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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 9

Speedup: 1.0×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+175}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+151}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-205}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+79}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.2e+175)
   (* x z)
   (if (<= z -4.9e+151)
     (* y z)
     (if (<= z -1.0)
       (* x z)
       (if (<= z 2.95e-205)
         y
         (if (<= z 0.22)
           x
           (if (<= z 1.05e+46)
             (* y z)
             (if (<= z 3.8e+79) (* x z) (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.2e+175) {
		tmp = x * z;
	} else if (z <= -4.9e+151) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 2.95e-205) {
		tmp = y;
	} else if (z <= 0.22) {
		tmp = x;
	} else if (z <= 1.05e+46) {
		tmp = y * z;
	} else if (z <= 3.8e+79) {
		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 (z <= (-7.2d+175)) then
        tmp = x * z
    else if (z <= (-4.9d+151)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 2.95d-205) then
        tmp = y
    else if (z <= 0.22d0) then
        tmp = x
    else if (z <= 1.05d+46) then
        tmp = y * z
    else if (z <= 3.8d+79) 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 (z <= -7.2e+175) {
		tmp = x * z;
	} else if (z <= -4.9e+151) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 2.95e-205) {
		tmp = y;
	} else if (z <= 0.22) {
		tmp = x;
	} else if (z <= 1.05e+46) {
		tmp = y * z;
	} else if (z <= 3.8e+79) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.2e+175:
		tmp = x * z
	elif z <= -4.9e+151:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 2.95e-205:
		tmp = y
	elif z <= 0.22:
		tmp = x
	elif z <= 1.05e+46:
		tmp = y * z
	elif z <= 3.8e+79:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.2e+175)
		tmp = Float64(x * z);
	elseif (z <= -4.9e+151)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 2.95e-205)
		tmp = y;
	elseif (z <= 0.22)
		tmp = x;
	elseif (z <= 1.05e+46)
		tmp = Float64(y * z);
	elseif (z <= 3.8e+79)
		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 (z <= -7.2e+175)
		tmp = x * z;
	elseif (z <= -4.9e+151)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 2.95e-205)
		tmp = y;
	elseif (z <= 0.22)
		tmp = x;
	elseif (z <= 1.05e+46)
		tmp = y * z;
	elseif (z <= 3.8e+79)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.2e+175], N[(x * z), $MachinePrecision], If[LessEqual[z, -4.9e+151], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.95e-205], y, If[LessEqual[z, 0.22], x, If[LessEqual[z, 1.05e+46], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.8e+79], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000067e175 or -4.8999999999999999e151 < z < -1 or 1.05e46 < z < 3.8000000000000002e79

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 59.6%

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

   5. Taylor expanded in z around inf 58.3%

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

   if -7.20000000000000067e175 < z < -4.8999999999999999e151 or 0.220000000000000001 < z < 1.05e46 or 3.8000000000000002e79 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 53.6%

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

      1. *-commutative 53.6%

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

      2. flip-+ 46.0%

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

      3. associate-*l/ 43.2%

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

      4. metadata-eval 43.2%

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

   4. Applied egg-rr 43.2%

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

   5. Taylor expanded in z around inf 41.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot {z}^{2}\right)}}{1 - z} \]
   6. Step-by-step derivation

      1. unpow2 41.7%

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

      2. associate-*r* 41.7%

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

      3. mul-1-neg 41.7%

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

   7. Simplified 41.7%

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

   8. Taylor expanded in z around inf 52.2%

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

   if -1 < z < 2.94999999999999987e-205

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 55.1%

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

   3. Taylor expanded in z around 0 55.1%

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

   if 2.94999999999999987e-205 < z < 0.220000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 53.0%

