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

Percentage Accurate: 100.0% → 98.8%

Time: 6.3s

Alternatives: 10

Speedup: 1.0×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \mathsf{fma}\left(z + 1, y, \left(z + 1\right) \cdot x\right) \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (fma (+ z 1.0) y (* (+ z 1.0) x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return fma((z + 1.0), y, ((z + 1.0) * x));
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return fma(Float64(z + 1.0), y, Float64(Float64(z + 1.0) * x))
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(z + 1.0), $MachinePrecision] * y + N[(N[(z + 1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-lft-in 99.2%

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

   4. fma-define 99.6%

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

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

   \[\leadsto \mathsf{fma}\left(z + 1, y, \left(z + 1\right) \cdot x\right) \]
6. Add Preprocessing

Alternative 2: 50.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+183}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+110} \lor \neg \left(z \leq 4.4 \cdot 10^{+244}\right) \land z \leq 1.36 \cdot 10^{+293}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+183)
   (* z x)
   (if (<= z -1.0)
     (* z y)
     (if (<= z 6e-158)
       x
       (if (<= z 4e+14)
         y
         (if (or (<= z 4e+110) (and (not (<= z 4.4e+244)) (<= z 1.36e+293)))
           (* z x)
           (* z y)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+183) {
		tmp = z * x;
	} else if (z <= -1.0) {
		tmp = z * y;
	} else if (z <= 6e-158) {
		tmp = x;
	} else if (z <= 4e+14) {
		tmp = y;
	} else if ((z <= 4e+110) || (!(z <= 4.4e+244) && (z <= 1.36e+293))) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-9d+183)) then
        tmp = z * x
    else if (z <= (-1.0d0)) then
        tmp = z * y
    else if (z <= 6d-158) then
        tmp = x
    else if (z <= 4d+14) then
        tmp = y
    else if ((z <= 4d+110) .or. (.not. (z <= 4.4d+244)) .and. (z <= 1.36d+293)) then
        tmp = z * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+183) {
		tmp = z * x;
	} else if (z <= -1.0) {
		tmp = z * y;
	} else if (z <= 6e-158) {
		tmp = x;
	} else if (z <= 4e+14) {
		tmp = y;
	} else if ((z <= 4e+110) || (!(z <= 4.4e+244) && (z <= 1.36e+293))) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -9e+183:
		tmp = z * x
	elif z <= -1.0:
		tmp = z * y
	elif z <= 6e-158:
		tmp = x
	elif z <= 4e+14:
		tmp = y
	elif (z <= 4e+110) or (not (z <= 4.4e+244) and (z <= 1.36e+293)):
		tmp = z * x
	else:
		tmp = z * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+183)
		tmp = Float64(z * x);
	elseif (z <= -1.0)
		tmp = Float64(z * y);
	elseif (z <= 6e-158)
		tmp = x;
	elseif (z <= 4e+14)
		tmp = y;
	elseif ((z <= 4e+110) || (!(z <= 4.4e+244) && (z <= 1.36e+293)))
		tmp = Float64(z * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+183)
		tmp = z * x;
	elseif (z <= -1.0)
		tmp = z * y;
	elseif (z <= 6e-158)
		tmp = x;
	elseif (z <= 4e+14)
		tmp = y;
	elseif ((z <= 4e+110) || (~((z <= 4.4e+244)) && (z <= 1.36e+293)))
		tmp = z * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -9e+183], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.0], N[(z * y), $MachinePrecision], If[LessEqual[z, 6e-158], x, If[LessEqual[z, 4e+14], y, If[Or[LessEqual[z, 4e+110], And[N[Not[LessEqual[z, 4.4e+244]], $MachinePrecision], LessEqual[z, 1.36e+293]]], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.00000000000000034e183 or 4e14 < z < 4.0000000000000001e110 or 4.40000000000000003e244 < z < 1.3600000000000001e293

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 96.9%

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

      4. fma-define 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in x around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. +-commutative 85.2%

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

      3. associate-+l+ 85.2%

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

      4. +-commutative 85.2%

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

      5. *-commutative 85.2%

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

      6. associate-/l* 86.6%

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

      7. *-rgt-identity 86.6%

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

      8. distribute-lft-out 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in z around inf 86.6%

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

   9. Taylor expanded in x around inf 58.8%

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

       1. *-commutative 58.8%

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

   11. Simplified 58.8%

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

   if -9.00000000000000034e183 < z < -1 or 4.0000000000000001e110 < z < 4.40000000000000003e244 or 1.3600000000000001e293 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in z around inf 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -1 < z < 6e-158

