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

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

Alternatives: 9

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, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in z around 0 100.0%

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

3. Final simplification 100.0%

   \[\leadsto y + \left(x + \left(y + x\right) \cdot z\right) \]

Alternative 2: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+232}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+180}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.1 \cdot 10^{+130}\right) \land \left(z \leq 3.8 \cdot 10^{+195} \lor \neg \left(z \leq 2.8 \cdot 10^{+257}\right) \land z \leq 6.8 \cdot 10^{+293}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e+232)
   (* y z)
   (if (<= z -4.5e+180)
     (* x z)
     (if (<= z -1.02e+125)
       (* y z)
       (if (<= z -1.0)
         (* x z)
         (if (<= z 7e-6)
           y
           (if (or (<= z 7.2e+41)
                   (and (not (<= z 1.1e+130))
                        (or (<= z 3.8e+195)
                            (and (not (<= z 2.8e+257)) (<= z 6.8e+293)))))
             (* x z)
             (* y z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e+232) {
		tmp = y * z;
	} else if (z <= -4.5e+180) {
		tmp = x * z;
	} else if (z <= -1.02e+125) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 7e-6) {
		tmp = y;
	} else if ((z <= 7.2e+41) || (!(z <= 1.1e+130) && ((z <= 3.8e+195) || (!(z <= 2.8e+257) && (z <= 6.8e+293))))) {
		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 <= (-1.2d+232)) then
        tmp = y * z
    else if (z <= (-4.5d+180)) then
        tmp = x * z
    else if (z <= (-1.02d+125)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 7d-6) then
        tmp = y
    else if ((z <= 7.2d+41) .or. (.not. (z <= 1.1d+130)) .and. (z <= 3.8d+195) .or. (.not. (z <= 2.8d+257)) .and. (z <= 6.8d+293)) 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 <= -1.2e+232) {
		tmp = y * z;
	} else if (z <= -4.5e+180) {
		tmp = x * z;
	} else if (z <= -1.02e+125) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 7e-6) {
		tmp = y;
	} else if ((z <= 7.2e+41) || (!(z <= 1.1e+130) && ((z <= 3.8e+195) || (!(z <= 2.8e+257) && (z <= 6.8e+293))))) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e+232:
		tmp = y * z
	elif z <= -4.5e+180:
		tmp = x * z
	elif z <= -1.02e+125:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 7e-6:
		tmp = y
	elif (z <= 7.2e+41) or (not (z <= 1.1e+130) and ((z <= 3.8e+195) or (not (z <= 2.8e+257) and (z <= 6.8e+293)))):
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e+232)
		tmp = Float64(y * z);
	elseif (z <= -4.5e+180)
		tmp = Float64(x * z);
	elseif (z <= -1.02e+125)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 7e-6)
		tmp = y;
	elseif ((z <= 7.2e+41) || (!(z <= 1.1e+130) && ((z <= 3.8e+195) || (!(z <= 2.8e+257) && (z <= 6.8e+293)))))
		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 <= -1.2e+232)
		tmp = y * z;
	elseif (z <= -4.5e+180)
		tmp = x * z;
	elseif (z <= -1.02e+125)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 7e-6)
		tmp = y;
	elseif ((z <= 7.2e+41) || (~((z <= 1.1e+130)) && ((z <= 3.8e+195) || (~((z <= 2.8e+257)) && (z <= 6.8e+293)))))
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e+232], N[(y * z), $MachinePrecision], If[LessEqual[z, -4.5e+180], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.02e+125], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 7e-6], y, If[Or[LessEqual[z, 7.2e+41], And[N[Not[LessEqual[z, 1.1e+130]], $MachinePrecision], Or[LessEqual[z, 3.8e+195], And[N[Not[LessEqual[z, 2.8e+257]], $MachinePrecision], LessEqual[z, 6.8e+293]]]]], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2000000000000001e232 or -4.49999999999999981e180 < z < -1.02e125 or 7.20000000000000051e41 < z < 1.09999999999999997e130 or 3.8e195 < z < 2.7999999999999998e257 or 6.8000000000000006e293 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   if -1.2000000000000001e232 < z < -4.49999999999999981e180 or -1.02e125 < z < -1 or 6.99999999999999989e-6 < z < 7.20000000000000051e41 or 1.09999999999999997e130 < z < 3.8e195 or 2.7999999999999998e257 < z < 6.8000000000000006e293

