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

Percentage Accurate: 100.0% → 100.0%

Time: 14.1s

Alternatives: 8

Speedup: 1.0×

• 21.0% 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, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

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

   2. distribute-lft-in N/A

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

   3. fma-define N/A

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

   4. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{fma}\left(x + y, 1, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right) \]

   5. fmm-undef N/A

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

   6. *-rgt-identity N/A

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

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

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

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

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

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

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

   10. +-lowering-+.f64 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 52.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;1 - z \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - z \leq 1.05:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 z))))
   (if (<= (- 1.0 z) 1.0) t_0 (if (<= (- 1.0 z) 1.05) (+ x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - z);
	double tmp;
	if ((1.0 - z) <= 1.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.05) {
		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 ((1.0d0 - z) <= 1.0d0) then
        tmp = t_0
    else if ((1.0d0 - z) <= 1.05d0) 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 ((1.0 - z) <= 1.0) {
		tmp = t_0;
	} else if ((1.0 - z) <= 1.05) {
		tmp = x + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - z)
	tmp = 0
	if (1.0 - z) <= 1.0:
		tmp = t_0
	elif (1.0 - z) <= 1.05:
		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 (Float64(1.0 - z) <= 1.0)
		tmp = t_0;
	elseif (Float64(1.0 - z) <= 1.05)
		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 ((1.0 - z) <= 1.0)
		tmp = t_0;
	elseif ((1.0 - z) <= 1.05)
		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[N[(1.0 - z), $MachinePrecision], 1.0], t$95$0, If[LessEqual[N[(1.0 - z), $MachinePrecision], 1.05], N[(x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) z) < 1 or 1.05000000000000004 < (-.f64 #s(literal 1 binary64) 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 50.0%

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

   5. Simplified 50.0%

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

   if 1 < (-.f64 #s(literal 1 binary64) z) < 1.05000000000000004

   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 36.4%

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

   5. Simplified 36.4%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq 1:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \mathbf{elif}\;1 - z \leq 1.05:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e-90) (* x (- 1.0 z)) (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-90) {
		tmp = x * (1.0 - 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 <= (-3.5d-90)) then
        tmp = x * (1.0d0 - 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 <= -3.5e-90) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e-90:
		tmp = x * (1.0 - z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e-90)
		tmp = Float64(x * Float64(1.0 - 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 <= -3.5e-90)
		tmp = x * (1.0 - z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e-90], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999999e-90

   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 75.1%

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

   5. Simplified 75.1%

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

   if -3.4999999999999999e-90 < x

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. fma-define N/A

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

      4. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{fma}\left(x + y, 1, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right) \]

      5. fmm-undef N/A

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

      6. *-rgt-identity N/A

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

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

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

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

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

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

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

      10. +-lowering-+.f64 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 80.1%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(y \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 62.1%

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

   10. Simplified 62.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.06e-91) (* x (- 1.0 z)) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e-91) {
		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 (x <= (-1.06d-91)) 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 (x <= -1.06e-91) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.06e-91:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.06e-91)
		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 (x <= -1.06e-91)
		tmp = x * (1.0 - z);
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.06e-91], 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 x < -1.06000000000000006e-91

   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 74.3%

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

   5. Simplified 74.3%

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

   if -1.06000000000000006e-91 < x

   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 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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]

Derivation

1. Initial program 100.0%

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

Alternative 6: 32.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -4.4e-90) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e-90) {
		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 (x <= (-4.4d-90)) 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 (x <= -4.4e-90) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e-90:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e-90)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e-90)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e-90], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -4.39999999999999972e-90

   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 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 36.2%

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

   if -4.39999999999999972e-90 < x

   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 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 33.1%

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

Alternative 7: 50.8% 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 50.1%

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

5. Simplified 50.1%

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

6. Final simplification 50.1%

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

Alternative 8: 25.7% 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 51.9%

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

5. Simplified 51.9%

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

6. Taylor expanded in z around 0

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

8. Simplified 26.1%

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

Reproduce

herbie shell --seed 2024141 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))