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

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

Alternatives: 8

Speedup: 1.0×

• 26.7% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 81.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+113} \lor \neg \left(z \leq 1.22 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+113) (not (<= z 1.22e+64)))
   (/ (* z -0.5) t)
   (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+113) || !(z <= 1.22e+64)) {
		tmp = (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 <= (-2.8d+113)) .or. (.not. (z <= 1.22d+64))) then
        tmp = (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 <= -2.8e+113) || !(z <= 1.22e+64)) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+113) or not (z <= 1.22e+64):
		tmp = (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 <= -2.8e+113) || !(z <= 1.22e+64))
		tmp = Float64(Float64(z * -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 <= -2.8e+113) || ~((z <= 1.22e+64)))
		tmp = (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, -2.8e+113], N[Not[LessEqual[z, 1.22e+64]], $MachinePrecision]], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999998e113 or 1.21999999999999994e64 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. associate-*r/ 82.9%

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

   5. Simplified 82.9%

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

   if -2.79999999999999998e113 < z < 1.21999999999999994e64

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 87.4%

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

      1. +-commutative 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+113} \lor \neg \left(z \leq 1.22 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-178}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.26e+53)
   (/ x (* t 2.0))
   (if (<= x 2.9e-178) (/ (* z -0.5) t) (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.26e+53) {
		tmp = x / (t * 2.0);
	} else if (x <= 2.9e-178) {
		tmp = (z * -0.5) / 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 (x <= (-1.26d+53)) then
        tmp = x / (t * 2.0d0)
    else if (x <= 2.9d-178) then
        tmp = (z * (-0.5d0)) / 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 (x <= -1.26e+53) {
		tmp = x / (t * 2.0);
	} else if (x <= 2.9e-178) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.26e+53:
		tmp = x / (t * 2.0)
	elif x <= 2.9e-178:
		tmp = (z * -0.5) / t
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.26e+53)
		tmp = Float64(x / Float64(t * 2.0));
	elseif (x <= 2.9e-178)
		tmp = Float64(Float64(z * -0.5) / 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 (x <= -1.26e+53)
		tmp = x / (t * 2.0);
	elseif (x <= 2.9e-178)
		tmp = (z * -0.5) / t;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.26e+53], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-178], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25999999999999999e53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 69.4%

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

   if -1.25999999999999999e53 < x < 2.8999999999999998e-178

   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. associate-*r/ 51.4%

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

   5. Simplified 51.4%

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

   if 2.8999999999999998e-178 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 41.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-178}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3e-8) (/ (- 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 <= 3e-8) {
		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 <= 3d-8) 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 <= 3e-8) {
		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 <= 3e-8:
		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 <= 3e-8)
		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 <= 3e-8)
		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, 3e-8], 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 < 2.99999999999999973e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.2%

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

   if 2.99999999999999973e-8 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.4%

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

Alternative 5: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.4e+25) (/ (- x z) (* t 2.0)) (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.4e+25) {
		tmp = (x - z) / (t * 2.0);
	} 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 (y <= 7.4d+25) then
        tmp = (x - z) / (t * 2.0d0)
    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 (y <= 7.4e+25) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.4e+25:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.4e+25)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	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 (y <= 7.4e+25)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.4e+25], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.3999999999999998e25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.6%

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

   if 7.3999999999999998e25 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 5.4e-8) (/ x (* t 2.0)) (/ y (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.4e-8) {
		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 <= 5.4d-8) 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 <= 5.4e-8) {
		tmp = x / (t * 2.0);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 5.4e-8:
		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 <= 5.4e-8)
		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 <= 5.4e-8)
		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, 5.4e-8], 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 < 5.40000000000000005e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 39.7%

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

   if 5.40000000000000005e-8 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 62.0%