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

   3. Taylor expanded in z around 0 53.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+175}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+151}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-205}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+79}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+179}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+150}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -0.00024:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.062:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ z 1.0))))
   (if (<= z -6e+179)
     (* x z)
     (if (<= z -2.75e+150)
       (* y z)
       (if (<= z -3.6e+46)
         (* x z)
         (if (<= z -0.00024)
           t_0
           (if (<= z 0.062)
             (+ x y)
             (if (<= z 1.4e+38) t_0 (if (<= z 5e+82) (* x z) (* y z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z + 1.0);
	double tmp;
	if (z <= -6e+179) {
		tmp = x * z;
	} else if (z <= -2.75e+150) {
		tmp = y * z;
	} else if (z <= -3.6e+46) {
		tmp = x * z;
	} else if (z <= -0.00024) {
		tmp = t_0;
	} else if (z <= 0.062) {
		tmp = x + y;
	} else if (z <= 1.4e+38) {
		tmp = t_0;
	} else if (z <= 5e+82) {
		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) :: t_0
    real(8) :: tmp
    t_0 = y * (z + 1.0d0)
    if (z <= (-6d+179)) then
        tmp = x * z
    else if (z <= (-2.75d+150)) then
        tmp = y * z
    else if (z <= (-3.6d+46)) then
        tmp = x * z
    else if (z <= (-0.00024d0)) then
        tmp = t_0
    else if (z <= 0.062d0) then
        tmp = x + y
    else if (z <= 1.4d+38) then
        tmp = t_0
    else if (z <= 5d+82) 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 t_0 = y * (z + 1.0);
	double tmp;
	if (z <= -6e+179) {
		tmp = x * z;
	} else if (z <= -2.75e+150) {
		tmp = y * z;
	} else if (z <= -3.6e+46) {
		tmp = x * z;
	} else if (z <= -0.00024) {
		tmp = t_0;
	} else if (z <= 0.062) {
		tmp = x + y;
	} else if (z <= 1.4e+38) {
		tmp = t_0;
	} else if (z <= 5e+82) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z + 1.0)
	tmp = 0
	if z <= -6e+179:
		tmp = x * z
	elif z <= -2.75e+150:
		tmp = y * z
	elif z <= -3.6e+46:
		tmp = x * z
	elif z <= -0.00024:
		tmp = t_0
	elif z <= 0.062:
		tmp = x + y
	elif z <= 1.4e+38:
		tmp = t_0
	elif z <= 5e+82:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z + 1.0))
	tmp = 0.0
	if (z <= -6e+179)
		tmp = Float64(x * z);
	elseif (z <= -2.75e+150)
		tmp = Float64(y * z);
	elseif (z <= -3.6e+46)
		tmp = Float64(x * z);
	elseif (z <= -0.00024)
		tmp = t_0;
	elseif (z <= 0.062)
		tmp = Float64(x + y);
	elseif (z <= 1.4e+38)
		tmp = t_0;
	elseif (z <= 5e+82)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z + 1.0);
	tmp = 0.0;
	if (z <= -6e+179)
		tmp = x * z;
	elseif (z <= -2.75e+150)
		tmp = y * z;
	elseif (z <= -3.6e+46)
		tmp = x * z;
	elseif (z <= -0.00024)
		tmp = t_0;
	elseif (z <= 0.062)
		tmp = x + y;
	elseif (z <= 1.4e+38)
		tmp = t_0;
	elseif (z <= 5e+82)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+179], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.75e+150], N[(y * z), $MachinePrecision], If[LessEqual[z, -3.6e+46], N[(x * z), $MachinePrecision], If[LessEqual[z, -0.00024], t$95$0, If[LessEqual[z, 0.062], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.4e+38], t$95$0, If[LessEqual[z, 5e+82], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999996e179 or -2.75000000000000008e150 < z < -3.5999999999999999e46 or 1.4e38 < z < 5.00000000000000015e82

   1. Initial program 100.0%

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

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 59.2%

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

   5. Taylor expanded in z around inf 59.2%

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

   if -5.9999999999999996e179 < z < -2.75000000000000008e150 or 5.00000000000000015e82 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

