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

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 8

Speedup: 1.0×

• 27.5% 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. Add Preprocessing

Alternative 2: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-13)
   (/ (* x 0.5) t)
   (if (<= (+ x y) 2e+17) (/ (* z -0.5) t) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-13) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 2e+17) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-5d-13)) then
        tmp = (x * 0.5d0) / t
    else if ((x + y) <= 2d+17) then
        tmp = (z * (-0.5d0)) / t
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-13) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 2e+17) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e-13:
		tmp = (x * 0.5) / t
	elif (x + y) <= 2e+17:
		tmp = (z * -0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e-13)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (Float64(x + y) <= 2e+17)
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e-13)
		tmp = (x * 0.5) / t;
	elseif ((x + y) <= 2e+17)
		tmp = (z * -0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-13], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e+17], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -4.9999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot x}}{t} \]

      5. *-lowering-*.f64 39.4

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

   5. Simplified 39.4%

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

   if -4.9999999999999999e-13 < (+.f64 x y) < 2e17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. *-lowering-*.f64 80.0

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

   5. Simplified 80.0%

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

   if 2e17 < (+.f64 x 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

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. *-lowering-*.f64 44.9

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

   5. Simplified 44.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-13)
   (/ (* x 0.5) t)
   (if (<= (+ x y) 2e+17) (* z (/ -0.5 t)) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-13) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 2e+17) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-5d-13)) then
        tmp = (x * 0.5d0) / t
    else if ((x + y) <= 2d+17) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-13) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 2e+17) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e-13:
		tmp = (x * 0.5) / t
	elif (x + y) <= 2e+17:
		tmp = z * (-0.5 / t)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e-13)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (Float64(x + y) <= 2e+17)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e-13)
		tmp = (x * 0.5) / t;
	elseif ((x + y) <= 2e+17)
		tmp = z * (-0.5 / t);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-13], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e+17], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -4.9999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot x}}{t} \]

      5. *-lowering-*.f64 39.4

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

   5. Simplified 39.4%

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

   if -4.9999999999999999e-13 < (+.f64 x y) < 2e17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. *-lowering-*.f64 80.0

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

   5. Simplified 80.0%

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

      2. metadata-eval N/A

         \[\leadsto z \cdot \frac{\color{blue}{\frac{1}{-2}}}{t} \]

      3. associate-/r* N/A

         \[\leadsto z \cdot \color{blue}{\frac{1}{-2 \cdot t}} \]

      4. *-commutative N/A

         \[\leadsto z \cdot \frac{1}{\color{blue}{t \cdot -2}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{t \cdot -2} \cdot z} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{t \cdot -2} \cdot z} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{\color{blue}{-2 \cdot t}} \cdot z \]

      8. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{-2}}{t}} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

      10. /-lowering-/.f64 79.7

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

   7. Applied egg-rr 79.7%

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

   if 2e17 < (+.f64 x 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

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. *-lowering-*.f64 44.9

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

   5. Simplified 44.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+43}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= z -2.4e+74) t_1 (if (<= z 7e+43) (/ (+ x y) (* t 2.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -2.4e+74) {
		tmp = t_1;
	} else if (z <= 7e+43) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    if (z <= (-2.4d+74)) then
        tmp = t_1
    else if (z <= 7d+43) then
        tmp = (x + y) / (t * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -2.4e+74) {
		tmp = t_1;
	} else if (z <= 7e+43) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	tmp = 0
	if z <= -2.4e+74:
		tmp = t_1
	elif z <= 7e+43:
		tmp = (x + y) / (t * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (z <= -2.4e+74)
		tmp = t_1;
	elseif (z <= 7e+43)
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	tmp = 0.0;
	if (z <= -2.4e+74)
		tmp = t_1;
	elseif (z <= 7e+43)
		tmp = (x + y) / (t * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.4e+74], t$95$1, If[LessEqual[z, 7e+43], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000008e74 or 7.0000000000000002e43 < 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

