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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 7

Speedup: 1.0×

• 20.3% 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

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

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. Final simplification 100.0%

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

Alternative 2: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+186}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+71} \lor \neg \left(z \leq 3.9 \cdot 10^{+223}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.75e+186)
   (* y z)
   (if (<= z -1.0)
     (* x z)
     (if (<= z 490000.0)
       (+ x y)
       (if (or (<= z 1.2e+71) (not (<= z 3.9e+223))) (* x z) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.75e+186) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 490000.0) {
		tmp = x + y;
	} else if ((z <= 1.2e+71) || !(z <= 3.9e+223)) {
		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 <= (-1.75d+186)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 490000.0d0) then
        tmp = x + y
    else if ((z <= 1.2d+71) .or. (.not. (z <= 3.9d+223))) 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 <= -1.75e+186) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 490000.0) {
		tmp = x + y;
	} else if ((z <= 1.2e+71) || !(z <= 3.9e+223)) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.75e+186:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 490000.0:
		tmp = x + y
	elif (z <= 1.2e+71) or not (z <= 3.9e+223):
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.75e+186)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 490000.0)
		tmp = Float64(x + y);
	elseif ((z <= 1.2e+71) || !(z <= 3.9e+223))
		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 <= -1.75e+186)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 490000.0)
		tmp = x + y;
	elseif ((z <= 1.2e+71) || ~((z <= 3.9e+223)))
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.75e+186], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 490000.0], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 1.2e+71], N[Not[LessEqual[z, 3.9e+223]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999993e186 or 1.1999999999999999e71 < z < 3.8999999999999999e223

   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%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 83.6%

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

   7. Taylor expanded in y around inf 57.1%

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

      1. *-commutative 57.1%

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

   9. Simplified 57.1%

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

   if -1.74999999999999993e186 < z < -1 or 4.9e5 < z < 1.1999999999999999e71 or 3.8999999999999999e223 < 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 97.9%

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

      1. +-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 42.0%

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

   if -1 < z < 4.9e5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+186}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+71} \lor \neg \left(z \leq 3.9 \cdot 10^{+223}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+225}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z 1.0))))
   (if (<= z -3.6e+186)
     (* y z)
     (if (<= z -1.15e-6)
       t_0
       (if (<= z 490000.0)
         (+ x y)
         (if (<= z 2.45e+73) t_0 (if (<= z 2.5e+225) (* y z) (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -3.6e+186) {
		tmp = y * z;
	} else if (z <= -1.15e-6) {
		tmp = t_0;
	} else if (z <= 490000.0) {
		tmp = x + y;
	} else if (z <= 2.45e+73) {
		tmp = t_0;
	} else if (z <= 2.5e+225) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + 1.0d0)
    if (z <= (-3.6d+186)) then
        tmp = y * z
    else if (z <= (-1.15d-6)) then
        tmp = t_0
    else if (z <= 490000.0d0) then
        tmp = x + y
    else if (z <= 2.45d+73) then
        tmp = t_0
    else if (z <= 2.5d+225) 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 t_0 = x * (z + 1.0);
	double tmp;
	if (z <= -3.6e+186) {
		tmp = y * z;
	} else if (z <= -1.15e-6) {
		tmp = t_0;
	} else if (z <= 490000.0) {
		tmp = x + y;
	} else if (z <= 2.45e+73) {
		tmp = t_0;
	} else if (z <= 2.5e+225) {
		tmp = y * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + 1.0)
	tmp = 0
	if z <= -3.6e+186:
		tmp = y * z
	elif z <= -1.15e-6:
		tmp = t_0
	elif z <= 490000.0:
		tmp = x + y
	elif z <= 2.45e+73:
		tmp = t_0
	elif z <= 2.5e+225:
		tmp = y * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (z <= -3.6e+186)
		tmp = Float64(y * z);
	elseif (z <= -1.15e-6)
		tmp = t_0;
	elseif (z <= 490000.0)
		tmp = Float64(x + y);
	elseif (z <= 2.45e+73)
		tmp = t_0;
	elseif (z <= 2.5e+225)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + 1.0);
	tmp = 0.0;
	if (z <= -3.6e+186)
		tmp = y * z;
	elseif (z <= -1.15e-6)
		tmp = t_0;
	elseif (z <= 490000.0)
		tmp = x + y;
	elseif (z <= 2.45e+73)
		tmp = t_0;
	elseif (z <= 2.5e+225)
		tmp = y * z;
	else
		tmp = x * 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[z, -3.6e+186], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.15e-6], t$95$0, If[LessEqual[z, 490000.0], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.45e+73], t$95$0, If[LessEqual[z, 2.5e+225], N[(y * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6000000000000002e186 or 2.45e73 < z < 2.4999999999999999e225

   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%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 83.6%

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

   7. Taylor expanded in y around inf 57.1%

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

      1. *-commutative 57.1%

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

   9. Simplified 57.1%

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

   if -3.6000000000000002e186 < z < -1.15e-6 or 4.9e5 < z < 2.45e73

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 45.5%

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

   if -1.15e-6 < z < 4.9e5

   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%

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

   if 2.4999999999999999e225 < 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%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 35.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+225}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* z (+ x y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x + y);
	} else {
		tmp = x + 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 ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x + y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * (x + y)
	else:
		tmp = x + y
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   if -1 < 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 99.5%

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

      1. +-commutative 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 98.9%

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

Alternative 5: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.4e+31) (* x (+ z 1.0)) (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e+31) {
		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 (y <= 2.4d+31) 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 (y <= 2.4e+31) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.4e+31:
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.4e+31)
		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 (y <= 2.4e+31)
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.4e+31], 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 y < 2.39999999999999982e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 55.4%

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

   if 2.39999999999999982e31 < 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 81.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 32.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-102}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -2.9e-102) (* x z) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.9e-102) {
		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 (x <= (-2.9d-102)) 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 (x <= -2.9e-102) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.9e-102:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.9e-102)
		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 (x <= -2.9e-102)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.9e-102], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999986e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 50.3%

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

      1. +-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in y around 0 37.4%

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

   if -2.89999999999999986e-102 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 55.4%

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

      1. +-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in y around inf 51.3%

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

   7. Taylor expanded in y around inf 38.2%

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

      1. *-commutative 38.2%

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

   9. Simplified 38.2%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-102}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 27.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf 53.9%

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

   1. +-commutative 53.9%

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

5. Simplified 53.9%

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

6. Taylor expanded in y around 0 26.2%

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

7. Final simplification 26.2%

   \[\leadsto x \cdot z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))