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

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

Alternatives: 8

Speedup: 1.0×

• 26.1% 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. Final simplification 100.0%

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

Alternative 2: 47.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-73} \lor \neg \left(x \leq -3.35 \cdot 10^{-121}\right) \land x \leq 3 \cdot 10^{-284}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e+24)
   (/ x (* t 2.0))
   (if (or (<= x -6.3e-73) (and (not (<= x -3.35e-121)) (<= x 3e-284)))
     (* (/ z t) -0.5)
     (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e+24) {
		tmp = x / (t * 2.0);
	} else if ((x <= -6.3e-73) || (!(x <= -3.35e-121) && (x <= 3e-284))) {
		tmp = (z / t) * -0.5;
	} 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 <= (-8.5d+24)) then
        tmp = x / (t * 2.0d0)
    else if ((x <= (-6.3d-73)) .or. (.not. (x <= (-3.35d-121))) .and. (x <= 3d-284)) then
        tmp = (z / t) * (-0.5d0)
    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 <= -8.5e+24) {
		tmp = x / (t * 2.0);
	} else if ((x <= -6.3e-73) || (!(x <= -3.35e-121) && (x <= 3e-284))) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e+24:
		tmp = x / (t * 2.0)
	elif (x <= -6.3e-73) or (not (x <= -3.35e-121) and (x <= 3e-284)):
		tmp = (z / t) * -0.5
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e+24)
		tmp = Float64(x / Float64(t * 2.0));
	elseif ((x <= -6.3e-73) || (!(x <= -3.35e-121) && (x <= 3e-284)))
		tmp = Float64(Float64(z / t) * -0.5);
	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 <= -8.5e+24)
		tmp = x / (t * 2.0);
	elseif ((x <= -6.3e-73) || (~((x <= -3.35e-121)) && (x <= 3e-284)))
		tmp = (z / t) * -0.5;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e+24], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -6.3e-73], And[N[Not[LessEqual[x, -3.35e-121]], $MachinePrecision], LessEqual[x, 3e-284]]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999959e24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.1%

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

   if -8.49999999999999959e24 < x < -6.29999999999999956e-73 or -3.3500000000000001e-121 < x < 3e-284

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 55.3%

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

      1. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   if -6.29999999999999956e-73 < x < -3.3500000000000001e-121 or 3e-284 < 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 44.8%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-73} \lor \neg \left(x \leq -3.35 \cdot 10^{-121}\right) \land x \leq 3 \cdot 10^{-284}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+47}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+68} \lor \neg \left(y \leq 1.5 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.9e+47)
   (/ (- x z) (* t 2.0))
   (if (or (<= y 1.5e+68) (not (<= y 1.5e+77)))
     (/ (+ x y) (* t 2.0))
     (* (/ z t) -0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9e+47) {
		tmp = (x - z) / (t * 2.0);
	} else if ((y <= 1.5e+68) || !(y <= 1.5e+77)) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = (z / t) * -0.5;
	}
	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 <= 1.9d+47) then
        tmp = (x - z) / (t * 2.0d0)
    else if ((y <= 1.5d+68) .or. (.not. (y <= 1.5d+77))) then
        tmp = (x + y) / (t * 2.0d0)
    else
        tmp = (z / t) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.9e+47) {
		tmp = (x - z) / (t * 2.0);
	} else if ((y <= 1.5e+68) || !(y <= 1.5e+77)) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = (z / t) * -0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.9e+47:
		tmp = (x - z) / (t * 2.0)
	elif (y <= 1.5e+68) or not (y <= 1.5e+77):
		tmp = (x + y) / (t * 2.0)
	else:
		tmp = (z / t) * -0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.9e+47)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	elseif ((y <= 1.5e+68) || !(y <= 1.5e+77))
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(z / t) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.9e+47)
		tmp = (x - z) / (t * 2.0);
	elseif ((y <= 1.5e+68) || ~((y <= 1.5e+77)))
		tmp = (x + y) / (t * 2.0);
	else
		tmp = (z / t) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.9e+47], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.5e+68], N[Not[LessEqual[y, 1.5e+77]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.9000000000000002e47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.5%

