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

Percentage Accurate: 100.0% → 100.0%

Time: 5.8s

Alternatives: 6

Speedup: 1.0×

• 21.3% 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: 47.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+181}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-75}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-265}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -5e+181)
   (+ x y)
   (if (<= (+ x y) -2e+79)
     (* x z)
     (if (<= (+ x y) -1e-75)
       (+ x y)
       (if (<= (+ x y) -1e-265) (* x z) (fma y z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -5e+181) {
		tmp = x + y;
	} else if ((x + y) <= -2e+79) {
		tmp = x * z;
	} else if ((x + y) <= -1e-75) {
		tmp = x + y;
	} else if ((x + y) <= -1e-265) {
		tmp = x * z;
	} else {
		tmp = fma(y, z, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -5e+181)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= -2e+79)
		tmp = Float64(x * z);
	elseif (Float64(x + y) <= -1e-75)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= -1e-265)
		tmp = Float64(x * z);
	else
		tmp = fma(y, z, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+181], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -2e+79], N[(x * z), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -1e-75], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -1e-265], N[(x * z), $MachinePrecision], N[(y * z + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5.0000000000000003e181 or -1.99999999999999993e79 < (+.f64 x y) < -9.9999999999999996e-76

   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 67.9

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

   5. Applied rewrites 67.9%

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

   if -5.0000000000000003e181 < (+.f64 x y) < -1.99999999999999993e79 or -9.9999999999999996e-76 < (+.f64 x y) < -9.99999999999999985e-266

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
   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 55.1

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 39.5%

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

   if -9.99999999999999985e-266 < (+.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

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 49.8

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

   5. Applied rewrites 49.8%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+181}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-75}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-265}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -5 \cdot 10^{+206}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -2:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq 1000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 5.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -5e+206)
   (* y z)
   (if (<= (+ z 1.0) -2.0)
     (* x z)
     (if (<= (+ z 1.0) 1000.0)
       (+ x y)
       (if (<= (+ z 1.0) 5.5e+181) (* y z) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -5e+206) {
		tmp = y * z;
	} else if ((z + 1.0) <= -2.0) {
		tmp = x * z;
	} else if ((z + 1.0) <= 1000.0) {
		tmp = x + y;
	} else if ((z + 1.0) <= 5.5e+181) {
		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) <= (-5d+206)) then
        tmp = y * z
    else if ((z + 1.0d0) <= (-2.0d0)) then
        tmp = x * z
    else if ((z + 1.0d0) <= 1000.0d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 5.5d+181) 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) <= -5e+206) {
		tmp = y * z;
	} else if ((z + 1.0) <= -2.0) {
		tmp = x * z;
	} else if ((z + 1.0) <= 1000.0) {
		tmp = x + y;
	} else if ((z + 1.0) <= 5.5e+181) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -5e+206:
		tmp = y * z
	elif (z + 1.0) <= -2.0:
		tmp = x * z
	elif (z + 1.0) <= 1000.0:
		tmp = x + y
	elif (z + 1.0) <= 5.5e+181:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -5e+206)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= -2.0)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= 1000.0)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 5.5e+181)
		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) <= -5e+206)
		tmp = y * z;
	elseif ((z + 1.0) <= -2.0)
		tmp = x * z;
	elseif ((z + 1.0) <= 1000.0)
		tmp = x + y;
	elseif ((z + 1.0) <= 5.5e+181)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -5e+206], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -2.0], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1000.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 5.5e+181], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -5.0000000000000002e206 or 1e3 < (+.f64 z #s(literal 1 binary64)) < 5.49999999999999991e181

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.3%

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

   if -5.0000000000000002e206 < (+.f64 z #s(literal 1 binary64)) < -2 or 5.49999999999999991e181 < (+.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

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
   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 52.9%

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

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

   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 96.5

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

   5. Applied rewrites 96.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -5 \cdot 10^{+206}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -2:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq 1000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 5.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -2:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -2.0) (* y z) (if (<= (+ z 1.0) 1000.0) (+ x y) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -2.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1000.0) {
		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 + 1.0d0) <= (-2.0d0)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 1000.0d0) 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 + 1.0) <= -2.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1000.0) {
		tmp = x + y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -2.0:
		tmp = y * z
	elif (z + 1.0) <= 1000.0:
		tmp = x + y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -2.0)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 1000.0)
		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 + 1.0) <= -2.0)
		tmp = y * z;
	elseif ((z + 1.0) <= 1000.0)
		tmp = x + y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -2.0], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1000.0], N[(x + y), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -2 or 1e3 < (+.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 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 46.6%

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

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

   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 96.5

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

   5. Applied rewrites 96.5%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -2:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-265) (fma z x x) (fma y z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-265) {
		tmp = fma(z, x, x);
	} else {
		tmp = fma(y, z, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-265)
		tmp = fma(z, x, x);
	else
		tmp = fma(y, z, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-265], N[(z * x + x), $MachinePrecision], N[(y * z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999985e-266

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
   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 50.6

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

   5. Applied rewrites 50.6%

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

   if -9.99999999999999985e-266 < (+.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

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 49.8

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

   5. Applied rewrites 49.8%

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

Alternative 6: 50.3% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + y), $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 52.0

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

5. Applied rewrites 52.0%

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

6. Final simplification 52.0%

   \[\leadsto x + y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024238 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))