      2. flip-+ 46.7%

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

      3. associate-*l/ 45.0%

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

      4. metadata-eval 45.0%

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

   4. Applied egg-rr 45.0%

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

   5. Taylor expanded in z around inf 45.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot {z}^{2}\right)}}{1 - z} \]
   6. Step-by-step derivation

      1. unpow2 45.0%

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

      2. associate-*r* 45.0%

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

      3. mul-1-neg 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in z around inf 55.6%

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

   if -3.5999999999999999e46 < z < -2.40000000000000006e-4 or 0.062 < z < 1.4e38

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 41.3%

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

   if -2.40000000000000006e-4 < z < 0.062

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+179}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+150}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -0.00024:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 0.062:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+178}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 29:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+178)
   (* x z)
   (if (<= z -2.75e+156)
     (* y z)
     (if (<= z -1.0)
       (* x z)
       (if (<= z 29.0)
         (+ x y)
         (if (<= z 1.15e+44) (* y z) (if (<= z 2.3e+82) (* x z) (* y z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+178) {
		tmp = x * z;
	} else if (z <= -2.75e+156) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 29.0) {
		tmp = x + y;
	} else if (z <= 1.15e+44) {
		tmp = y * z;
	} else if (z <= 2.3e+82) {
		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 (z <= (-9d+178)) then
        tmp = x * z
    else if (z <= (-2.75d+156)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 29.0d0) then
        tmp = x + y
    else if (z <= 1.15d+44) then
        tmp = y * z
    else if (z <= 2.3d+82) 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 (z <= -9e+178) {
		tmp = x * z;
	} else if (z <= -2.75e+156) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 29.0) {
		tmp = x + y;
	} else if (z <= 1.15e+44) {
		tmp = y * z;
	} else if (z <= 2.3e+82) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+178:
		tmp = x * z
	elif z <= -2.75e+156:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 29.0:
		tmp = x + y
	elif z <= 1.15e+44:
		tmp = y * z
	elif z <= 2.3e+82:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+178)
		tmp = Float64(x * z);
	elseif (z <= -2.75e+156)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 29.0)
		tmp = Float64(x + y);
	elseif (z <= 1.15e+44)
		tmp = Float64(y * z);
	elseif (z <= 2.3e+82)
		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 (z <= -9e+178)
		tmp = x * z;
	elseif (z <= -2.75e+156)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 29.0)
		tmp = x + y;
	elseif (z <= 1.15e+44)
		tmp = y * z;
	elseif (z <= 2.3e+82)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+178], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.75e+156], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 29.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.15e+44], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.3e+82], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999994e178 or -2.7500000000000001e156 < z < -1 or 1.15000000000000002e44 < z < 2.29999999999999988e82

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 59.6%

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

   5. Taylor expanded in z around inf 58.3%

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

   if -8.9999999999999994e178 < z < -2.7500000000000001e156 or 29 < z < 1.15000000000000002e44 or 2.29999999999999988e82 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 52.9%

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

      1. *-commutative 52.9%

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

      2. flip-+ 45.2%

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

      3. associate-*l/ 42.3%

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

      4. metadata-eval 42.3%

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

   4. Applied egg-rr 42.3%

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

   5. Taylor expanded in z around inf 42.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot {z}^{2}\right)}}{1 - z} \]
   6. Step-by-step derivation

