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

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 11

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, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. distribute-rgt-in N/A

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

   2. *-lft-identity N/A

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

   3. +-commutative N/A

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

   4. associate-+r+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(x + y\right) + y\right), \color{blue}{x}\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(x + y\right)\right), y\right), x\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\left(x + y\right) \cdot z\right), y\right), x\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x + y\right), z\right), y\right), x\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), y\right), x\right) \]

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -50000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq 1.01:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+142}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -50000.0)
   (* x z)
   (if (<= (+ z 1.0) 1.01)
     (+ x y)
     (if (<= (+ z 1.0) 1e+142) (* y (+ z 1.0)) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -50000.0) {
		tmp = x * z;
	} else if ((z + 1.0) <= 1.01) {
		tmp = x + y;
	} else if ((z + 1.0) <= 1e+142) {
		tmp = y * (z + 1.0);
	} 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) <= (-50000.0d0)) then
        tmp = x * z
    else if ((z + 1.0d0) <= 1.01d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 1d+142) then
        tmp = y * (z + 1.0d0)
    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) <= -50000.0) {
		tmp = x * z;
	} else if ((z + 1.0) <= 1.01) {
		tmp = x + y;
	} else if ((z + 1.0) <= 1e+142) {
		tmp = y * (z + 1.0);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -50000.0:
		tmp = x * z
	elif (z + 1.0) <= 1.01:
		tmp = x + y
	elif (z + 1.0) <= 1e+142:
		tmp = y * (z + 1.0)
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -50000.0)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= 1.01)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 1e+142)
		tmp = Float64(y * Float64(z + 1.0));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z + 1.0) <= -50000.0)
		tmp = x * z;
	elseif ((z + 1.0) <= 1.01)
		tmp = x + y;
	elseif ((z + 1.0) <= 1e+142)
		tmp = y * (z + 1.0);
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -50000.0], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.01], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1e+142], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -5e4 or 1.00000000000000005e142 < (+.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

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 61.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 61.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 59.7%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 59.7%

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

   if -5e4 < (+.f64 z #s(literal 1 binary64)) < 1.01000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 98.0%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 98.0%

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

   if 1.01000000000000001 < (+.f64 z #s(literal 1 binary64)) < 1.00000000000000005e142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 35.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -50000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq 1.01:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 10^{+142}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.325:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* x z) (if (<= z -8.5e-246) x (if (<= z 0.325) y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -8.5e-246) {
		tmp = x;
	} else if (z <= 0.325) {
		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 <= (-8.5d-246)) then
        tmp = x
    else if (z <= 0.325d0) 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 <= -8.5e-246) {
		tmp = x;
	} else if (z <= 0.325) {
		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 <= -8.5e-246:
		tmp = x
	elif z <= 0.325:
		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 <= -8.5e-246)
		tmp = x;
	elseif (z <= 0.325)
		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 <= -8.5e-246)
		tmp = x;
	elseif (z <= 0.325)
		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, -8.5e-246], x, If[LessEqual[z, 0.325], y, N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 0.325000000000000011 < 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

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 63.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 60.9%

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

   if -1 < z < -8.4999999999999998e-246

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 52.6%

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

   if -8.4999999999999998e-246 < z < 0.325000000000000011

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 96.7%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 96.7%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 62.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.325:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9000:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* y z) (if (<= z -4.1e-246) x (if (<= z 9000.0) y (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -4.1e-246) {
		tmp = x;
	} else if (z <= 9000.0) {
		tmp = 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)) then
        tmp = y * z
    else if (z <= (-4.1d-246)) then
        tmp = x
    else if (z <= 9000.0d0) then
        tmp = 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) {
		tmp = y * z;
	} else if (z <= -4.1e-246) {
		tmp = x;
	} else if (z <= 9000.0) {
		tmp = y;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = y * z
	elif z <= -4.1e-246:
		tmp = x
	elif z <= 9000.0:
		tmp = y
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= -4.1e-246)
		tmp = x;
	elseif (z <= 9000.0)
		tmp = 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)
		tmp = y * z;
	elseif (z <= -4.1e-246)
		tmp = x;
	elseif (z <= 9000.0)
		tmp = y;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -4.1e-246], x, If[LessEqual[z, 9000.0], y, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 9e3 < 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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{z}\right) \]
   4. Step-by-step derivation