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 46.1%

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

   6. Taylor expanded in z around 0 46.0%

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

   if 6e-158 < z < 4e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 50.2%

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

   4. Taylor expanded in z around 0 43.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+183}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+110} \lor \neg \left(z \leq 4.4 \cdot 10^{+244}\right) \land z \leq 1.36 \cdot 10^{+293}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+111} \lor \neg \left(z \leq 1.05 \cdot 10^{+249}\right) \land z \leq 1.7 \cdot 10^{+292}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+182)
   (* z x)
   (if (<= z -1.0)
     (* z y)
     (if (<= z 4e+14)
       (+ y x)
       (if (or (<= z 1.18e+111) (and (not (<= z 1.05e+249)) (<= z 1.7e+292)))
         (* z x)
         (* z y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+182) {
		tmp = z * x;
	} else if (z <= -1.0) {
		tmp = z * y;
	} else if (z <= 4e+14) {
		tmp = y + x;
	} else if ((z <= 1.18e+111) || (!(z <= 1.05e+249) && (z <= 1.7e+292))) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-9.5d+182)) then
        tmp = z * x
    else if (z <= (-1.0d0)) then
        tmp = z * y
    else if (z <= 4d+14) then
        tmp = y + x
    else if ((z <= 1.18d+111) .or. (.not. (z <= 1.05d+249)) .and. (z <= 1.7d+292)) then
        tmp = z * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+182) {
		tmp = z * x;
	} else if (z <= -1.0) {
		tmp = z * y;
	} else if (z <= 4e+14) {
		tmp = y + x;
	} else if ((z <= 1.18e+111) || (!(z <= 1.05e+249) && (z <= 1.7e+292))) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -9.5e+182:
		tmp = z * x
	elif z <= -1.0:
		tmp = z * y
	elif z <= 4e+14:
		tmp = y + x
	elif (z <= 1.18e+111) or (not (z <= 1.05e+249) and (z <= 1.7e+292)):
		tmp = z * x
	else:
		tmp = z * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+182)
		tmp = Float64(z * x);
	elseif (z <= -1.0)
		tmp = Float64(z * y);
	elseif (z <= 4e+14)
		tmp = Float64(y + x);
	elseif ((z <= 1.18e+111) || (!(z <= 1.05e+249) && (z <= 1.7e+292)))
		tmp = Float64(z * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e+182)
		tmp = z * x;
	elseif (z <= -1.0)
		tmp = z * y;
	elseif (z <= 4e+14)
		tmp = y + x;
	elseif ((z <= 1.18e+111) || (~((z <= 1.05e+249)) && (z <= 1.7e+292)))
		tmp = z * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -9.5e+182], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.0], N[(z * y), $MachinePrecision], If[LessEqual[z, 4e+14], N[(y + x), $MachinePrecision], If[Or[LessEqual[z, 1.18e+111], And[N[Not[LessEqual[z, 1.05e+249]], $MachinePrecision], LessEqual[z, 1.7e+292]]], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000002e182 or 4e14 < z < 1.1799999999999999e111 or 1.0499999999999999e249 < z < 1.7000000000000001e292

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 96.9%

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

      4. fma-define 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in x around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. +-commutative 85.2%

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

      3. associate-+l+ 85.2%

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

      4. +-commutative 85.2%

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

      5. *-commutative 85.2%

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

      6. associate-/l* 86.6%

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

      7. *-rgt-identity 86.6%

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

      8. distribute-lft-out 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in z around inf 86.6%

