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

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 9

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

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

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%

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

   1. +-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-rgt-identity 100.0%

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

4. Applied egg-rr 100.0%

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

Alternative 2: 49.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-112}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0165:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.9e+117)
   (* y z)
   (if (<= z -1.7e+70)
     (* x z)
     (if (<= z -1.0)
       (* y z)
       (if (<= z -7.4e-69)
         x
         (if (<= z -7.2e-112)
           y
           (if (<= z -2.2e-201)
             x
             (if (<= z 0.0165) y (if (<= z 8.2e+138) (* y z) (* x z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.9e+117) {
		tmp = y * z;
	} else if (z <= -1.7e+70) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -7.4e-69) {
		tmp = x;
	} else if (z <= -7.2e-112) {
		tmp = y;
	} else if (z <= -2.2e-201) {
		tmp = x;
	} else if (z <= 0.0165) {
		tmp = y;
	} else if (z <= 8.2e+138) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.9d+117)) then
        tmp = y * z
    else if (z <= (-1.7d+70)) then
        tmp = x * z
    else if (z <= (-1.0d0)) then
        tmp = y * z
    else if (z <= (-7.4d-69)) then
        tmp = x
    else if (z <= (-7.2d-112)) then
        tmp = y
    else if (z <= (-2.2d-201)) then
        tmp = x
    else if (z <= 0.0165d0) then
        tmp = y
    else if (z <= 8.2d+138) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.9e+117) {
		tmp = y * z;
	} else if (z <= -1.7e+70) {
		tmp = x * z;
	} else if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -7.4e-69) {
		tmp = x;
	} else if (z <= -7.2e-112) {
		tmp = y;
	} else if (z <= -2.2e-201) {
		tmp = x;
	} else if (z <= 0.0165) {
		tmp = y;
	} else if (z <= 8.2e+138) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.9e+117:
		tmp = y * z
	elif z <= -1.7e+70:
		tmp = x * z
	elif z <= -1.0:
		tmp = y * z
	elif z <= -7.4e-69:
		tmp = x
	elif z <= -7.2e-112:
		tmp = y
	elif z <= -2.2e-201:
		tmp = x
	elif z <= 0.0165:
		tmp = y
	elif z <= 8.2e+138:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.9e+117)
		tmp = Float64(y * z);
	elseif (z <= -1.7e+70)
		tmp = Float64(x * z);
	elseif (z <= -1.0)
		tmp = Float64(y * z);
	elseif (z <= -7.4e-69)
		tmp = x;
	elseif (z <= -7.2e-112)
		tmp = y;
	elseif (z <= -2.2e-201)
		tmp = x;
	elseif (z <= 0.0165)
		tmp = y;
	elseif (z <= 8.2e+138)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.9e+117)
		tmp = y * z;
	elseif (z <= -1.7e+70)
		tmp = x * z;
	elseif (z <= -1.0)
		tmp = y * z;
	elseif (z <= -7.4e-69)
		tmp = x;
	elseif (z <= -7.2e-112)
		tmp = y;
	elseif (z <= -2.2e-201)
		tmp = x;
	elseif (z <= 0.0165)
		tmp = y;
	elseif (z <= 8.2e+138)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.9e+117], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.7e+70], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(y * z), $MachinePrecision], If[LessEqual[z, -7.4e-69], x, If[LessEqual[z, -7.2e-112], y, If[LessEqual[z, -2.2e-201], x, If[LessEqual[z, 0.0165], y, If[LessEqual[z, 8.2e+138], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9000000000000001e117 or -1.7e70 < z < -1 or 0.016500000000000001 < z < 8.19999999999999961e138

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.5%

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

   4. Taylor expanded in x around 0 50.9%

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

   if -4.9000000000000001e117 < z < -1.7e70 or 8.19999999999999961e138 < 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 100.0%

