= 4.9e+204)) {
		tmp = y * z;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.6e+268:
		tmp = y * z
	elif z <= -1.15e+184:
		tmp = x * z
	elif z <= -7.5e+114:
		tmp = y * z
	elif z <= -9e+89:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 5600.0:
		tmp = x + y
	elif (z <= 2.7e+140) or not (z <= 4.9e+204):
		tmp = y * z
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.6e+268)
		tmp = Float64(y * z);
	elseif (z <= -1.15e+184)
		tmp = Float64(x * z);
	elseif (z <= -7.5e+114)
		tmp = Float64(y * z);
	elseif (z <= -9e+89)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 5600.0)
		tmp = Float64(x + y);
	elseif ((z <= 2.7e+140) || !(z <= 4.9e+204))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.6e+268)
		tmp = y * z;
	elseif (z <= -1.15e+184)
		tmp = x * z;
	elseif (z <= -7.5e+114)
		tmp = y * z;
	elseif (z <= -9e+89)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 5600.0)
		tmp = x + y;
	elseif ((z <= 2.7e+140) || ~((z <= 4.9e+204)))
		tmp = y * z;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.6e+268], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.15e+184], N[(x * z), $MachinePrecision], If[LessEqual[z, -7.5e+114], N[(y * z), $MachinePrecision], If[LessEqual[z, -9e+89], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 5600.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 2.7e+140], N[Not[LessEqual[z, 4.9e+204]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000024e268 or -1.15e184 < z < -7.5000000000000001e114 or -9e89 < z < -1 or 5600 < z < 2.70000000000000018e140 or 4.8999999999999997e204 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

   4. Simplified 97.0%

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

      1. distribute-lft-in 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in y around inf 48.2%

      \[\leadsto \color{blue}{y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 48.2%

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

   9. Simplified 48.2%

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

   if -4.60000000000000024e268 < z < -1.15e184 or -7.5000000000000001e114 < z < -9e89

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

      1. distribute-lft-in 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 46.8%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 46.8%

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

   9. Simplified 46.8%

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

   if -1 < z < 5600

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.8%

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

      1. +-commutative 96.8%

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

   4. Simplified 96.8%

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

   if 2.70000000000000018e140 < z < 4.8999999999999997e204

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+268}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+184}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+114}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+89}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5600:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+140} \lor \neg \left(z \leq 4.9 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 3: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+270}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{+182}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+113}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5600:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+138} \lor \neg \left(z \leq 1.16 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+270)
   (* y z)
   (if (<= z -6.7e+182)
     (* x z)
     (if (<= z -5.9e+113)
       (* y z)
       (if (<= z -1.4e+89)
         (* x z)
         (if (<= z -1.0)
           (* y z)
           (if (<= z 5600.0)
             (+ x y)
             (if (or (<= z 1.2e+138) (not (<= z 1.16e+207)))
               (* y z)
               (* x z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+270) {
		tmp = y * z;
	} else if (z <= -6.7e+182) {
		tmp = x * z;
	} else if (z <= -5.9e+113) {
		tmp = y * z;
	} else if (z <= -1.4e+89) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 5600.0) {
		tmp = x + y;
	} else if ((z <= 1.2e+138) || !(z <= 1.16e+207)) {
		tmp = y * z;
	} else {
		tmp = x * 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 (z <= (-4d+270)) then
        tmp = y * z
    else if (z <= (-6.7d+182)) then
        tmp = x * z
    else if (z <= (-5.9d+113)) then
        tmp = y * z
    else if (z <= (-1.4d+89)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 5600.0d0) then
        tmp = x + y
    else if ((z <= 1.2d+138) .or. (.not. (z <= 1.16d+207))) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+270) {
		tmp = y * z;
	} else if (z <= -6.7e+182) {
		tmp = x * z;
	} else if (z <= -5.9e+113) {
		tmp = y * z;
	} else if (z <= -1.4e+89) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 5600.0) {
		tmp = x + y;
	} else if ((z <= 1.2e+138) || !(z <= 1.16e+207)) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+270:
		tmp = y * z
	elif z <= -6.7e+182:
		tmp = x * z
	elif z <= -5.9e+113:
		tmp = y * z
	elif z <= -1.4e+89:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 5600.0:
		tmp = x + y
	elif (z <= 1.2e+138) or not (z <= 1.16e+207):
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+270)
		tmp = Float64(y * z);
	elseif (z <= -6.7e+182)
		tmp = Float64(x * z);
	elseif (z <= -5.9e+113)
		tmp = Float64(y * z);
	elseif (z <= -1.4e+89)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 5600.0)
		tmp = Float64(x + y);
	elseif ((z <= 1.2e+138) || !(z <= 1.16e+207))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e+270)
		tmp = y * z;
	elseif (z <= -6.7e+182)
		tmp = x * z;
	elseif (z <= -5.9e+113)
		tmp = y * z;
	elseif (z <= -1.4e+89)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 5600.0)
		tmp = x + y;
	elseif ((z <= 1.2e+138) || ~((z <= 1.16e+207)))
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+270], N[(y * z), $MachinePrecision], If[LessEqual[z, -6.7e+182], N[(x * z), $MachinePrecision], If[LessEqual[z, -5.9e+113], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.4e+89], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 5600.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1.2e+138], N[Not[LessEqual[z, 1.16e+207]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000002e270 or -6.7000000000000006e182 < z < -5.90000000000000023e113 or -1.3999999999999999e89 < z < -1 or 5600 < z < 1.2e138 or 1.16e207 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