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

   9. Taylor expanded in x around inf 58.8%

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

       1. *-commutative 58.8%

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

   11. Simplified 58.8%

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

   if -9.50000000000000002e182 < z < -1 or 1.1799999999999999e111 < z < 1.0499999999999999e249 or 1.7000000000000001e292 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in z around inf 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -1 < z < 4e14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+111} \lor \neg \left(z \leq 1.05 \cdot 10^{+249}\right) \land z \leq 1.7 \cdot 10^{+292}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+180}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-7}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+111}:\\ \;\;\;\;\left(z + 1\right) \cdot x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+249} \lor \neg \left(z \leq 6.8 \cdot 10^{+292}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e+180)
   (* z x)
   (if (<= z -1.0)
     (* z y)
     (if (<= z 2.05e-7)
       (+ y x)
       (if (<= z 1.5e+111)
         (* (+ z 1.0) x)
         (if (or (<= z 3.2e+249) (not (<= z 6.8e+292))) (* z y) (* z x)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e+180) {
		tmp = z * x;
	} else if (z <= -1.0) {
		tmp = z * y;
	} else if (z <= 2.05e-7) {
		tmp = y + x;
	} else if (z <= 1.5e+111) {
		tmp = (z + 1.0) * x;
	} else if ((z <= 3.2e+249) || !(z <= 6.8e+292)) {
		tmp = z * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-2.4d+180)) then
        tmp = z * x
    else if (z <= (-1.0d0)) then
        tmp = z * y
    else if (z <= 2.05d-7) then
        tmp = y + x
    else if (z <= 1.5d+111) then
        tmp = (z + 1.0d0) * x
    else if ((z <= 3.2d+249) .or. (.not. (z <= 6.8d+292))) then
        tmp = z * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e+180) {
		tmp = z * x;
	} else if (z <= -1.0) {
		tmp = z * y;
	} else if (z <= 2.05e-7) {
		tmp = y + x;
	} else if (z <= 1.5e+111) {
		tmp = (z + 1.0) * x;
	} else if ((z <= 3.2e+249) || !(z <= 6.8e+292)) {
		tmp = z * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -2.4e+180:
		tmp = z * x
	elif z <= -1.0:
		tmp = z * y
	elif z <= 2.05e-7:
		tmp = y + x
	elif z <= 1.5e+111:
		tmp = (z + 1.0) * x
	elif (z <= 3.2e+249) or not (z <= 6.8e+292):
		tmp = z * y
	else:
		tmp = z * x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e+180)
		tmp = Float64(z * x);
	elseif (z <= -1.0)
		tmp = Float64(z * y);
	elseif (z <= 2.05e-7)
		tmp = Float64(y + x);
	elseif (z <= 1.5e+111)
		tmp = Float64(Float64(z + 1.0) * x);
	elseif ((z <= 3.2e+249) || !(z <= 6.8e+292))
		tmp = Float64(z * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.4e+180)
		tmp = z * x;
	elseif (z <= -1.0)
		tmp = z * y;
	elseif (z <= 2.05e-7)
		tmp = y + x;
	elseif (z <= 1.5e+111)
		tmp = (z + 1.0) * x;
	elseif ((z <= 3.2e+249) || ~((z <= 6.8e+292)))
		tmp = z * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -2.4e+180], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.0], N[(z * y), $MachinePrecision], If[LessEqual[z, 2.05e-7], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.5e+111], N[(N[(z + 1.0), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[z, 3.2e+249], N[Not[LessEqual[z, 6.8e+292]], $MachinePrecision]], N[(z * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3999999999999998e180 or 3.20000000000000014e249 < z < 6.8000000000000003e292

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 95.3%

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

      4. fma-define 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in x around inf 86.6%

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

      1. +-commutative 86.6%

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

      2. +-commutative 86.6%

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

      3. associate-+l+ 86.6%

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

      4. +-commutative 86.6%

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

      5. *-commutative 86.6%

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

      6. associate-/l* 88.8%

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

      7. *-rgt-identity 88.8%

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

      8. distribute-lft-out 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in z around inf 88.8%

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

   9. Taylor expanded in x around inf 54.5%

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

       1. *-commutative 54.5%

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

   11. Simplified 54.5%

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

   if -2.3999999999999998e180 < z < -1 or 1.5e111 < z < 3.20000000000000014e249 or 6.8000000000000003e292 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in z around inf 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -1 < z < 2.05e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   if 2.05e-7 < z < 1.5e111

