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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 7

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -1 \cdot 10^{+238}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -2000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 5000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+103}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -1e+238)
   (* y z)
   (if (<= (+ z 1.0) -5e+42)
     (* x z)
     (if (<= (+ z 1.0) -2000.0)
       (* y z)
       (if (<= (+ z 1.0) 5000000000000.0)
         (+ x y)
         (if (<= (+ z 1.0) 1e+103) (* y z) (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -1e+238) {
		tmp = y * z;
	} else if ((z + 1.0) <= -5e+42) {
		tmp = x * z;
	} else if ((z + 1.0) <= -2000.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 5000000000000.0) {
		tmp = x + y;
	} else if ((z + 1.0) <= 1e+103) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z + 1.0d0) <= (-1d+238)) then
        tmp = y * z
    else if ((z + 1.0d0) <= (-5d+42)) then
        tmp = x * z
    else if ((z + 1.0d0) <= (-2000.0d0)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 5000000000000.0d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 1d+103) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -1e+238) {
		tmp = y * z;
	} else if ((z + 1.0) <= -5e+42) {
		tmp = x * z;
	} else if ((z + 1.0) <= -2000.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 5000000000000.0) {
		tmp = x + y;
	} else if ((z + 1.0) <= 1e+103) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -1e+238:
		tmp = y * z
	elif (z + 1.0) <= -5e+42:
		tmp = x * z
	elif (z + 1.0) <= -2000.0:
		tmp = y * z
	elif (z + 1.0) <= 5000000000000.0:
		tmp = x + y
	elif (z + 1.0) <= 1e+103:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -1e+238)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= -5e+42)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= -2000.0)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 5000000000000.0)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 1e+103)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z + 1.0) <= -1e+238)
		tmp = y * z;
	elseif ((z + 1.0) <= -5e+42)
		tmp = x * z;
	elseif ((z + 1.0) <= -2000.0)
		tmp = y * z;
	elseif ((z + 1.0) <= 5000000000000.0)
		tmp = x + y;
	elseif ((z + 1.0) <= 1e+103)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -1e+238], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -5e+42], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -2000.0], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 5000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1e+103], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -1e238 or -5.00000000000000007e42 < (+.f64 z #s(literal 1 binary64)) < -2e3 or 5e12 < (+.f64 z #s(literal 1 binary64)) < 1e103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 54.3%

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

   4. Taylor expanded in z around inf 52.6%

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

      1. *-commutative 52.6%

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

   6. Simplified 52.6%

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

   if -1e238 < (+.f64 z #s(literal 1 binary64)) < -5.00000000000000007e42 or 1e103 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.7%

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

   4. Taylor expanded in z around inf 56.7%

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

   if -2e3 < (+.f64 z #s(literal 1 binary64)) < 5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.1%

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

      1. +-commutative 96.1%

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

   5. Simplified 96.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -1 \cdot 10^{+238}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -2000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 5000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+103}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+236}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+107}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.2e+236)
   (* y z)
   (if (<= z -1.5e+41)
     (* x z)
     (if (<= z -1.0)
       (* y z)
       (if (<= z 6.4e-215)
         x
         (if (<= z 1.0) y (if (<= z 3e+107) (* y z) (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.2e+236) {
		tmp = y * z;
	} else if (z <= -1.5e+41) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 6.4e-215) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = y;
	} else if (z <= 3e+107) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7.2d+236)) then
        tmp = y * z
    else if (z <= (-1.5d+41)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= 6.4d-215) then
        tmp = x
    else if (z <= 1.0d0) then
        tmp = y
    else if (z <= 3d+107) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.2e+236) {
		tmp = y * z;
	} else if (z <= -1.5e+41) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= 6.4e-215) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = y;
	} else if (z <= 3e+107) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.2e+236:
		tmp = y * z
	elif z <= -1.5e+41:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= 6.4e-215:
		tmp = x
	elif z <= 1.0:
		tmp = y
	elif z <= 3e+107:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.2e+236)
		tmp = Float64(y * z);
	elseif (z <= -1.5e+41)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= 6.4e-215)
		tmp = x;
	elseif (z <= 1.0)
		tmp = y;
	elseif (z <= 3e+107)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.2e+236)
		tmp = y * z;
	elseif (z <= -1.5e+41)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= 6.4e-215)
		tmp = x;
	elseif (z <= 1.0)
		tmp = y;
	elseif (z <= 3e+107)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.2e+236], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.5e+41], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 6.4e-215], x, If[LessEqual[z, 1.0], y, If[LessEqual[z, 3e+107], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.1999999999999999e236 or -1.4999999999999999e41 < z < -1 or 1 < z < 3.00000000000000023e107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 53.1%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

   6. Simplified 50.4%

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

   if -7.1999999999999999e236 < z < -1.4999999999999999e41 or 3.00000000000000023e107 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.7%

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

   4. Taylor expanded in z around inf 56.7%

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

   if -1 < z < 6.4000000000000003e-215

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 39.6%

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

   if 6.4000000000000003e-215 < 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 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around inf 48.2%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+236}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+107}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.7:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* x z) (if (<= z 1e-208) x (if (<= z 0.7) y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 1e-208) {
		tmp = x;
	} else if (z <= 0.7) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 1d-208) then
        tmp = x
    else if (z <= 0.7d0) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 1e-208) {
		tmp = x;
	} else if (z <= 0.7) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 1e-208:
		tmp = x
	elif z <= 0.7:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 1e-208)
		tmp = x;
	elseif (z <= 0.7)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= 1e-208)
		tmp = x;
	elseif (z <= 0.7)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 1e-208], x, If[LessEqual[z, 0.7], y, N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 0.69999999999999996 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.1%

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

   4. Taylor expanded in z around inf 56.0%

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

   if -1 < z < 1.0000000000000001e-208

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 39.6%

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

   if 1.0000000000000001e-208 < z < 0.69999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.4%

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

      1. +-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around inf 48.2%

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

Alternative 5: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-263) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-263) {
		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 + y) <= (-1d-263)) 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 + y) <= -1e-263) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-263:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-263)
		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 + y) <= -1e-263)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-263], 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 (+.f64 x y) < -1e-263

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 50.7%

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

   if -1e-263 < (+.f64 x 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 54.2%

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

Alternative 6: 32.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.4e-71) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e-71) {
		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 (y <= 1.4d-71) 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 (y <= 1.4e-71) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.4e-71:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.4e-71)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.4e-71)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.4e-71], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.4e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 51.0%

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

      1. +-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in y around 0 30.6%

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

   if 1.4e-71 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 52.8%

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

      1. +-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around inf 46.9%

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

Alternative 7: 26.5% 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. Add Preprocessing

3. Taylor expanded in z around 0 51.5%

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

   1. +-commutative 51.5%

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

5. Simplified 51.5%

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

6. Taylor expanded in y around 0 23.3%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024128 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))