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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 8

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, 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 52.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z + 1 \leq -4 \cdot 10^{+79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z + 1 \leq 1.000005:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= (+ z 1.0) -4e+79)
     (* y z)
     (if (<= (+ z 1.0) 1.0)
       t_0
       (if (<= (+ z 1.0) 1.000005)
         (+ x y)
         (if (<= (+ z 1.0) 2e+172) t_0 (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if ((z + 1.0) <= -4e+79) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1.0) {
		tmp = t_0;
	} else if ((z + 1.0) <= 1.000005) {
		tmp = x + y;
	} else if ((z + 1.0) <= 2e+172) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + 1.0d0)
    if ((z + 1.0d0) <= (-4d+79)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 1.0d0) then
        tmp = t_0
    else if ((z + 1.0d0) <= 1.000005d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 2d+172) then
        tmp = t_0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if ((z + 1.0) <= -4e+79) {
		tmp = y * z;
	} else if ((z + 1.0) <= 1.0) {
		tmp = t_0;
	} else if ((z + 1.0) <= 1.000005) {
		tmp = x + y;
	} else if ((z + 1.0) <= 2e+172) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if (z + 1.0) <= -4e+79:
		tmp = y * z
	elif (z + 1.0) <= 1.0:
		tmp = t_0
	elif (z + 1.0) <= 1.000005:
		tmp = x + y
	elif (z + 1.0) <= 2e+172:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (Float64(z + 1.0) <= -4e+79)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 1.0)
		tmp = t_0;
	elseif (Float64(z + 1.0) <= 1.000005)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 2e+172)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if ((z + 1.0) <= -4e+79)
		tmp = y * z;
	elseif ((z + 1.0) <= 1.0)
		tmp = t_0;
	elseif ((z + 1.0) <= 1.000005)
		tmp = x + y;
	elseif ((z + 1.0) <= 2e+172)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z + 1.0), $MachinePrecision], -4e+79], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.0], t$95$0, If[LessEqual[N[(z + 1.0), $MachinePrecision], 1.000005], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 2e+172], t$95$0, N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -3.99999999999999987e79 or 2.0000000000000002e172 < (+.f64 z #s(literal 1 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in x around 0 50.5%

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

   if -3.99999999999999987e79 < (+.f64 z #s(literal 1 binary64)) < 1 or 1.00000500000000003 < (+.f64 z #s(literal 1 binary64)) < 2.0000000000000002e172

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 46.6%

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

   if 1 < (+.f64 z #s(literal 1 binary64)) < 1.00000500000000003

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -4 \cdot 10^{+79}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 1:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z + 1 \leq 1.000005:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+177}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.65e+63)
   (* y z)
   (if (<= z -1.0)
     (* x z)
     (if (<= z -2.3e-191)
       x
       (if (<= z 4.0) y (if (<= z 9.5e+177) (* x z) (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+63) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -2.3e-191) {
		tmp = x;
	} else if (z <= 4.0) {
		tmp = y;
	} else if (z <= 9.5e+177) {
		tmp = x * z;
	} 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 <= (-1.65d+63)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= (-2.3d-191)) then
        tmp = x
    else if (z <= 4.0d0) then
        tmp = y
    else if (z <= 9.5d+177) then
        tmp = x * z
    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 <= -1.65e+63) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= -2.3e-191) {
		tmp = x;
	} else if (z <= 4.0) {
		tmp = y;
	} else if (z <= 9.5e+177) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.65e+63:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= -2.3e-191:
		tmp = x
	elif z <= 4.0:
		tmp = y
	elif z <= 9.5e+177:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.65e+63)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= -2.3e-191)
		tmp = x;
	elseif (z <= 4.0)
		tmp = y;
	elseif (z <= 9.5e+177)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.65e+63)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= -2.3e-191)
		tmp = x;
	elseif (z <= 4.0)
		tmp = y;
	elseif (z <= 9.5e+177)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.65e+63], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.3e-191], x, If[LessEqual[z, 4.0], y, If[LessEqual[z, 9.5e+177], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6500000000000001e63 or 9.49999999999999996e177 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in x around 0 50.5%

