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

Percentage Accurate: 99.9% → 99.9%

Time: 4.6s

Alternatives: 7

Speedup: 1.0×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

2. Final simplification 100.0%

   \[\leadsto \frac{\left(x + y\right) - z}{t \cdot 2} \]

Alternative 2: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+173} \lor \neg \left(z \leq -1.44 \cdot 10^{+144} \lor \neg \left(z \leq -4.5 \cdot 10^{+126}\right) \land z \leq 3 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e+173)
         (not
          (or (<= z -1.44e+144) (and (not (<= z -4.5e+126)) (<= z 3e+97)))))
   (* (/ z t) -0.5)
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+173) || !((z <= -1.44e+144) || (!(z <= -4.5e+126) && (z <= 3e+97)))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3d+173)) .or. (.not. (z <= (-1.44d+144)) .or. (.not. (z <= (-4.5d+126))) .and. (z <= 3d+97))) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = 0.5d0 * ((x + y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+173) || !((z <= -1.44e+144) || (!(z <= -4.5e+126) && (z <= 3e+97)))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e+173) or not ((z <= -1.44e+144) or (not (z <= -4.5e+126) and (z <= 3e+97))):
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e+173) || !((z <= -1.44e+144) || (!(z <= -4.5e+126) && (z <= 3e+97))))
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3e+173) || ~(((z <= -1.44e+144) || (~((z <= -4.5e+126)) && (z <= 3e+97)))))
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e+173], N[Not[Or[LessEqual[z, -1.44e+144], And[N[Not[LessEqual[z, -4.5e+126]], $MachinePrecision], LessEqual[z, 3e+97]]]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999998e173 or -1.44e144 < z < -4.49999999999999974e126 or 2.9999999999999998e97 < z

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   4. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   if -2.9999999999999998e173 < z < -1.44e144 or -4.49999999999999974e126 < z < 2.9999999999999998e97

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in z around 0 92.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   3. Step-by-step derivation

      1. +-commutative 92.6%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   4. Simplified 92.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+173} \lor \neg \left(z \leq -1.44 \cdot 10^{+144} \lor \neg \left(z \leq -4.5 \cdot 10^{+126}\right) \land z \leq 3 \cdot 10^{+97}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 3: 46.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1050000:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-276}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1050000.0)
   (* 0.5 (/ x t))
   (if (<= x -2.4e-276) (* (/ z t) -0.5) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1050000.0) {
		tmp = 0.5 * (x / t);
	} else if (x <= -2.4e-276) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1050000.0d0)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= (-2.4d-276)) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1050000.0) {
		tmp = 0.5 * (x / t);
	} else if (x <= -2.4e-276) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1050000.0:
		tmp = 0.5 * (x / t)
	elif x <= -2.4e-276:
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1050000.0)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= -2.4e-276)
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1050000.0)
		tmp = 0.5 * (x / t);
	elseif (x <= -2.4e-276)
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1050000.0], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-276], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e6

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

   if -1.05e6 < x < -2.39999999999999983e-276

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in z around inf 56.6%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   3. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   4. Simplified 56.6%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

   if -2.39999999999999983e-276 < x

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around inf 39.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1050000:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-276}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-11}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.3e-11) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.3e-11) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2.3d-11) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * ((x + y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.3e-11) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.3e-11:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.3e-11)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.3e-11)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.3e-11], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.30000000000000014e-11

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around 0 78.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if 2.30000000000000014e-11 < y

   1. Initial program 99.9%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in z around 0 80.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   3. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   4. Simplified 80.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-11}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 5: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{-113}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.05e-113) (* 0.5 (/ (- x z) t)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.05e-113) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2.05d-113) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = (y - z) * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.05e-113) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.05e-113:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.05e-113)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.05e-113)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.05e-113], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.05e-113

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if 2.05e-113 < y

   1. Initial program 99.9%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in x around 0 73.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y - z}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 73.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

      2. associate-*l/ 73.2%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]

      3. *-commutative 73.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{0.5}{t}} \]

   4. Simplified 73.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{-113}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]

Alternative 6: 44.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-106}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.7e-106) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.7e-106) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.7d-106) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.7e-106) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.7e-106:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.7e-106)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.7e-106)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.7e-106], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.69999999999999991e-106

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in x around inf 52.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

   if 1.69999999999999991e-106 < y

   1. Initial program 99.9%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

   2. Taylor expanded in y around inf 52.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-106}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \frac{x}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 0.5 (/ x t)))

C

double code(double x, double y, double z, double t) {
	return 0.5 * (x / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.5d0 * (x / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.5 * (x / t);
}

Python

def code(x, y, z, t):
	return 0.5 * (x / t)

Julia

function code(x, y, z, t)
	return Float64(0.5 * Float64(x / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.5 * (x / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

2. Taylor expanded in x around inf 45.0%

   \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

3. Final simplification 45.0%

   \[\leadsto 0.5 \cdot \frac{x}{t} \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))