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 64.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+180}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-7}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+111}:\\ \;\;\;\;\left(z + 1\right) \cdot x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+249} \lor \neg \left(z \leq 6.8 \cdot 10^{+292}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-286}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4e-12)
   (* z x)
   (if (<= z -1.56e-208)
     x
     (if (<= z 1.15e-286)
       y
       (if (<= z 3.8e-157) x (if (<= z 4e+14) y (* z x)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-12) {
		tmp = z * x;
	} else if (z <= -1.56e-208) {
		tmp = x;
	} else if (z <= 1.15e-286) {
		tmp = y;
	} else if (z <= 3.8e-157) {
		tmp = x;
	} else if (z <= 4e+14) {
		tmp = y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-5.4d-12)) then
        tmp = z * x
    else if (z <= (-1.56d-208)) then
        tmp = x
    else if (z <= 1.15d-286) then
        tmp = y
    else if (z <= 3.8d-157) then
        tmp = x
    else if (z <= 4d+14) then
        tmp = y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-12) {
		tmp = z * x;
	} else if (z <= -1.56e-208) {
		tmp = x;
	} else if (z <= 1.15e-286) {
		tmp = y;
	} else if (z <= 3.8e-157) {
		tmp = x;
	} else if (z <= 4e+14) {
		tmp = y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -5.4e-12:
		tmp = z * x
	elif z <= -1.56e-208:
		tmp = x
	elif z <= 1.15e-286:
		tmp = y
	elif z <= 3.8e-157:
		tmp = x
	elif z <= 4e+14:
		tmp = y
	else:
		tmp = z * x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4e-12)
		tmp = Float64(z * x);
	elseif (z <= -1.56e-208)
		tmp = x;
	elseif (z <= 1.15e-286)
		tmp = y;
	elseif (z <= 3.8e-157)
		tmp = x;
	elseif (z <= 4e+14)
		tmp = y;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4e-12)
		tmp = z * x;
	elseif (z <= -1.56e-208)
		tmp = x;
	elseif (z <= 1.15e-286)
		tmp = y;
	elseif (z <= 3.8e-157)
		tmp = x;
	elseif (z <= 4e+14)
		tmp = y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -5.4e-12], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.56e-208], x, If[LessEqual[z, 1.15e-286], y, If[LessEqual[z, 3.8e-157], x, If[LessEqual[z, 4e+14], y, N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999961e-12 or 4e14 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-in 98.5%

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

      4. fma-define 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in x around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. +-commutative 82.6%

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

      3. associate-+l+ 82.6%

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

      4. +-commutative 82.6%

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

      5. *-commutative 82.6%

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

      6. associate-/l* 83.2%

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

      7. *-rgt-identity 83.2%

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

      8. distribute-lft-out 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around inf 82.6%

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

   9. Taylor expanded in x around inf 46.5%

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

       1. *-commutative 46.5%

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

   11. Simplified 46.5%

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

   if -5.39999999999999961e-12 < z < -1.56e-208 or 1.1500000000000001e-286 < z < 3.8000000000000002e-157

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 42.1%

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

   6. Taylor expanded in z around 0 42.0%

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

   if -1.56e-208 < z < 1.1500000000000001e-286 or 3.8000000000000002e-157 < z < 4e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 46.1%

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

   4. Taylor expanded in z around 0 41.9%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-286}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* z (+ y x)) (+ y x)))

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (y + x)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (y + x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * (y + x);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision], N[(y + x), $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. Add Preprocessing

   3. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.8%

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

      1. +-commutative 98.8%

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

   5. Simplified 98.8%

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

4. Final simplification 98.2%

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

Alternative 7: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.56 \cdot 10^{-146}:\\ \;\;\;\;\left(z + 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z + 1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 1.56e-146) (* (+ z 1.0) x) (* (+ z 1.0) y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.56e-146) {
		tmp = (z + 1.0) * x;
	} else {
		tmp = (z + 1.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= 1.56d-146) then
        tmp = (z + 1.0d0) * x
    else
        tmp = (z + 1.0d0) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.56e-146) {
		tmp = (z + 1.0) * x;
	} else {
		tmp = (z + 1.0) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 1.56e-146:
		tmp = (z + 1.0) * x
	else:
		tmp = (z + 1.0) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 1.56e-146)
		tmp = Float64(Float64(z + 1.0) * x);
	else
		tmp = Float64(Float64(z + 1.0) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.56e-146)
		tmp = (z + 1.0) * x;
	else
		tmp = (z + 1.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 1.56e-146], N[(N[(z + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(z + 1.0), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5599999999999999e-146

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.5%

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

   if 1.5599999999999999e-146 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.56 \cdot 10^{-146}:\\ \;\;\;\;\left(z + 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z + 1\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* (+ z 1.0) (+ y x)))

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (z + 1.0d0) * (y + x)
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (z + 1.0) * (y + x)

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(z + 1.0) * Float64(y + x))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (z + 1.0) * (y + x);
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(z + 1.0), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 9: 42.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y 8.8e-132) x y))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.8e-132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= 8.8d-132) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.8e-132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 8.8e-132:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 8.8e-132)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8.8e-132)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 8.8e-132], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 8.79999999999999963e-132

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-rgt-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 55.5%

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

   6. Taylor expanded in z around 0 28.4%

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

   if 8.79999999999999963e-132 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 71.4%

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

   4. Taylor expanded in z around 0 27.2%

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

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 25.9% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in y around 0 47.6%

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

6. Taylor expanded in z around 0 23.5%

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

7. Final simplification 23.5%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))