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

Alternative 7: 46.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.2e-8) (/ x (* t 2.0)) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.2e-8) {
		tmp = x / (t * 2.0);
	} 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 <= 4.2d-8) then
        tmp = x / (t * 2.0d0)
    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 <= 4.2e-8) {
		tmp = x / (t * 2.0);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.2e-8:
		tmp = x / (t * 2.0)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.2e-8)
		tmp = Float64(x / Float64(t * 2.0));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.2e-8)
		tmp = x / (t * 2.0);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.2e-8], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.19999999999999989e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 39.7%

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

   if 4.19999999999999989e-8 < y

   1. Initial program 99.9%

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

      1. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

      2. inv-pow 99.7%

         \[\leadsto \color{blue}{{\left(\frac{t \cdot 2}{\left(x + y\right) - z}\right)}^{-1}} \]

      3. associate--l+ 99.7%

         \[\leadsto {\left(\frac{t \cdot 2}{\color{blue}{x + \left(y - z\right)}}\right)}^{-1} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{{\left(\frac{t \cdot 2}{x + \left(y - z\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot 2}{x + \left(y - z\right)}}} \]

      2. associate-/l* 99.6%

         \[\leadsto \frac{1}{\color{blue}{t \cdot \frac{2}{x + \left(y - z\right)}}} \]

      3. associate-+r- 99.6%

         \[\leadsto \frac{1}{t \cdot \frac{2}{\color{blue}{\left(x + y\right) - z}}} \]

      4. +-commutative 99.6%

         \[\leadsto \frac{1}{t \cdot \frac{2}{\color{blue}{\left(y + x\right)} - z}} \]

      5. associate-+r- 99.6%

         \[\leadsto \frac{1}{t \cdot \frac{2}{\color{blue}{y + \left(x - z\right)}}} \]

   6. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{1}{t \cdot \frac{2}{y + \left(x - z\right)}}} \]

   7. Taylor expanded in y around inf 62.0%

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

      1. associate-*r/ 62.0%

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

   9. Simplified 62.0%

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

       1. *-commutative 62.0%

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

       2. associate-/l* 61.8%

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

   11. Applied egg-rr 61.8%

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

Alternative 8: 37.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(y * 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. Step-by-step derivation

   1. clear-num 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot 2}{\left(x + y\right) - z}}} \]

   2. inv-pow 99.4%

      \[\leadsto \color{blue}{{\left(\frac{t \cdot 2}{\left(x + y\right) - z}\right)}^{-1}} \]

   3. associate--l+ 99.4%

      \[\leadsto {\left(\frac{t \cdot 2}{\color{blue}{x + \left(y - z\right)}}\right)}^{-1} \]

4. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{{\left(\frac{t \cdot 2}{x + \left(y - z\right)}\right)}^{-1}} \]
5. Step-by-step derivation

   1. unpow-1 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot 2}{x + \left(y - z\right)}}} \]

   2. associate-/l* 99.3%

      \[\leadsto \frac{1}{\color{blue}{t \cdot \frac{2}{x + \left(y - z\right)}}} \]

   3. associate-+r- 99.3%

      \[\leadsto \frac{1}{t \cdot \frac{2}{\color{blue}{\left(x + y\right) - z}}} \]

   4. +-commutative 99.3%

      \[\leadsto \frac{1}{t \cdot \frac{2}{\color{blue}{\left(y + x\right)} - z}} \]

   5. associate-+r- 99.3%

      \[\leadsto \frac{1}{t \cdot \frac{2}{\color{blue}{y + \left(x - z\right)}}} \]

6. Simplified 99.3%

   \[\leadsto \color{blue}{\frac{1}{t \cdot \frac{2}{y + \left(x - z\right)}}} \]

7. Taylor expanded in y around inf 39.4%

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

   1. associate-*r/ 39.4%

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

9. Simplified 39.4%

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

    1. *-commutative 39.4%

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

    2. associate-/l* 39.3%

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

11. Applied egg-rr 39.3%

    \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024132 
(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)))