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

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

Alternatives: 9

Speedup: 1.0×

• 27.0% 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+135} \lor \neg \left(z \leq 1.75 \cdot 10^{+53}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e+135) (not (<= z 1.75e+53)))
   (* (- y z) (/ 0.5 t))
   (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+135) || !(z <= 1.75e+53)) {
		tmp = (y - z) * (0.5 / t);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	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 <= (-2.6d+135)) .or. (.not. (z <= 1.75d+53))) then
        tmp = (y - z) * (0.5d0 / t)
    else
        tmp = (x + y) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+135) || !(z <= 1.75e+53)) {
		tmp = (y - z) * (0.5 / t);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e+135) or not (z <= 1.75e+53):
		tmp = (y - z) * (0.5 / t)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e+135) || !(z <= 1.75e+53))
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e+135) || ~((z <= 1.75e+53)))
		tmp = (y - z) * (0.5 / t);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e+135], N[Not[LessEqual[z, 1.75e+53]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e135 or 1.75000000000000009e53 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.6%

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

      1. associate-*r/ 91.6%

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

      2. associate-*l/ 91.4%

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

      3. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   if -2.6e135 < z < 1.75000000000000009e53

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.8%

      \[\leadsto \frac{\color{blue}{x + y}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative 86.8%

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

   5. Simplified 86.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+135} \lor \neg \left(z \leq 1.75 \cdot 10^{+53}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+137}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.2e-305)
   (/ x (* t 2.0))
   (if (<= y 4.6e+137) (/ (* -0.5 z) t) (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.2e-305) {
		tmp = x / (t * 2.0);
	} else if (y <= 4.6e+137) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = y / (t * 2.0);
	}
	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 <= 3.2d-305) then
        tmp = x / (t * 2.0d0)
    else if (y <= 4.6d+137) then
        tmp = ((-0.5d0) * z) / t
    else
        tmp = y / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.2e-305) {
		tmp = x / (t * 2.0);
	} else if (y <= 4.6e+137) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.2e-305:
		tmp = x / (t * 2.0)
	elif y <= 4.6e+137:
		tmp = (-0.5 * z) / t
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.2e-305)
		tmp = Float64(x / Float64(t * 2.0));
	elseif (y <= 4.6e+137)
		tmp = Float64(Float64(-0.5 * z) / t);
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.2e-305)
		tmp = x / (t * 2.0);
	elseif (y <= 4.6e+137)
		tmp = (-0.5 * z) / t;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.2e-305], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+137], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.20000000000000009e-305

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 35.2%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]

   if 3.20000000000000009e-305 < y < 4.59999999999999999e137

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*l/ 50.6%

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

   5. Simplified 50.6%

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

   if 4.59999999999999999e137 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+137}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.3e+98) (/ x (* t 2.0)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3e+98) {
		tmp = x / (t * 2.0);
	} 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 (x <= (-3.3d+98)) then
        tmp = x / (t * 2.0d0)
    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 (x <= -3.3e+98) {
		tmp = x / (t * 2.0);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3e+98:
		tmp = x / (t * 2.0)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3e+98)
		tmp = Float64(x / Float64(t * 2.0));
	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 (x <= -3.3e+98)
		tmp = x / (t * 2.0);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3e+98], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000028e98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 61.0%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]

   if -3.30000000000000028e98 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. associate-*l/ 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9.6e-147) (/ (- x z) (* t 2.0)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.6e-147) {
		tmp = (x - z) / (t * 2.0);
	} 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 <= 9.6d-147) then
        tmp = (x - z) / (t * 2.0d0)
    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 <= 9.6e-147) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.6e-147:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.6e-147)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	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 <= 9.6e-147)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.6e-147], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.59999999999999994e-147

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.6%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if 9.59999999999999994e-147 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. associate-*l/ 79.4%

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

      3. *-commutative 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.38 \cdot 10^{-154}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.38e-154) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.38e-154) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	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 <= 1.38d-154) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.38e-154) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.38e-154:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.38e-154)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.38e-154)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.38e-154], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.37999999999999995e-154

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if 1.37999999999999995e-154 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.38 \cdot 10^{-154}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.38 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.38e-154) (/ x (* t 2.0)) (/ y (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.38e-154) {
		tmp = x / (t * 2.0);
	} else {
		tmp = y / (t * 2.0);
	}
	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 <= 1.38d-154) then
        tmp = x / (t * 2.0d0)
    else
        tmp = y / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.38e-154) {
		tmp = x / (t * 2.0);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.38e-154:
		tmp = x / (t * 2.0)
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.38e-154)
		tmp = Float64(x / Float64(t * 2.0));
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.38e-154)
		tmp = x / (t * 2.0);
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.38e-154], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.37999999999999995e-154

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 38.5%

      \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]

   if 1.37999999999999995e-154 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 53.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.38 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.9% 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. Add Preprocessing

3. Taylor expanded in x around 0 96.9%

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

   1. div-sub 95.0%

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

   2. distribute-lft-out 95.0%

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

   3. +-commutative 95.0%

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

   4. div-sub 96.9%

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

5. Simplified 96.9%

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

6. Taylor expanded in x around inf 34.4%

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

   1. *-commutative 34.4%

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

   2. associate-*l/ 34.7%

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

   3. associate-*r/ 34.6%

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

8. Simplified 34.6%

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

9. Final simplification 34.6%

   \[\leadsto x \cdot \frac{0.5}{t} \]
10. Add Preprocessing

Alternative 9: 38.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t \cdot 2} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / (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 / (t * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 34.7%

   \[\leadsto \frac{\color{blue}{x}}{t \cdot 2} \]

4. Final simplification 34.7%

   \[\leadsto \frac{x}{t \cdot 2} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))