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

   4. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

   6. Simplified 52.6%

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

   if -1 < z < -7.4000000000000005e-69 or -7.2000000000000002e-112 < z < -2.2e-201

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 47.8%

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

   if -7.4000000000000005e-69 < z < -7.2000000000000002e-112 or -2.2e-201 < z < 0.016500000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around inf 42.4%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-112}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0165:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-109}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-227}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0165:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* y z)
   (if (<= z -7.4e-69)
     x
     (if (<= z -1.1e-109)
       y
       (if (<= z -1.9e-198)
         x
         (if (<= z 2.6e-227)
           y
           (if (<= z 2.8e-198) x (if (<= z 0.0165) y (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y * z;
	} else if (z <= -7.4e-69) {
		tmp = x;
	} else if (z <= -1.1e-109) {
		tmp = y;
	} else if (z <= -1.9e-198) {
		tmp = x;
	} else if (z <= 2.6e-227) {
		tmp = y;
	} else if (z <= 2.8e-198) {
		tmp = x;
	} else if (z <= 0.0165) {
		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 <= (-7.4d-69)) then
        tmp = x
    else if (z <= (-1.1d-109)) then
        tmp = y
    else if (z <= (-1.9d-198)) then
        tmp = x
    else if (z <= 2.6d-227) then
        tmp = y
    else if (z <= 2.8d-198) then
        tmp = x
    else if (z <= 0.0165d0) 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 <= -7.4e-69) {
		tmp = x;
	} else if (z <= -1.1e-109) {
		tmp = y;
	} else if (z <= -1.9e-198) {
		tmp = x;
	} else if (z <= 2.6e-227) {
		tmp = y;
	} else if (z <= 2.8e-198) {
		tmp = x;
	} else if (z <= 0.0165) {
		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 <= -7.4e-69:
		tmp = x
	elif z <= -1.1e-109:
		tmp = y
	elif z <= -1.9e-198:
		tmp = x
	elif z <= 2.6e-227:
		tmp = y
	elif z <= 2.8e-198:
		tmp = x
	elif z <= 0.0165:
		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 <= -7.4e-69)
		tmp = x;
	elseif (z <= -1.1e-109)
		tmp = y;
	elseif (z <= -1.9e-198)
		tmp = x;
	elseif (z <= 2.6e-227)
		tmp = y;
	elseif (z <= 2.8e-198)
		tmp = x;
	elseif (z <= 0.0165)
		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 <= -7.4e-69)
		tmp = x;
	elseif (z <= -1.1e-109)
		tmp = y;
	elseif (z <= -1.9e-198)
		tmp = x;
	elseif (z <= 2.6e-227)
		tmp = y;
	elseif (z <= 2.8e-198)
		tmp = x;
	elseif (z <= 0.0165)
		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, -7.4e-69], x, If[LessEqual[z, -1.1e-109], y, If[LessEqual[z, -1.9e-198], x, If[LessEqual[z, 2.6e-227], y, If[LessEqual[z, 2.8e-198], x, If[LessEqual[z, 0.0165], y, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 0.016500000000000001 < 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 98.0%

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

   4. Taylor expanded in x around 0 51.5%

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

   if -1 < z < -7.4000000000000005e-69 or -1.1e-109 < z < -1.9000000000000001e-198 or 2.60000000000000011e-227 < z < 2.7999999999999999e-198

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 50.0%

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

   if -7.4000000000000005e-69 < z < -1.1e-109 or -1.9000000000000001e-198 < z < 2.60000000000000011e-227 or 2.7999999999999999e-198 < z < 0.016500000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf 42.2%