   5. Simplified 97.8%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 44.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   8. Simplified 44.5%

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

   if -1 < z < -4.09999999999999986e-246

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 52.6%

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

   if -4.09999999999999986e-246 < z < 9e3

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 95.5%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 61.4%

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

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 370000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* x z) (if (<= z 370000000.0) (+ x y) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 370000000.0) {
		tmp = x + 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 <= 370000000.0d0) then
        tmp = x + 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 <= 370000000.0) {
		tmp = x + y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 370000000.0:
		tmp = x + 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 <= 370000000.0)
		tmp = Float64(x + 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 <= 370000000.0)
		tmp = x + 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, 370000000.0], N[(x + y), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3.7e8 < 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

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 62.7%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.6%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 61.6%

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

   if -1 < z < 3.7e8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 94.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 370000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-220) (+ x (* x z)) (+ y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-220) {
		tmp = x + (x * z);
	} else {
		tmp = y + (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 + y) <= (-1d-220)) then
        tmp = x + (x * z)
    else
        tmp = y + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-220) {
		tmp = x + (x * z);
	} else {
		tmp = y + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-220:
		tmp = x + (x * z)
	else:
		tmp = y + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-220)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(y + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-220)
		tmp = x + (x * z);
	else
		tmp = y + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-220], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999992e-221

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. distribute-rgt-in N/A

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

      2. *-lft-identity N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(x + y\right) + y\right), \color{blue}{x}\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \left(x + y\right)\right), y\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\left(x + y\right) \cdot z\right), y\right), x\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x + y\right), z\right), y\right), x\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), y\right), x\right) \]

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot z\right)}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot x\right), x\right) \]

      2. *-lowering-*.f64 61.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), x\right) \]

   7. Simplified 61.2%

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

   if -9.99999999999999992e-221 < (+.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

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.9%

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

         \[\leadsto y \cdot z + y \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, z\right), y\right) \]

   7. Applied egg-rr 57.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-220) (* x (+ z 1.0)) (+ y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-220) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (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 + y) <= (-1d-220)) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-220) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -1e-220:
		tmp = x * (z + 1.0)
	else:
		tmp = y + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-220)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x + y) <= -1e-220)
		tmp = x * (z + 1.0);
	else
		tmp = y + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-220], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.99999999999999992e-221

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   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

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 61.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 61.2%

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

   if -9.99999999999999992e-221 < (+.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

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.9%

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

         \[\leadsto y \cdot z + y \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, z\right), y\right) \]

   7. Applied egg-rr 57.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-220) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-220) {
		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-220)) 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-220) {
		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-220:
		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-220)
		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-220)
		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-220], 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) < -9.99999999999999992e-221

   1. Initial program 99.9%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   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

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + z\right), \color{blue}{x}\right) \]

      3. +-lowering-+.f64 61.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, z\right), x\right) \]

   5. Simplified 61.2%

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

   if -9.99999999999999992e-221 < (+.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

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(z, 1\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 57.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 10: 31.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.2e-128) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.2e-128) {
		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 <= 1.2d-128) 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 <= 1.2e-128) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.2e-128:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.2e-128)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.2e-128)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.2e-128], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.1999999999999999e-128

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 45.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 45.1%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 27.4%

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

   if 1.1999999999999999e-128 < 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

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 56.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   5. Simplified 56.5%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 41.8%

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

Alternative 11: 26.4% 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 99.9%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 49.7%

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

5. Simplified 49.7%

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

6. Taylor expanded in y around 0

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

8. Simplified 23.2%

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))