   4. Simplified 97.0%

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

      1. distribute-lft-in 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in y around inf 48.2%

      \[\leadsto \color{blue}{y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 48.2%

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

   9. Simplified 48.2%

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

   if -4.0000000000000002e270 < z < -6.7000000000000006e182 or -5.90000000000000023e113 < z < -1.3999999999999999e89 or 1.2e138 < z < 1.16e207

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 53.2%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 53.2%

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

   9. Simplified 53.2%

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

   if -1 < z < 5600

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.8%

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

      1. +-commutative 96.8%

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

   4. Simplified 96.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+270}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{+182}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+113}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5600:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+138} \lor \neg \left(z \leq 1.16 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4: 97.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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

   2. Taylor expanded in z around inf 97.6%

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

      1. +-commutative 97.6%

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

   4. Simplified 97.6%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   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%

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

Alternative 5: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.45e-127) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	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) :: tmp
    if (y <= 1.45d-127) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * (z + 1.0d0)
    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 * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.45e-127)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.45e-127], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.45e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.2%

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

   if 1.45e-127 < y

   1. Initial program 100.0%

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

   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%

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

Alternative 6: 31.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-165}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.65e-165) (* x z) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.65e-165) {
		tmp = x * z;
	} else {
		tmp = 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 (y <= 1.65d-165) then
        tmp = x * z
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.65e-165) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.65e-165:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.65e-165)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.65e-165)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.65e-165], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6499999999999999e-165

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 48.0%

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

      1. +-commutative 48.0%

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

   4. Simplified 48.0%

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

      1. distribute-lft-in 46.7%

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

   6. Applied egg-rr 46.7%

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

   7. Taylor expanded in y around 0 32.6%

      \[\leadsto \color{blue}{x \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 32.6%

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

   9. Simplified 32.6%

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

   if 1.6499999999999999e-165 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 52.0%

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

      1. +-commutative 52.0%

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

   4. Simplified 52.0%

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

      1. distribute-lft-in 52.0%

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

   6. Applied egg-rr 52.0%

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

   7. Taylor expanded in y around inf 35.9%

      \[\leadsto \color{blue}{y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 35.9%

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

   9. Simplified 35.9%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-165}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 27.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x * z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * z), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in z around inf 49.6%

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

   1. +-commutative 49.6%

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

4. Simplified 49.6%

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

   1. distribute-lft-in 48.9%

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

6. Applied egg-rr 48.9%

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

7. Taylor expanded in y around 0 28.4%

   \[\leadsto \color{blue}{x \cdot z} \]
8. Step-by-step derivation

   1. *-commutative 28.4%

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

9. Simplified 28.4%

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

10. Final simplification 28.4%

    \[\leadsto x \cdot z \]

Reproduce

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