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

   if -1.6500000000000001e63 < z < -1 or 4 < z < 9.49999999999999996e177

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 95.2%

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

   4. Taylor expanded in x around inf 50.4%

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

      1. *-commutative 50.4%

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

   6. Simplified 50.4%

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

   if -1 < z < -2.30000000000000011e-191

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.3%

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

      1. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around 0 31.4%

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

   if -2.30000000000000011e-191 < z < 4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.0%

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

      1. +-commutative 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in y around inf 49.4%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+177}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 5000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+184}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e+60)
   (* y z)
   (if (<= z -1.0)
     (* x z)
     (if (<= z 5000.0) (+ x y) (if (<= z 1.3e+184) (* x z) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e+60) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 5000.0) {
		tmp = x + y;
	} else if (z <= 1.3e+184) {
		tmp = x * z;
	} 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 <= (-4.8d+60)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 5000.0d0) then
        tmp = x + y
    else if (z <= 1.3d+184) then
        tmp = x * z
    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 <= -4.8e+60) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 5000.0) {
		tmp = x + y;
	} else if (z <= 1.3e+184) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.8e+60:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 5000.0:
		tmp = x + y
	elif z <= 1.3e+184:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e+60)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 5000.0)
		tmp = Float64(x + y);
	elseif (z <= 1.3e+184)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.8e+60)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 5000.0)
		tmp = x + y;
	elseif (z <= 1.3e+184)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e+60], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 5000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.3e+184], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e60 or 1.29999999999999997e184 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in x around 0 50.5%

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

   if -4.8e60 < z < -1 or 5e3 < z < 1.29999999999999997e184

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 97.9%

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

   4. Taylor expanded in x around inf 52.4%

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

      1. *-commutative 52.4%

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

   6. Simplified 52.4%

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

   if -1 < z < 5e3

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 5000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+184}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* y z) (if (<= z -9.2e-198) x (if (<= z 1.0) y (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -9.2e-198) {
		tmp = x;
	} else if (z <= 1.0) {
		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 <= (-9.2d-198)) then
        tmp = x
    else if (z <= 1.0d0) 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 <= -9.2e-198) {
		tmp = x;
	} else if (z <= 1.0) {
		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 <= -9.2e-198:
		tmp = x
	elif z <= 1.0:
		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 <= -9.2e-198)
		tmp = x;
	elseif (z <= 1.0)
		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 <= -9.2e-198)
		tmp = x;
	elseif (z <= 1.0)
		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, -9.2e-198], x, If[LessEqual[z, 1.0], y, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 98.1%

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

   4. Taylor expanded in x around 0 51.0%

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

   if -1 < z < -9.20000000000000053e-198

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.3%

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

      1. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around 0 31.4%

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

   if -9.20000000000000053e-198 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.0%

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

      1. +-commutative 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in y around inf 49.4%

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

Alternative 6: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -2e-282) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -2e-282) {
		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) <= (-2d-282)) 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) <= -2e-282) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -2e-282:
		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) <= -2e-282)
		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) <= -2e-282)
		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], -2e-282], 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) < -2e-282

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 48.0%

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

   if -2e-282 < (+.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 54.6%

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

Alternative 7: 32.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3e-39) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3e-39) {
		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 <= 3d-39) 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 <= 3e-39) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3e-39:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3e-39)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3e-39)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3e-39], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.00000000000000028e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 49.2%

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

      1. +-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in y around 0 29.0%

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

   if 3.00000000000000028e-39 < 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 49.2%

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

      1. +-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in y around inf 44.9%

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

Alternative 8: 26.9% 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%

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

3. Taylor expanded in z around 0 49.2%

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

   1. +-commutative 49.2%

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

5. Simplified 49.2%

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

6. Taylor expanded in y around 0 22.8%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))