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

Percentage Accurate: 100.0% → 100.0%

Time: 5.8s

Alternatives: 9

Speedup: 1.0×

• 26.4% 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: 100.0% 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: 100.0% 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: 46.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-125} \lor \neg \left(x \leq -2.9 \cdot 10^{-209}\right) \land x \leq 1.55 \cdot 10^{-280}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.7e+20)
   (/ 0.5 (/ t x))
   (if (or (<= x -3.3e-125) (and (not (<= x -2.9e-209)) (<= x 1.55e-280)))
     (* (/ z t) -0.5)
     (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.7e+20) {
		tmp = 0.5 / (t / x);
	} else if ((x <= -3.3e-125) || (!(x <= -2.9e-209) && (x <= 1.55e-280))) {
		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 <= (-4.7d+20)) then
        tmp = 0.5d0 / (t / x)
    else if ((x <= (-3.3d-125)) .or. (.not. (x <= (-2.9d-209))) .and. (x <= 1.55d-280)) 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 <= -4.7e+20) {
		tmp = 0.5 / (t / x);
	} else if ((x <= -3.3e-125) || (!(x <= -2.9e-209) && (x <= 1.55e-280))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.7e+20:
		tmp = 0.5 / (t / x)
	elif (x <= -3.3e-125) or (not (x <= -2.9e-209) and (x <= 1.55e-280)):
		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 <= -4.7e+20)
		tmp = Float64(0.5 / Float64(t / x));
	elseif ((x <= -3.3e-125) || (!(x <= -2.9e-209) && (x <= 1.55e-280)))
		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 <= -4.7e+20)
		tmp = 0.5 / (t / x);
	elseif ((x <= -3.3e-125) || (~((x <= -2.9e-209)) && (x <= 1.55e-280)))
		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, -4.7e+20], N[(0.5 / N[(t / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.3e-125], And[N[Not[LessEqual[x, -2.9e-209]], $MachinePrecision], LessEqual[x, 1.55e-280]]], 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 < -4.7e20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.8%

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

      1. associate-*r/ 60.8%

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

      2. associate-/l* 60.7%

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

   4. Simplified 60.7%

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

   if -4.7e20 < x < -3.3000000000000001e-125 or -2.90000000000000026e-209 < x < 1.55000000000000011e-280

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.6%

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

      1. *-commutative 58.6%

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

   4. Simplified 58.6%

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

   if -3.3000000000000001e-125 < x < -2.90000000000000026e-209 or 1.55000000000000011e-280 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 39.2%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-125} \lor \neg \left(x \leq -2.9 \cdot 10^{-209}\right) \land x \leq 1.55 \cdot 10^{-280}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-124} \lor \neg \left(x \leq -4.4 \cdot 10^{-209}\right) \land x \leq 1.02 \cdot 10^{-280}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e+20)
   (/ (* x 0.5) t)
   (if (or (<= x -8.5e-124) (and (not (<= x -4.4e-209)) (<= x 1.02e-280)))
     (* (/ z t) -0.5)
     (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e+20) {
		tmp = (x * 0.5) / t;
	} else if ((x <= -8.5e-124) || (!(x <= -4.4e-209) && (x <= 1.02e-280))) {
		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 <= (-6d+20)) then
        tmp = (x * 0.5d0) / t
    else if ((x <= (-8.5d-124)) .or. (.not. (x <= (-4.4d-209))) .and. (x <= 1.02d-280)) 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 <= -6e+20) {
		tmp = (x * 0.5) / t;
	} else if ((x <= -8.5e-124) || (!(x <= -4.4e-209) && (x <= 1.02e-280))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e+20:
		tmp = (x * 0.5) / t
	elif (x <= -8.5e-124) or (not (x <= -4.4e-209) and (x <= 1.02e-280)):
		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 <= -6e+20)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif ((x <= -8.5e-124) || (!(x <= -4.4e-209) && (x <= 1.02e-280)))
		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 <= -6e+20)
		tmp = (x * 0.5) / t;
	elseif ((x <= -8.5e-124) || (~((x <= -4.4e-209)) && (x <= 1.02e-280)))
		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, -6e+20], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[x, -8.5e-124], And[N[Not[LessEqual[x, -4.4e-209]], $MachinePrecision], LessEqual[x, 1.02e-280]]], 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 < -6e20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.8%

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

      1. associate-*r/ 60.8%

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

   4. Simplified 60.8%

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

   if -6e20 < x < -8.5000000000000002e-124 or -4.40000000000000019e-209 < x < 1.02000000000000005e-280

