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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

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. Final simplification 100.0%

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

Alternative 2: 74.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 24:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.25e+125)
   (* y z)
   (if (<= z -9.5e+49)
     (* x z)
     (if (<= z -2.1e+30)
       (* y z)
       (if (<= z -1.0) (* x z) (if (<= z 24.0) (+ x y) (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.25e+125) {
		tmp = y * z;
	} else if (z <= -9.5e+49) {
		tmp = x * z;
	} else if (z <= -2.1e+30) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 24.0) {
		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 <= (-1.25d+125)) then
        tmp = y * z
    else if (z <= (-9.5d+49)) then
        tmp = x * z
    else if (z <= (-2.1d+30)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 24.0d0) 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 <= -1.25e+125) {
		tmp = y * z;
	} else if (z <= -9.5e+49) {
		tmp = x * z;
	} else if (z <= -2.1e+30) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 24.0) {
		tmp = x + y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.25e+125:
		tmp = y * z
	elif z <= -9.5e+49:
		tmp = x * z
	elif z <= -2.1e+30:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 24.0:
		tmp = x + y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.25e+125)
		tmp = Float64(y * z);
	elseif (z <= -9.5e+49)
		tmp = Float64(x * z);
	elseif (z <= -2.1e+30)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 24.0)
		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 <= -1.25e+125)
		tmp = y * z;
	elseif (z <= -9.5e+49)
		tmp = x * z;
	elseif (z <= -2.1e+30)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 24.0)
		tmp = x + y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.25e+125], N[(y * z), $MachinePrecision], If[LessEqual[z, -9.5e+49], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.1e+30], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 24.0], N[(x + y), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999991e125 or -9.49999999999999969e49 < z < -2.1e30 or 24 < 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 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 57.9%

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

   if -1.24999999999999991e125 < z < -9.49999999999999969e49 or -2.1e30 < 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 inf 93.9%

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

      1. +-commutative 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in y around 0 39.3%

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

   if -1 < z < 24

   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 3 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 24:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+128}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+50}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -0.105:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 80:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+128)
   (* y z)
   (if (<= z -1.16e+50)
     (* x z)
     (if (<= z -1.95e+30)
       (* y z)
       (if (<= z -0.105) (* x (+ z 1.0)) (if (<= z 80.0) (+ x y) (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+128) {
		tmp = y * z;
	} else if (z <= -1.16e+50) {
		tmp = x * z;
	} else if (z <= -1.95e+30) {
		tmp = y * z;
	} else if (z <= -0.105) {
		tmp = x * (z + 1.0);
	} else if (z <= 80.0) {
		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 <= (-1.8d+128)) then
        tmp = y * z
    else if (z <= (-1.16d+50)) then
        tmp = x * z
    else if (z <= (-1.95d+30)) then
        tmp = y * z
    else if (z <= (-0.105d0)) then
        tmp = x * (z + 1.0d0)
    else if (z <= 80.0d0) 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 <= -1.8e+128) {
		tmp = y * z;
	} else if (z <= -1.16e+50) {
		tmp = x * z;
	} else if (z <= -1.95e+30) {
		tmp = y * z;
	} else if (z <= -0.105) {
		tmp = x * (z + 1.0);
	} else if (z <= 80.0) {
		tmp = x + y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+128:
		tmp = y * z
	elif z <= -1.16e+50:
		tmp = x * z
	elif z <= -1.95e+30:
		tmp = y * z
	elif z <= -0.105:
		tmp = x * (z + 1.0)
	elif z <= 80.0:
		tmp = x + y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+128)
		tmp = Float64(y * z);
	elseif (z <= -1.16e+50)
		tmp = Float64(x * z);
	elseif (z <= -1.95e+30)
		tmp = Float64(y * z);
	elseif (z <= -0.105)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= 80.0)
		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 <= -1.8e+128)
		tmp = y * z;
	elseif (z <= -1.16e+50)
		tmp = x * z;
	elseif (z <= -1.95e+30)
		tmp = y * z;
	elseif (z <= -0.105)
		tmp = x * (z + 1.0);
	elseif (z <= 80.0)
		tmp = x + y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+128], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.16e+50], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.95e+30], N[(y * z), $MachinePrecision], If[LessEqual[z, -0.105], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 80.0], N[(x + y), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.80000000000000014e128 or -1.16e50 < z < -1.95000000000000005e30 or 80 < 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 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 57.9%

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

   if -1.80000000000000014e128 < z < -1.16e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 33.5%

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

   if -1.95000000000000005e30 < z < -0.104999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.7%

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

   if -0.104999999999999996 < z < 80

   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 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+128}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+50}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -0.105:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 80:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.6% 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 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   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 98.1%

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

Alternative 5: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e-127) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-127) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.9d-127)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-127) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e-127:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e-127)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.9e-127)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e-127], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000001e-127

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.1%

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

   if -1.90000000000000001e-127 < 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 63.8%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 32.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -3.5e-122) (* x z) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-122) {
		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 (x <= (-3.5d-122)) 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 (x <= -3.5e-122) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e-122:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e-122)
		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 (x <= -3.5e-122)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e-122], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000001e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. +-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around 0 32.2%

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

   if -3.5000000000000001e-122 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. +-commutative 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in y around inf 33.0%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 26.9% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf 43.8%

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

   1. +-commutative 43.8%

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

5. Simplified 43.8%

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

6. Taylor expanded in y around 0 22.9%

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

7. Final simplification 22.9%

   \[\leadsto x \cdot z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))