      1. unpow2 42.3%

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

      2. associate-*r* 42.3%

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

      3. mul-1-neg 42.3%

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

   7. Simplified 42.3%

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

   8. Taylor expanded in z around inf 52.8%

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

   if -1 < z < 29

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+178}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 29:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+82}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-59} \lor \neg \left(x \leq -1.15 \cdot 10^{-88}\right) \land x \leq -2.3 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.6e-59) (and (not (<= x -1.15e-88)) (<= x -2.3e-117)))
   (* x (+ z 1.0))
   (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.6e-59) || (!(x <= -1.15e-88) && (x <= -2.3e-117))) {
		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 ((x <= (-2.6d-59)) .or. (.not. (x <= (-1.15d-88))) .and. (x <= (-2.3d-117))) 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 ((x <= -2.6e-59) || (!(x <= -1.15e-88) && (x <= -2.3e-117))) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.6e-59) or (not (x <= -1.15e-88) and (x <= -2.3e-117)):
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.6e-59) || (!(x <= -1.15e-88) && (x <= -2.3e-117)))
		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 ((x <= -2.6e-59) || (~((x <= -1.15e-88)) && (x <= -2.3e-117)))
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.6e-59], And[N[Not[LessEqual[x, -1.15e-88]], $MachinePrecision], LessEqual[x, -2.3e-117]]], 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 x < -2.59999999999999998e-59 or -1.14999999999999993e-88 < x < -2.29999999999999994e-117

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 77.0%

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

   if -2.59999999999999998e-59 < x < -1.14999999999999993e-88 or -2.29999999999999994e-117 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 62.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-59} \lor \neg \left(x \leq -1.15 \cdot 10^{-88}\right) \land x \leq -2.3 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 6: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e-10)
   (* y z)
   (if (<= z 3.15e-204) y (if (<= z 0.36) x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-10) {
		tmp = y * z;
	} else if (z <= 3.15e-204) {
		tmp = y;
	} else if (z <= 0.36) {
		tmp = x;
	} 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 (z <= (-7.8d-10)) then
        tmp = y * z
    else if (z <= 3.15d-204) then
        tmp = y
    else if (z <= 0.36d0) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-10) {
		tmp = y * z;
	} else if (z <= 3.15e-204) {
		tmp = y;
	} else if (z <= 0.36) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e-10:
		tmp = y * z
	elif z <= 3.15e-204:
		tmp = y
	elif z <= 0.36:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e-10)
		tmp = Float64(y * z);
	elseif (z <= 3.15e-204)
		tmp = y;
	elseif (z <= 0.36)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.8e-10)
		tmp = y * z;
	elseif (z <= 3.15e-204)
		tmp = y;
	elseif (z <= 0.36)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e-10], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.15e-204], y, If[LessEqual[z, 0.36], x, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.7999999999999999e-10 or 0.35999999999999999 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 48.4%

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

      1. *-commutative 48.4%

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

      2. flip-+ 45.2%

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

      3. associate-*l/ 40.5%

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

      4. metadata-eval 40.5%

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

   4. Applied egg-rr 40.5%

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

   5. Taylor expanded in z around inf 39.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot {z}^{2}\right)}}{1 - z} \]
   6. Step-by-step derivation

      1. unpow2 39.9%

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

      2. associate-*r* 39.9%

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

      3. mul-1-neg 39.9%

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

   7. Simplified 39.9%

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

   8. Taylor expanded in z around inf 47.9%

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

   if -7.7999999999999999e-10 < z < 3.14999999999999996e-204

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 56.8%

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

   3. Taylor expanded in z around 0 56.8%

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

   if 3.14999999999999996e-204 < z < 0.35999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 53.0%

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

   3. Taylor expanded in z around 0 53.0%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 98.0% 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 99.0%

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

   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 96.5%

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

4. Final simplification 98.0%

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

Alternative 8: 31.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.8e-129) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-129) {
		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 (x <= (-1.8d-129)) 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 (x <= -1.8e-129) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.8e-129:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e-129)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.8e-129)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e-129], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-129

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 70.1%

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

   3. Taylor expanded in z around 0 28.1%

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

   if -1.8e-129 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 60.9%

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

   3. Taylor expanded in z around 0 28.5%

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

4. Final simplification 28.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 27.0% 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%

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

2. Taylor expanded in x around inf 52.8%

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

3. Taylor expanded in z around 0 21.0%

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

4. Final simplification 21.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))