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

Percentage Accurate: 99.9% → 99.9%

Time: 4.4s

Alternatives: 7

Speedup: 1.0×

• 26.9% 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: 47.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-183} \lor \neg \left(x \leq -8.8 \cdot 10^{-262}\right) \land \left(x \leq -1.25 \cdot 10^{-296} \lor \neg \left(x \leq 2.1 \cdot 10^{-286}\right) \land x \leq 1.62 \cdot 10^{-236}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e+72)
   (* x (/ 0.5 t))
   (if (or (<= x -1.25e-183)
           (and (not (<= x -8.8e-262))
                (or (<= x -1.25e-296)
                    (and (not (<= x 2.1e-286)) (<= x 1.62e-236)))))
     (* (/ z t) -0.5)
     (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+72) {
		tmp = x * (0.5 / t);
	} else if ((x <= -1.25e-183) || (!(x <= -8.8e-262) && ((x <= -1.25e-296) || (!(x <= 2.1e-286) && (x <= 1.62e-236))))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = (y * 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 (x <= (-1.3d+72)) then
        tmp = x * (0.5d0 / t)
    else if ((x <= (-1.25d-183)) .or. (.not. (x <= (-8.8d-262))) .and. (x <= (-1.25d-296)) .or. (.not. (x <= 2.1d-286)) .and. (x <= 1.62d-236)) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = (y * 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 (x <= -1.3e+72) {
		tmp = x * (0.5 / t);
	} else if ((x <= -1.25e-183) || (!(x <= -8.8e-262) && ((x <= -1.25e-296) || (!(x <= 2.1e-286) && (x <= 1.62e-236))))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e+72:
		tmp = x * (0.5 / t)
	elif (x <= -1.25e-183) or (not (x <= -8.8e-262) and ((x <= -1.25e-296) or (not (x <= 2.1e-286) and (x <= 1.62e-236)))):
		tmp = (z / t) * -0.5
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e+72)
		tmp = Float64(x * Float64(0.5 / t));
	elseif ((x <= -1.25e-183) || (!(x <= -8.8e-262) && ((x <= -1.25e-296) || (!(x <= 2.1e-286) && (x <= 1.62e-236)))))
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e+72)
		tmp = x * (0.5 / t);
	elseif ((x <= -1.25e-183) || (~((x <= -8.8e-262)) && ((x <= -1.25e-296) || (~((x <= 2.1e-286)) && (x <= 1.62e-236)))))
		tmp = (z / t) * -0.5;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e+72], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.25e-183], And[N[Not[LessEqual[x, -8.8e-262]], $MachinePrecision], Or[LessEqual[x, -1.25e-296], And[N[Not[LessEqual[x, 2.1e-286]], $MachinePrecision], LessEqual[x, 1.62e-236]]]]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.29999999999999991e72

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.5%

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

      1. div-sub 81.6%

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

      2. distribute-lft-out 81.6%

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

      3. div-sub 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in x around inf 64.4%

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

      1. associate-*r/ 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r/ 65.7%

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

   7. Simplified 65.7%

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

   if -1.29999999999999991e72 < x < -1.2500000000000001e-183 or -8.79999999999999954e-262 < x < -1.25000000000000008e-296 or 2.09999999999999988e-286 < x < 1.62e-236

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 61.6%

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

      1. *-commutative 61.6%

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

   4. Simplified 61.6%

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

   if -1.2500000000000001e-183 < x < -8.79999999999999954e-262 or -1.25000000000000008e-296 < x < 2.09999999999999988e-286 or 1.62e-236 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 46.2%

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

      1. associate-*r/ 46.2%

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

   4. Simplified 46.2%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-183} \lor \neg \left(x \leq -8.8 \cdot 10^{-262}\right) \land \left(x \leq -1.25 \cdot 10^{-296} \lor \neg \left(x \leq 2.1 \cdot 10^{-286}\right) \land x \leq 1.62 \cdot 10^{-236}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 3: 55.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -950000000000 \lor \neg \left(z \leq 3.8 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -950000000000.0) (not (<= z 3.8e+115)))
   (* (/ z t) -0.5)
   (* 0.5 (/ x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -950000000000.0) || !(z <= 3.8e+115)) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (x / 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 <= (-950000000000.0d0)) .or. (.not. (z <= 3.8d+115))) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = 0.5d0 * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -950000000000.0) || !(z <= 3.8e+115)) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -950000000000.0) or not (z <= 3.8e+115):
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -950000000000.0) || !(z <= 3.8e+115))
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(0.5 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -950000000000.0) || ~((z <= 3.8e+115)))
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -950000000000.0], N[Not[LessEqual[z, 3.8e+115]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e11 or 3.8000000000000001e115 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

   4. Simplified 76.9%

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

   if -9.5e11 < z < 3.8000000000000001e115

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 49.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -950000000000 \lor \neg \left(z \leq 3.8 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 4: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.6e+43) (* 0.5 (/ (- x z) t)) (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.6e+43) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y * 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 <= 2.6d+43) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = (y * 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 <= 2.6e+43) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.6e+43:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.6e+43)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.6e+43)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.6e+43], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.60000000000000021e43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.5%

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

   if 2.60000000000000021e43 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 63.2%

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

      1. associate-*r/ 63.2%

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

   4. Simplified 63.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]

Alternative 5: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.1e+15) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+15) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / 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 <= (-2.1d+15)) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+15) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e+15:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e+15)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.1e+15)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.1e+15], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e15

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.7%

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

   if -2.1e15 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 6: 37.6% 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 36.4%

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

3. Final simplification 36.4%

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

Alternative 7: 37.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * (0.5 / 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 = x * (0.5d0 / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 95.4%

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

   1. div-sub 93.0%

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

   2. distribute-lft-out 93.0%

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

   3. div-sub 95.4%

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

4. Simplified 95.4%

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

5. Taylor expanded in x around inf 36.4%

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

   1. associate-*r/ 36.6%

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

   2. *-commutative 36.6%

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

   3. associate-*r/ 36.6%

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

7. Simplified 36.6%

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

8. Final simplification 36.6%

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

Reproduce

herbie shell --seed 2023320 
(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)))