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

Alternative 4: 74.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + 1 \leq -2 \cdot 10^{+118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -5000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 10000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 4 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ z 1.0) -2e+118)
   (* y z)
   (if (<= (+ z 1.0) -2e+70)
     (* x z)
     (if (<= (+ z 1.0) -5000.0)
       (* y z)
       (if (<= (+ z 1.0) 10000000000000.0)
         (+ x y)
         (if (<= (+ z 1.0) 4e+138) (* y z) (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -2e+118) {
		tmp = y * z;
	} else if ((z + 1.0) <= -2e+70) {
		tmp = x * z;
	} else if ((z + 1.0) <= -5000.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 10000000000000.0) {
		tmp = x + y;
	} else if ((z + 1.0) <= 4e+138) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z + 1.0d0) <= (-2d+118)) then
        tmp = y * z
    else if ((z + 1.0d0) <= (-2d+70)) then
        tmp = x * z
    else if ((z + 1.0d0) <= (-5000.0d0)) then
        tmp = y * z
    else if ((z + 1.0d0) <= 10000000000000.0d0) then
        tmp = x + y
    else if ((z + 1.0d0) <= 4d+138) then
        tmp = y * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z + 1.0) <= -2e+118) {
		tmp = y * z;
	} else if ((z + 1.0) <= -2e+70) {
		tmp = x * z;
	} else if ((z + 1.0) <= -5000.0) {
		tmp = y * z;
	} else if ((z + 1.0) <= 10000000000000.0) {
		tmp = x + y;
	} else if ((z + 1.0) <= 4e+138) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z + 1.0) <= -2e+118:
		tmp = y * z
	elif (z + 1.0) <= -2e+70:
		tmp = x * z
	elif (z + 1.0) <= -5000.0:
		tmp = y * z
	elif (z + 1.0) <= 10000000000000.0:
		tmp = x + y
	elif (z + 1.0) <= 4e+138:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z + 1.0) <= -2e+118)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= -2e+70)
		tmp = Float64(x * z);
	elseif (Float64(z + 1.0) <= -5000.0)
		tmp = Float64(y * z);
	elseif (Float64(z + 1.0) <= 10000000000000.0)
		tmp = Float64(x + y);
	elseif (Float64(z + 1.0) <= 4e+138)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z + 1.0) <= -2e+118)
		tmp = y * z;
	elseif ((z + 1.0) <= -2e+70)
		tmp = x * z;
	elseif ((z + 1.0) <= -5000.0)
		tmp = y * z;
	elseif ((z + 1.0) <= 10000000000000.0)
		tmp = x + y;
	elseif ((z + 1.0) <= 4e+138)
		tmp = y * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z + 1.0), $MachinePrecision], -2e+118], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -2e+70], N[(x * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], -5000.0], N[(y * z), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 10000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[N[(z + 1.0), $MachinePrecision], 4e+138], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 z #s(literal 1 binary64)) < -1.99999999999999993e118 or -2.00000000000000015e70 < (+.f64 z #s(literal 1 binary64)) < -5e3 or 1e13 < (+.f64 z #s(literal 1 binary64)) < 4.0000000000000001e138

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.7%

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

   4. Taylor expanded in x around 0 52.7%

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

   if -1.99999999999999993e118 < (+.f64 z #s(literal 1 binary64)) < -2.00000000000000015e70 or 4.0000000000000001e138 < (+.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 z around inf 100.0%

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

   4. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

   6. Simplified 52.6%

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

   if -5e3 < (+.f64 z #s(literal 1 binary64)) < 1e13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + 1 \leq -2 \cdot 10^{+118}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq -2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z + 1 \leq -5000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z + 1 \leq 10000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z + 1 \leq 4 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -4e-224) (* x (+ z 1.0)) (+ y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -4e-224) {
		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) <= (-4d-224)) 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) <= -4e-224) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -4e-224:
		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) <= -4e-224)
		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) <= -4e-224)
		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], -4e-224], 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) < -4.0000000000000001e-224

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 55.5%

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

   if -4.0000000000000001e-224 < (+.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 51.4%

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

      1. distribute-lft-in 51.5%

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

      2. *-rgt-identity 51.5%

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

   5. Applied egg-rr 51.5%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -4e-224) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -4e-224) {
		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) <= (-4d-224)) 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) <= -4e-224) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + y) <= -4e-224:
		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) <= -4e-224)
		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) <= -4e-224)
		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], -4e-224], 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) < -4.0000000000000001e-224

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 55.5%

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

   if -4.0000000000000001e-224 < (+.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 51.4%

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

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 8: 30.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.3e-148) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.3e-148) {
		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 <= 2.3d-148) 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 <= 2.3e-148) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.3e-148:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.3e-148)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.3e-148)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.3e-148], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.29999999999999997e-148

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 57.1%

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

      1. +-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y around 0 37.6%

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

   if 2.29999999999999997e-148 < 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 43.1%

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

      1. +-commutative 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in y around inf 29.9%

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

Alternative 9: 26.7% 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%

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

3. Taylor expanded in z around 0 51.7%

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

   1. +-commutative 51.7%

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

5. Simplified 51.7%

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

6. Taylor expanded in y around 0 29.4%

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))