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

   if 1.9000000000000002e47 < y < 1.5000000000000001e68 or 1.4999999999999999e77 < 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 86.9%

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

      1. +-commutative 86.9%

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

   5. Simplified 86.9%

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

   if 1.5000000000000001e68 < y < 1.4999999999999999e77

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 93.8%

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

      1. *-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{+47}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+68} \lor \neg \left(y \leq 1.5 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+181} \lor \neg \left(z \leq 3.7 \cdot 10^{+207}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.9e+181) (not (<= z 3.7e+207)))
   (* (/ z t) -0.5)
   (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e+181) || !(z <= 3.7e+207)) {
		tmp = (z / t) * -0.5;
	} 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 <= (-5.9d+181)) .or. (.not. (z <= 3.7d+207))) then
        tmp = (z / t) * (-0.5d0)
    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 <= -5.9e+181) || !(z <= 3.7e+207)) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.9e+181) or not (z <= 3.7e+207):
		tmp = (z / t) * -0.5
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.9e+181) || !(z <= 3.7e+207))
		tmp = Float64(Float64(z / t) * -0.5);
	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 <= -5.9e+181) || ~((z <= 3.7e+207)))
		tmp = (z / t) * -0.5;
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.9e+181], N[Not[LessEqual[z, 3.7e+207]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8999999999999997e181 or 3.7e207 < 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 88.9%

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

      1. *-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -5.8999999999999997e181 < z < 3.7e207

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+181} \lor \neg \left(z \leq 3.7 \cdot 10^{+207}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1850000:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1850000.0) (/ (- 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 <= 1850000.0) {
		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 <= 1850000.0d0) 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 <= 1850000.0) {
		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 <= 1850000.0:
		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 <= 1850000.0)
		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 <= 1850000.0)
		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, 1850000.0], 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 < 1.85e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.1%

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

   if 1.85e6 < 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 84.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1850000:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e+24) (/ x (* t 2.0)) (* (/ z t) -0.5)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e+24) {
		tmp = x / (t * 2.0);
	} else {
		tmp = (z / t) * -0.5;
	}
	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 <= (-8.5d+24)) then
        tmp = x / (t * 2.0d0)
    else
        tmp = (z / t) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e+24) {
		tmp = x / (t * 2.0);
	} else {
		tmp = (z / t) * -0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e+24:
		tmp = x / (t * 2.0)
	else:
		tmp = (z / t) * -0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e+24)
		tmp = Float64(x / Float64(t * 2.0));
	else
		tmp = Float64(Float64(z / t) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e+24)
		tmp = x / (t * 2.0);
	else
		tmp = (z / t) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e+24], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999959e24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.1%

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

   if -8.49999999999999959e24 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 39.8%

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

      1. *-commutative 39.8%

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

   5. Simplified 39.8%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(z * 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 z around inf 35.9%

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

   1. associate-*r/ 35.9%

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

   2. metadata-eval 35.9%

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

   3. distribute-lft-neg-in 35.9%

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

   4. *-commutative 35.9%

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

   5. distribute-neg-frac 35.9%

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

   6. associate-*r/ 35.8%

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

   7. distribute-rgt-neg-in 35.8%

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

   8. distribute-neg-frac 35.8%

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

   9. metadata-eval 35.8%

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

5. Simplified 35.8%

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

6. Final simplification 35.8%

   \[\leadsto z \cdot \frac{-0.5}{t} \]
7. Add Preprocessing

Alternative 8: 37.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 = (z / t) * (-0.5d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf 35.9%

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

   1. *-commutative 35.9%

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

5. Simplified 35.9%

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

6. Final simplification 35.9%

   \[\leadsto \frac{z}{t} \cdot -0.5 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))