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 94.5%

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

   3. Taylor expanded in y around 0 48.4%

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

   if -1 < z < 6.99999999999999989e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 47.7%

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

   3. Taylor expanded in z around 0 46.8%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+232}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+180}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.1 \cdot 10^{+130}\right) \land \left(z \leq 3.8 \cdot 10^{+195} \lor \neg \left(z \leq 2.8 \cdot 10^{+257}\right) \land z \leq 6.8 \cdot 10^{+293}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+226}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+180}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+124}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 9.5:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.8 \cdot 10^{+130}\right) \land \left(z \leq 1.9 \cdot 10^{+205} \lor \neg \left(z \leq 4.4 \cdot 10^{+261}\right) \land z \leq 1.75 \cdot 10^{+295}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+226)
   (* y z)
   (if (<= z -2.8e+180)
     (* x z)
     (if (<= z -6.8e+124)
       (* y z)
       (if (<= z -1.0)
         (* x z)
         (if (<= z 9.5)
           (+ y x)
           (if (or (<= z 8.2e+41)
                   (and (not (<= z 1.8e+130))
                        (or (<= z 1.9e+205)
                            (and (not (<= z 4.4e+261)) (<= z 1.75e+295)))))
             (* x z)
             (* y z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+226) {
		tmp = y * z;
	} else if (z <= -2.8e+180) {
		tmp = x * z;
	} else if (z <= -6.8e+124) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 9.5) {
		tmp = y + x;
	} else if ((z <= 8.2e+41) || (!(z <= 1.8e+130) && ((z <= 1.9e+205) || (!(z <= 4.4e+261) && (z <= 1.75e+295))))) {
		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 <= (-2d+226)) then
        tmp = y * z
    else if (z <= (-2.8d+180)) then
        tmp = x * z
    else if (z <= (-6.8d+124)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 9.5d0) then
        tmp = y + x
    else if ((z <= 8.2d+41) .or. (.not. (z <= 1.8d+130)) .and. (z <= 1.9d+205) .or. (.not. (z <= 4.4d+261)) .and. (z <= 1.75d+295)) 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 <= -2e+226) {
		tmp = y * z;
	} else if (z <= -2.8e+180) {
		tmp = x * z;
	} else if (z <= -6.8e+124) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 9.5) {
		tmp = y + x;
	} else if ((z <= 8.2e+41) || (!(z <= 1.8e+130) && ((z <= 1.9e+205) || (!(z <= 4.4e+261) && (z <= 1.75e+295))))) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+226:
		tmp = y * z
	elif z <= -2.8e+180:
		tmp = x * z
	elif z <= -6.8e+124:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 9.5:
		tmp = y + x
	elif (z <= 8.2e+41) or (not (z <= 1.8e+130) and ((z <= 1.9e+205) or (not (z <= 4.4e+261) and (z <= 1.75e+295)))):
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+226)
		tmp = Float64(y * z);
	elseif (z <= -2.8e+180)
		tmp = Float64(x * z);
	elseif (z <= -6.8e+124)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 9.5)
		tmp = Float64(y + x);
	elseif ((z <= 8.2e+41) || (!(z <= 1.8e+130) && ((z <= 1.9e+205) || (!(z <= 4.4e+261) && (z <= 1.75e+295)))))
		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 <= -2e+226)
		tmp = y * z;
	elseif (z <= -2.8e+180)
		tmp = x * z;
	elseif (z <= -6.8e+124)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 9.5)
		tmp = y + x;
	elseif ((z <= 8.2e+41) || (~((z <= 1.8e+130)) && ((z <= 1.9e+205) || (~((z <= 4.4e+261)) && (z <= 1.75e+295)))))
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+226], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.8e+180], N[(x * z), $MachinePrecision], If[LessEqual[z, -6.8e+124], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 9.5], N[(y + x), $MachinePrecision], If[Or[LessEqual[z, 8.2e+41], And[N[Not[LessEqual[z, 1.8e+130]], $MachinePrecision], Or[LessEqual[z, 1.9e+205], And[N[Not[LessEqual[z, 4.4e+261]], $MachinePrecision], LessEqual[z, 1.75e+295]]]]], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999992e226 or -2.80000000000000012e180 < z < -6.8e124 or 8.2000000000000007e41 < z < 1.8000000000000001e130 or 1.9e205 < z < 4.39999999999999969e261 or 1.74999999999999997e295 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   if -1.99999999999999992e226 < z < -2.80000000000000012e180 or -6.8e124 < z < -1 or 9.5 < z < 8.2000000000000007e41 or 1.8000000000000001e130 < z < 1.9e205 or 4.39999999999999969e261 < z < 1.74999999999999997e295