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 57.9%

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

      1. *-commutative 57.9%

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

   4. Simplified 57.9%

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

   if -8.5000000000000002e-124 < x < -4.40000000000000019e-209 or 1.02000000000000005e-280 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 39.0%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-124} \lor \neg \left(x \leq -4.4 \cdot 10^{-209}\right) \land x \leq 1.02 \cdot 10^{-280}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 56.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+46} \lor \neg \left(z \leq 1.55 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e+46) (not (<= z 1.55e+53)))
   (* (/ z t) -0.5)
   (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e+46) || !(z <= 1.55e+53)) {
		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 ((z <= (-2.25d+46)) .or. (.not. (z <= 1.55d+53))) 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 ((z <= -2.25e+46) || !(z <= 1.55e+53)) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e+46) or not (z <= 1.55e+53):
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.25e+46) || !(z <= 1.55e+53))
		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 ((z <= -2.25e+46) || ~((z <= 1.55e+53)))
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.25e+46], N[Not[LessEqual[z, 1.55e+53]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25000000000000005e46 or 1.5500000000000001e53 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 74.7%

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

      1. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -2.25000000000000005e46 < z < 1.5500000000000001e53

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 50.9%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+46} \lor \neg \left(z \leq 1.55 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+121}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.25e+121) (* 0.5 (/ (- x z) t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.25e+121) {
		tmp = 0.5 * ((x - z) / 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 <= 1.25d+121) then
        tmp = 0.5d0 * ((x - z) / 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 <= 1.25e+121) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.25e+121:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.25e+121)
		tmp = Float64(0.5 * Float64(Float64(x - z) / 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 <= 1.25e+121)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.25e+121], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.25000000000000002e121

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.8%

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

   if 1.25000000000000002e121 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+121}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-56}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.65e-56) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.65e-56) {
		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 (y <= 1.65d-56) 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 (y <= 1.65e-56) {
		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 y <= 1.65e-56:
		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 (y <= 1.65e-56)
		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 (y <= 1.65e-56)
		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[y, 1.65e-56], 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 y < 1.64999999999999992e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.7%

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

   if 1.64999999999999992e-56 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 80.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-56}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 7: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right) \end{array} \]

FPCore

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

C

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

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 / t) * (x + (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 96.8%

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

   1. associate-*r/ 96.8%

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

   2. associate-*l/ 96.7%

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

   3. associate-*r/ 96.7%

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

   4. associate-*l/ 96.6%

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

   5. distribute-lft-in 99.7%

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

4. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 8: 38.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 38.2%

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

3. Final simplification 38.2%

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

Alternative 9: 4.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x 0.0))

C

double code(double x, double y, double z, double t) {
	return x * 0.0;
}

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 * 0.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * 0.0;
}

Python

def code(x, y, z, t):
	return x * 0.0

Julia

function code(x, y, z, t)
	return Float64(x * 0.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * 0.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * 0.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf 34.2%

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

   1. associate-*r/ 34.2%

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

4. Simplified 34.2%

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

   1. expm1-log1p-u 20.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{0.5 \cdot x}{t}\right)\right)} \]

   2. expm1-udef 14.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{0.5 \cdot x}{t}\right)} - 1} \]

   3. associate-*l/ 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{0.5}{t} \cdot x}\right)} - 1 \]

   4. *-commutative 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{x \cdot \frac{0.5}{t}}\right)} - 1 \]

   5. clear-num 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{1}{\frac{t}{0.5}}}\right)} - 1 \]

   6. div-inv 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\color{blue}{t \cdot \frac{1}{0.5}}}\right)} - 1 \]

   7. metadata-eval 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{t \cdot \color{blue}{2}}\right)} - 1 \]

   8. *-commutative 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\color{blue}{2 \cdot t}}\right)} - 1 \]

   9. count-2 14.3%

      \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\color{blue}{t + t}}\right)} - 1 \]

   10. flip-+ 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}}\right)} - 1 \]

   11. +-inverses 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\frac{\color{blue}{0}}{t - t}}\right)} - 1 \]

   12. +-inverses 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\frac{\color{blue}{t - t}}{t - t}}\right)} - 1 \]

   13. +-inverses 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\frac{t - t}{\color{blue}{0}}}\right)} - 1 \]

   14. +-inverses 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \frac{1}{\frac{t - t}{\color{blue}{t \cdot t - t \cdot t}}}\right)} - 1 \]

   15. clear-num 0.0%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}\right)} - 1 \]

   16. flip-+ 2.3%

       \[\leadsto e^{\mathsf{log1p}\left(x \cdot \color{blue}{\left(t + t\right)}\right)} - 1 \]

6. Applied egg-rr 2.3%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(t + t\right)\right)} - 1} \]

8. Simplified 3.5%

   \[\leadsto \color{blue}{0 \cdot x} \]

9. Final simplification 3.5%

   \[\leadsto x \cdot 0 \]

Reproduce

herbie shell --seed 2023274 
(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)))