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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 6

Speedup: 1.0×

• 20.6% 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

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

FPCore

(FPCore (x y z) :precision binary64 (* (+ 1.0 z) (+ y x)))

C

double code(double x, double y, double z) {
	return (1.0 + z) * (y + 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 = (1.0d0 + z) * (y + x)
end function

Java

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

Python

def code(x, y, z):
	return (1.0 + z) * (y + x)

Julia

function code(x, y, z)
	return Float64(Float64(1.0 + z) * Float64(y + x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 + z) * (y + x);
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 + z), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 47.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y + x \leq 10^{+54}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y + x \leq 2 \cdot 10^{+122}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y + x \leq 5 \cdot 10^{+258}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ y x) -5e-251)
   (fma z x x)
   (if (<= (+ y x) 1e+54)
     (+ y x)
     (if (<= (+ y x) 2e+122)
       (* z y)
       (if (<= (+ y x) 5e+258) (+ y x) (* z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y + x) <= -5e-251) {
		tmp = fma(z, x, x);
	} else if ((y + x) <= 1e+54) {
		tmp = y + x;
	} else if ((y + x) <= 2e+122) {
		tmp = z * y;
	} else if ((y + x) <= 5e+258) {
		tmp = y + x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y + x) <= -5e-251)
		tmp = fma(z, x, x);
	elseif (Float64(y + x) <= 1e+54)
		tmp = Float64(y + x);
	elseif (Float64(y + x) <= 2e+122)
		tmp = Float64(z * y);
	elseif (Float64(y + x) <= 5e+258)
		tmp = Float64(y + x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y + x), $MachinePrecision], -5e-251], N[(z * x + x), $MachinePrecision], If[LessEqual[N[(y + x), $MachinePrecision], 1e+54], N[(y + x), $MachinePrecision], If[LessEqual[N[(y + x), $MachinePrecision], 2e+122], N[(z * y), $MachinePrecision], If[LessEqual[N[(y + x), $MachinePrecision], 5e+258], N[(y + x), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5.0000000000000003e-251

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 51.9

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

   5. Applied rewrites 51.9%

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

   if -5.0000000000000003e-251 < (+.f64 x y) < 1.0000000000000001e54 or 2.00000000000000003e122 < (+.f64 x y) < 5e258

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if 1.0000000000000001e54 < (+.f64 x y) < 2.00000000000000003e122 or 5e258 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.4%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y + x \leq 10^{+54}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y + x \leq 2 \cdot 10^{+122}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y + x \leq 5 \cdot 10^{+258}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 + z \leq -1 \cdot 10^{+128}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;1 + z \leq -500000000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;1 + z \leq 200000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ 1.0 z) -1e+128)
   (* z x)
   (if (<= (+ 1.0 z) -500000000.0)
     (* z y)
     (if (<= (+ 1.0 z) 200000000.0) (+ y x) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 + z) <= -1e+128) {
		tmp = z * x;
	} else if ((1.0 + z) <= -500000000.0) {
		tmp = z * y;
	} else if ((1.0 + z) <= 200000000.0) {
		tmp = y + x;
	} else {
		tmp = z * x;
	}
	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 ((1.0d0 + z) <= (-1d+128)) then
        tmp = z * x
    else if ((1.0d0 + z) <= (-500000000.0d0)) then
        tmp = z * y
    else if ((1.0d0 + z) <= 200000000.0d0) then
        tmp = y + x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 + z) <= -1e+128) {
		tmp = z * x;
	} else if ((1.0 + z) <= -500000000.0) {
		tmp = z * y;
	} else if ((1.0 + z) <= 200000000.0) {
		tmp = y + x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 + z) <= -1e+128:
		tmp = z * x
	elif (1.0 + z) <= -500000000.0:
		tmp = z * y
	elif (1.0 + z) <= 200000000.0:
		tmp = y + x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 + z) <= -1e+128)
		tmp = Float64(z * x);
	elseif (Float64(1.0 + z) <= -500000000.0)
		tmp = Float64(z * y);
	elseif (Float64(1.0 + z) <= 200000000.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 + z) <= -1e+128)
		tmp = z * x;
	elseif ((1.0 + z) <= -500000000.0)
		tmp = z * y;
	elseif ((1.0 + z) <= 200000000.0)
		tmp = y + x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 + z), $MachinePrecision], -1e+128], N[(z * x), $MachinePrecision], If[LessEqual[N[(1.0 + z), $MachinePrecision], -500000000.0], N[(z * y), $MachinePrecision], If[LessEqual[N[(1.0 + z), $MachinePrecision], 200000000.0], N[(y + x), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -1.0000000000000001e128 or 2e8 < (+.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 y around 0

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 55.9

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.3%

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

   if -1.0000000000000001e128 < (+.f64 z #s(literal 1 binary64)) < -5e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.0%

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

   if -5e8 < (+.f64 z #s(literal 1 binary64)) < 2e8

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 97.4

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

   5. Applied rewrites 97.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + z \leq -1 \cdot 10^{+128}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;1 + z \leq -500000000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;1 + z \leq 200000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 + z \leq -500000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;1 + z \leq 200000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ 1.0 z) -500000000.0)
   (* z x)
   (if (<= (+ 1.0 z) 200000000.0) (+ y x) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 + z) <= -500000000.0) {
		tmp = z * x;
	} else if ((1.0 + z) <= 200000000.0) {
		tmp = y + x;
	} else {
		tmp = z * x;
	}
	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 ((1.0d0 + z) <= (-500000000.0d0)) then
        tmp = z * x
    else if ((1.0d0 + z) <= 200000000.0d0) then
        tmp = y + x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 + z) <= -500000000.0) {
		tmp = z * x;
	} else if ((1.0 + z) <= 200000000.0) {
		tmp = y + x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 + z) <= -500000000.0:
		tmp = z * x
	elif (1.0 + z) <= 200000000.0:
		tmp = y + x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 + z) <= -500000000.0)
		tmp = Float64(z * x);
	elseif (Float64(1.0 + z) <= 200000000.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 + z) <= -500000000.0)
		tmp = z * x;
	elseif ((1.0 + z) <= 200000000.0)
		tmp = y + x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 + z), $MachinePrecision], -500000000.0], N[(z * x), $MachinePrecision], If[LessEqual[N[(1.0 + z), $MachinePrecision], 200000000.0], N[(y + x), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -5e8 or 2e8 < (+.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 y around 0

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 54.5

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

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 53.9%

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

   if -5e8 < (+.f64 z #s(literal 1 binary64)) < 2e8

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 97.4

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

   5. Applied rewrites 97.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + z \leq -500000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;1 + z \leq 200000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ y x) -5e-251) (fma z x x) (fma z y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y + x) <= -5e-251) {
		tmp = fma(z, x, x);
	} else {
		tmp = fma(z, y, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y + x) <= -5e-251)
		tmp = fma(z, x, x);
	else
		tmp = fma(z, y, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y + x), $MachinePrecision], -5e-251], N[(z * x + x), $MachinePrecision], N[(z * y + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000003e-251

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 51.9

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

   5. Applied rewrites 51.9%

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

   if -5.0000000000000003e-251 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

      4. lower-fma.f64 49.9

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

   5. Applied rewrites 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.3% accurate, 3.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return y + 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 = y + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y + x), $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 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 50.9

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

5. Applied rewrites 50.9%

   \[\leadsto \color{blue}{y + x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024244 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))