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 95.8%

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

   3. Taylor expanded in y around 0 49.0%

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

   if -1 < z < 9.5

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+226}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+180}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+124}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 9.5:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.8 \cdot 10^{+130}\right) \land \left(z \leq 1.9 \cdot 10^{+205} \lor \neg \left(z \leq 4.4 \cdot 10^{+261}\right) \land z \leq 1.75 \cdot 10^{+295}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+230}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+180}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7.4:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+204} \lor \neg \left(z \leq 1.55 \cdot 10^{+258}\right) \land z \leq 7 \cdot 10^{+294}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5e+230)
   (* y z)
   (if (<= z -2.3e+180)
     (* x z)
     (if (<= z -1.02e+125)
       (* y z)
       (if (<= z -1.0)
         (* x z)
         (if (<= z 7.4)
           (+ y x)
           (if (<= z 4.5e+42)
             (* x z)
             (if (<= z 4e+129)
               (* y (+ z 1.0))
               (if (or (<= z 1.08e+204)
                       (and (not (<= z 1.55e+258)) (<= z 7e+294)))
                 (* x z)
                 (* y z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+230) {
		tmp = y * z;
	} else if (z <= -2.3e+180) {
		tmp = x * z;
	} else if (z <= -1.02e+125) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 7.4) {
		tmp = y + x;
	} else if (z <= 4.5e+42) {
		tmp = x * z;
	} else if (z <= 4e+129) {
		tmp = y * (z + 1.0);
	} else if ((z <= 1.08e+204) || (!(z <= 1.55e+258) && (z <= 7e+294))) {
		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 <= (-5.5d+230)) then
        tmp = y * z
    else if (z <= (-2.3d+180)) then
        tmp = x * z
    else if (z <= (-1.02d+125)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 7.4d0) then
        tmp = y + x
    else if (z <= 4.5d+42) then
        tmp = x * z
    else if (z <= 4d+129) then
        tmp = y * (z + 1.0d0)
    else if ((z <= 1.08d+204) .or. (.not. (z <= 1.55d+258)) .and. (z <= 7d+294)) 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 <= -5.5e+230) {
		tmp = y * z;
	} else if (z <= -2.3e+180) {
		tmp = x * z;
	} else if (z <= -1.02e+125) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 7.4) {
		tmp = y + x;
	} else if (z <= 4.5e+42) {
		tmp = x * z;
	} else if (z <= 4e+129) {
		tmp = y * (z + 1.0);
	} else if ((z <= 1.08e+204) || (!(z <= 1.55e+258) && (z <= 7e+294))) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5e+230:
		tmp = y * z
	elif z <= -2.3e+180:
		tmp = x * z
	elif z <= -1.02e+125:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 7.4:
		tmp = y + x
	elif z <= 4.5e+42:
		tmp = x * z
	elif z <= 4e+129:
		tmp = y * (z + 1.0)
	elif (z <= 1.08e+204) or (not (z <= 1.55e+258) and (z <= 7e+294)):
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5e+230)
		tmp = Float64(y * z);
	elseif (z <= -2.3e+180)
		tmp = Float64(x * z);
	elseif (z <= -1.02e+125)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 7.4)
		tmp = Float64(y + x);
	elseif (z <= 4.5e+42)
		tmp = Float64(x * z);
	elseif (z <= 4e+129)
		tmp = Float64(y * Float64(z + 1.0));
	elseif ((z <= 1.08e+204) || (!(z <= 1.55e+258) && (z <= 7e+294)))
		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 <= -5.5e+230)
		tmp = y * z;
	elseif (z <= -2.3e+180)
		tmp = x * z;
	elseif (z <= -1.02e+125)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 7.4)
		tmp = y + x;
	elseif (z <= 4.5e+42)
		tmp = x * z;
	elseif (z <= 4e+129)
		tmp = y * (z + 1.0);
	elseif ((z <= 1.08e+204) || (~((z <= 1.55e+258)) && (z <= 7e+294)))
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5e+230], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.3e+180], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.02e+125], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 7.4], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.5e+42], N[(x * z), $MachinePrecision], If[LessEqual[z, 4e+129], N[(y * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.08e+204], And[N[Not[LessEqual[z, 1.55e+258]], $MachinePrecision], LessEqual[z, 7e+294]]], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999979e230 or -2.2999999999999999e180 < z < -1.02e125 or 1.08e204 < z < 1.5499999999999999e258 or 7.0000000000000003e294 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

