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

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

Alternatives: 7

Speedup: 1.0×

• 20.7% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-137} \lor \neg \left(x \leq -2.35 \cdot 10^{-163}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e-77)
   (* x (+ z 1.0))
   (if (or (<= x -1.9e-137) (not (<= x -2.35e-163))) (* y (+ z 1.0)) (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-77) {
		tmp = x * (z + 1.0);
	} else if ((x <= -1.9e-137) || !(x <= -2.35e-163)) {
		tmp = y * (z + 1.0);
	} 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 (x <= (-6.5d-77)) then
        tmp = x * (z + 1.0d0)
    else if ((x <= (-1.9d-137)) .or. (.not. (x <= (-2.35d-163)))) then
        tmp = y * (z + 1.0d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-77) {
		tmp = x * (z + 1.0);
	} else if ((x <= -1.9e-137) || !(x <= -2.35e-163)) {
		tmp = y * (z + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e-77:
		tmp = x * (z + 1.0)
	elif (x <= -1.9e-137) or not (x <= -2.35e-163):
		tmp = y * (z + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e-77)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((x <= -1.9e-137) || !(x <= -2.35e-163))
		tmp = Float64(y * Float64(z + 1.0));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.5e-77)
		tmp = x * (z + 1.0);
	elseif ((x <= -1.9e-137) || ~((x <= -2.35e-163)))
		tmp = y * (z + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e-77], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.9e-137], N[Not[LessEqual[x, -2.35e-163]], $MachinePrecision]], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4999999999999999e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.3%

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

   if -6.4999999999999999e-77 < x < -1.89999999999999999e-137 or -2.35e-163 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 65.6%

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

   if -1.89999999999999999e-137 < x < -2.35e-163

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.6%

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

      1. +-commutative 76.6%

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

   5. Simplified 76.6%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-137} \lor \neg \left(x \leq -2.35 \cdot 10^{-163}\right):\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 56:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+122)
   (* y z)
   (if (<= z -1.9e-5) (* x (+ z 1.0)) (if (<= z 56.0) (+ x y) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+122) {
		tmp = y * z;
	} else if (z <= -1.9e-5) {
		tmp = x * (z + 1.0);
	} else if (z <= 56.0) {
		tmp = x + y;
	} 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 <= (-4.5d+122)) then
        tmp = y * z
    else if (z <= (-1.9d-5)) then
        tmp = x * (z + 1.0d0)
    else if (z <= 56.0d0) then
        tmp = x + y
    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 <= -4.5e+122) {
		tmp = y * z;
	} else if (z <= -1.9e-5) {
		tmp = x * (z + 1.0);
	} else if (z <= 56.0) {
		tmp = x + y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+122:
		tmp = y * z
	elif z <= -1.9e-5:
		tmp = x * (z + 1.0)
	elif z <= 56.0:
		tmp = x + y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+122)
		tmp = Float64(y * z);
	elseif (z <= -1.9e-5)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= 56.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+122)
		tmp = y * z;
	elseif (z <= -1.9e-5)
		tmp = x * (z + 1.0);
	elseif (z <= 56.0)
		tmp = x + y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+122], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.9e-5], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 56.0], N[(x + y), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999997e122 or 56 < 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 54.2%

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

      1. +-commutative 54.2%

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

      2. distribute-lft-in 54.2%

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

      3. *-rgt-identity 54.2%

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

   5. Applied egg-rr 54.2%

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

   6. Taylor expanded in z around inf 53.1%

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

   if -4.49999999999999997e122 < z < -1.9000000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 33.5%

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

   if -1.9000000000000001e-5 < z < 56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 56:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.5× 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. Add Preprocessing

   3. Taylor expanded in z around inf 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

   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 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 97.9%

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

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 65\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 65.0))) (* y z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 65.0)) {
		tmp = y * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 65.0d0))) then
        tmp = y * z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 65.0)) {
		tmp = y * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 65.0):
		tmp = y * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 65.0))
		tmp = Float64(y * z);
	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 <= 65.0)))
		tmp = y * z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 65.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 65 < 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 56.5%

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

      1. +-commutative 56.5%

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

      2. distribute-lft-in 56.4%

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

      3. *-rgt-identity 56.4%

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

   5. Applied egg-rr 56.4%

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

   6. Taylor expanded in z around inf 53.6%

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

   if -1 < z < 65

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 65\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.21 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.21) (not (<= z 1.0))) (* y z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.21) || !(z <= 1.0)) {
		tmp = y * z;
	} 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 ((z <= (-0.21d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = y * z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.21) || !(z <= 1.0)) {
		tmp = y * z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.21) or not (z <= 1.0):
		tmp = y * z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.21) || !(z <= 1.0))
		tmp = Float64(y * z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.21) || ~((z <= 1.0)))
		tmp = y * z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.21], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y * z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if z < -0.209999999999999992 or 1 < 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 56.8%

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

      1. +-commutative 56.8%

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

      2. distribute-lft-in 56.8%

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

      3. *-rgt-identity 56.8%

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

   5. Applied egg-rr 56.8%

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

   6. Taylor expanded in z around inf 53.2%

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

   if -0.209999999999999992 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 55.6%

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

   4. Taylor expanded in z around 0 55.2%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.21 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 26.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 56.2%

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

4. Taylor expanded in z around 0 29.0%

   \[\leadsto \color{blue}{y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))