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

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 7

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - z \cdot \left(x + y\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 0.0 (* z (+ x y)))))
   (if (<= z -1.0) t_0 (if (<= z 1.0) (+ x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 0.0 - (z * (x + y));
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 0.0d0 - (z * (x + y))
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 0.0 - (z * (x + y));
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.0 - (z * (x + y))
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.0 - Float64(z * Float64(x + y)))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.0 - (z * (x + y));
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.0 - N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. flip-+ N/A

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

      3. flip-- N/A

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

      4. frac-times N/A

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

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

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

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

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

      7. --lowering--.f64 N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot x\right)\right), \left(1 \cdot 1 - z \cdot z\right)\right), \left(\left(y - x\right) \cdot \left(1 + z\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, x\right)\right), \left(1 \cdot 1 - z \cdot z\right)\right), \left(\left(y - x\right) \cdot \left(1 + z\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, x\right)\right), \left(1 - z \cdot z\right)\right), \left(\left(y - x\right) \cdot \left(1 + z\right)\right)\right) \]

      11. --lowering--.f64 N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, x\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\left(y - x\right) \cdot \left(1 + z\right)\right)\right) \]

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

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

      14. --lowering--.f64 N/A

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

      15. +-lowering-+.f64 26.4%

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

   4. Applied egg-rr 26.4%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. clear-num N/A

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

      4. metadata-eval N/A

         \[\leadsto \frac{y \cdot y - x \cdot x}{y - x} \cdot \frac{1}{\frac{1}{\frac{1 \cdot 1 - z \cdot z}{1 + z}}} \]

      5. flip-- N/A

         \[\leadsto \frac{y \cdot y - x \cdot x}{y - x} \cdot \frac{1}{\frac{1}{1 - \color{blue}{z}}} \]

      6. un-div-inv N/A

         \[\leadsto \frac{\frac{y \cdot y - x \cdot x}{y - x}}{\color{blue}{\frac{1}{1 - z}}} \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y \cdot y - x \cdot x}{y - x}\right), \color{blue}{\left(\frac{1}{1 - z}\right)}\right) \]

      8. flip-+ N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{y + x}{\frac{1}{1 - z}}} \]

   7. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 95.6%

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

   9. Simplified 95.6%

      \[\leadsto \frac{y + x}{\color{blue}{\frac{-1}{z}}} \]
   10. Step-by-step derivation

       1. frac-2neg N/A

          \[\leadsto \frac{\mathsf{neg}\left(\left(y + x\right)\right)}{\color{blue}{\mathsf{neg}\left(\frac{-1}{z}\right)}} \]

       2. distribute-frac-neg N/A

          \[\leadsto \mathsf{neg}\left(\frac{y + x}{\mathsf{neg}\left(\frac{-1}{z}\right)}\right) \]

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

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{y + x}{\mathsf{neg}\left(\frac{-1}{z}\right)}\right)\right) \]

       4. div-inv N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(y + x\right) \cdot \frac{1}{\mathsf{neg}\left(\frac{-1}{z}\right)}\right)\right) \]

       5. distribute-neg-frac N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(y + x\right) \cdot \frac{1}{\frac{\mathsf{neg}\left(-1\right)}{z}}\right)\right) \]

       6. metadata-eval N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(y + x\right) \cdot \frac{1}{\frac{1}{z}}\right)\right) \]

       7. remove-double-div N/A

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

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

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

       9. +-lowering-+.f64 95.7%

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

   11. Applied egg-rr 95.7%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;0 - z \cdot \left(x + y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;0 - z \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;z \leq -0.25:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))))
   (if (<= z -0.25) t_0 (if (<= z 3.8e-7) (+ x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if (z <= -0.25) {
		tmp = t_0;
	} else if (z <= 3.8e-7) {
		tmp = x + y;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - z)
    if (z <= (-0.25d0)) then
        tmp = t_0
    else if (z <= 3.8d-7) then
        tmp = x + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if (z <= -0.25) {
		tmp = t_0;
	} else if (z <= 3.8e-7) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	tmp = 0
	if z <= -0.25:
		tmp = t_0
	elif z <= 3.8e-7:
		tmp = x + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (z <= -0.25)
		tmp = t_0;
	elseif (z <= 3.8e-7)
		tmp = Float64(x + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - z);
	tmp = 0.0;
	if (z <= -0.25)
		tmp = t_0;
	elseif (z <= 3.8e-7)
		tmp = x + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.25], t$95$0, If[LessEqual[z, 3.8e-7], N[(x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.25 or 3.80000000000000015e-7 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 55.7%

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

   5. Simplified 55.7%

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

   if -0.25 < z < 3.80000000000000015e-7

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   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 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.25:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6.8e-121) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.8e-121) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - 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 (y <= 6.8d-121) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.8e-121) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.8e-121:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.8e-121)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6.8e-121)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.8e-121], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.80000000000000003e-121

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   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 57.3%

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

   5. Simplified 57.3%

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

   if 6.80000000000000003e-121 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 31.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.4e-124) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.4e-124) {
		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 <= 3.4d-124) 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 <= 3.4e-124) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.4e-124:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.4e-124)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.4e-124)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.4e-124], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.4000000000000001e-124

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   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 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 32.1%

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

   if 3.4000000000000001e-124 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 42.5%

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

Alternative 6: 50.6% accurate, 2.3× 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%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
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 55.9%

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

5. Simplified 55.9%

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

6. Final simplification 55.9%

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

Alternative 7: 26.1% 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%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]
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 46.7%

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

5. Simplified 46.7%

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

6. Taylor expanded in z around 0

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

8. Simplified 25.5%

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))