   3. Taylor expanded in y around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

   if -5.49999999999999979e230 < z < -2.2999999999999999e180 or -1.02e125 < z < -1 or 7.4000000000000004 < z < 4.50000000000000012e42 or 4e129 < z < 1.08e204 or 1.5499999999999999e258 < z < 7.0000000000000003e294

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 95.8%

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

   3. Taylor expanded in y around 0 49.0%

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

   if -1 < z < 7.4000000000000004

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.3%

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

   if 4.50000000000000012e42 < z < 4e129

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+230}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+180}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7.4:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+204} \lor \neg \left(z \leq 1.55 \cdot 10^{+258}\right) \land z \leq 7 \cdot 10^{+294}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 63.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-30} \lor \neg \left(x \leq -3.95 \cdot 10^{-112}\right) \land x \leq -2.2 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-30) (and (not (<= x -3.95e-112)) (<= x -2.2e-129)))
   (* x (+ z 1.0))
   (* y (+ z 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-30) || (!(x <= -3.95e-112) && (x <= -2.2e-129))) {
		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 <= (-2.8d-30)) .or. (.not. (x <= (-3.95d-112))) .and. (x <= (-2.2d-129))) 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 <= -2.8e-30) || (!(x <= -3.95e-112) && (x <= -2.2e-129))) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-30) or (not (x <= -3.95e-112) and (x <= -2.2e-129)):
		tmp = x * (z + 1.0)
	else:
		tmp = y * (z + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-30) || (!(x <= -3.95e-112) && (x <= -2.2e-129)))
		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 <= -2.8e-30) || (~((x <= -3.95e-112)) && (x <= -2.2e-129)))
		tmp = x * (z + 1.0);
	else
		tmp = y * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-30], And[N[Not[LessEqual[x, -3.95e-112]], $MachinePrecision], LessEqual[x, -2.2e-129]]], 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 x < -2.79999999999999988e-30 or -3.95e-112 < x < -2.20000000000000003e-129

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.9%

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

   if -2.79999999999999988e-30 < x < -3.95e-112 or -2.20000000000000003e-129 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 57.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-30} \lor \neg \left(x \leq -3.95 \cdot 10^{-112}\right) \land x \leq -2.2 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 6: 97.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision], N[(y + x), $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. Taylor expanded in z around inf 97.7%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.0%

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

Alternative 7: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (* x z) (if (<= z 7e-6) y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 7e-6) {
		tmp = y;
	} 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)) then
        tmp = x * z
    else if (z <= 7d-6) then
        tmp = y
    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) {
		tmp = x * z;
	} else if (z <= 7e-6) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 7e-6:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 7e-6)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= 7e-6)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 7e-6], y, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 6.99999999999999989e-6 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.0%

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

   3. Taylor expanded in y around 0 50.6%

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

   if -1 < z < 6.99999999999999989e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 47.7%

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

   3. Taylor expanded in z around 0 46.8%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 9: 26.9% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 49.1%

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

3. Taylor expanded in z around 0 26.8%

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

4. Final simplification 26.8%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))