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. *-lowering-*.f64 73.1

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

   5. Simplified 73.1%

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

   if -2.40000000000000008e74 < z < 7.0000000000000002e43

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 88.5

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

   5. Simplified 88.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+43}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-202}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-202) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-202) {
		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 ((x + y) <= (-5d-202)) 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 ((x + y) <= -5e-202) {
		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 (x + y) <= -5e-202:
		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 (Float64(x + y) <= -5e-202)
		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 ((x + y) <= -5e-202)
		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[N[(x + y), $MachinePrecision], -5e-202], 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 (+.f64 x y) < -4.99999999999999973e-202

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 65.1

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

   5. Simplified 65.1%

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

   if -4.99999999999999973e-202 < (+.f64 x 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

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

      1. --lowering--.f64 71.0

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

   5. Simplified 71.0%

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

Alternative 6: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+17) (/ (- x z) (* t 2.0)) (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+17) {
		tmp = (x - z) / (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 ((x + y) <= 2d+17) then
        tmp = (x - z) / (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 ((x + y) <= 2e+17) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e+17:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e+17)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2e+17)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e+17], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 2e17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 73.0

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

   5. Simplified 73.0%

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

   if 2e17 < (+.f64 x 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

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. *-lowering-*.f64 44.9

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

   5. Simplified 44.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-13) (/ (* x 0.5) t) (* z (/ -0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-13) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 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 + y) <= (-5d-13)) then
        tmp = (x * 0.5d0) / t
    else
        tmp = 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 + y) <= -5e-13) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e-13:
		tmp = (x * 0.5) / t
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e-13)
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e-13)
		tmp = (x * 0.5) / t;
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-13], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot x}}{t} \]

      5. *-lowering-*.f64 39.4

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

   5. Simplified 39.4%

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

   if -4.9999999999999999e-13 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. *-lowering-*.f64 48.8

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

   5. Simplified 48.8%

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

      2. metadata-eval N/A

         \[\leadsto z \cdot \frac{\color{blue}{\frac{1}{-2}}}{t} \]

      3. associate-/r* N/A

         \[\leadsto z \cdot \color{blue}{\frac{1}{-2 \cdot t}} \]

      4. *-commutative N/A

         \[\leadsto z \cdot \frac{1}{\color{blue}{t \cdot -2}} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{t \cdot -2} \cdot z} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{t \cdot -2} \cdot z} \]

      7. *-commutative N/A

         \[\leadsto \frac{1}{\color{blue}{-2 \cdot t}} \cdot z \]

      8. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{-2}}{t}} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

      10. /-lowering-/.f64 48.7

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

   7. Applied egg-rr 48.7%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.9% accurate, 1.4× 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

   \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

   3. *-commutative N/A

      \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

   4. *-lowering-*.f64 39.6

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

5. Simplified 39.6%

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

   1. associate-/l* N/A

      \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

   2. metadata-eval N/A

      \[\leadsto z \cdot \frac{\color{blue}{\frac{1}{-2}}}{t} \]

   3. associate-/r* N/A

      \[\leadsto z \cdot \color{blue}{\frac{1}{-2 \cdot t}} \]

   4. *-commutative N/A

      \[\leadsto z \cdot \frac{1}{\color{blue}{t \cdot -2}} \]

   5. *-commutative N/A

      \[\leadsto \color{blue}{\frac{1}{t \cdot -2} \cdot z} \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{t \cdot -2} \cdot z} \]

   7. *-commutative N/A

      \[\leadsto \frac{1}{\color{blue}{-2 \cdot t}} \cdot z \]

   8. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{1}{-2}}{t}} \cdot z \]

   9. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

   10. /-lowering-/.f64 39.5

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

7. Applied egg-rr 39.5%

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

8. Final simplification 39.5%

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

Reproduce

herbie shell --seed 2024196 
(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)))