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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 10

Speedup: 1.0×

• 26.2% 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: 46.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -850:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-202} \lor \neg \left(x \leq 2 \cdot 10^{-174}\right) \land x \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -850.0)
   (* 0.5 (/ x t))
   (if (or (<= x -2.5e-202) (and (not (<= x 2e-174)) (<= x 9.5e-138)))
     (/ -0.5 (/ t z))
     (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -850.0) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -2.5e-202) || (!(x <= 2e-174) && (x <= 9.5e-138))) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-850.0d0)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-2.5d-202)) .or. (.not. (x <= 2d-174)) .and. (x <= 9.5d-138)) then
        tmp = (-0.5d0) / (t / z)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -850.0) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -2.5e-202) || (!(x <= 2e-174) && (x <= 9.5e-138))) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -850.0:
		tmp = 0.5 * (x / t)
	elif (x <= -2.5e-202) or (not (x <= 2e-174) and (x <= 9.5e-138)):
		tmp = -0.5 / (t / z)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -850.0)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -2.5e-202) || (!(x <= 2e-174) && (x <= 9.5e-138)))
		tmp = Float64(-0.5 / Float64(t / z));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -850.0)
		tmp = 0.5 * (x / t);
	elseif ((x <= -2.5e-202) || (~((x <= 2e-174)) && (x <= 9.5e-138)))
		tmp = -0.5 / (t / z);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -850.0], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.5e-202], And[N[Not[LessEqual[x, 2e-174]], $MachinePrecision], LessEqual[x, 9.5e-138]]], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -850

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.0%

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

   if -850 < x < -2.49999999999999986e-202 or 2e-174 < x < 9.49999999999999997e-138

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. associate-/l* 44.4%

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

   5. Simplified 44.4%

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

   if -2.49999999999999986e-202 < x < 2e-174 or 9.49999999999999997e-138 < 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 46.1%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -850:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-202} \lor \neg \left(x \leq 2 \cdot 10^{-174}\right) \land x \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -13.5:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-200} \lor \neg \left(x \leq 9 \cdot 10^{-175}\right) \land x \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -13.5)
   (* 0.5 (/ x t))
   (if (or (<= x -7e-200) (and (not (<= x 9e-175)) (<= x 2.2e-138)))
     (/ (* -0.5 z) t)
     (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -13.5) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -7e-200) || (!(x <= 9e-175) && (x <= 2.2e-138))) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-13.5d0)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-7d-200)) .or. (.not. (x <= 9d-175)) .and. (x <= 2.2d-138)) then
        tmp = ((-0.5d0) * z) / t
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -13.5) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -7e-200) || (!(x <= 9e-175) && (x <= 2.2e-138))) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -13.5:
		tmp = 0.5 * (x / t)
	elif (x <= -7e-200) or (not (x <= 9e-175) and (x <= 2.2e-138)):
		tmp = (-0.5 * z) / t
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -13.5)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -7e-200) || (!(x <= 9e-175) && (x <= 2.2e-138)))
		tmp = Float64(Float64(-0.5 * z) / t);
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -13.5)
		tmp = 0.5 * (x / t);
	elseif ((x <= -7e-200) || (~((x <= 9e-175)) && (x <= 2.2e-138)))
		tmp = (-0.5 * z) / t;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -13.5], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7e-200], And[N[Not[LessEqual[x, 9e-175]], $MachinePrecision], LessEqual[x, 2.2e-138]]], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -13.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.0%

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

   if -13.5 < x < -7.00000000000000045e-200 or 8.99999999999999996e-175 < x < 2.1999999999999999e-138

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-*l/ 44.5%

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

   5. Simplified 44.5%

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

   if -7.00000000000000045e-200 < x < 8.99999999999999996e-175 or 2.1999999999999999e-138 < 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 46.1%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -13.5:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-200} \lor \neg \left(x \leq 9 \cdot 10^{-175}\right) \land x \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+57} \lor \neg \left(z \leq 5.2 \cdot 10^{+180}\right):\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e+57) (not (<= z 5.2e+180)))
   (/ (* -0.5 z) t)
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+57) || !(z <= 5.2e+180)) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.5d+57)) .or. (.not. (z <= 5.2d+180))) then
        tmp = ((-0.5d0) * z) / t
    else
        tmp = 0.5d0 * ((x + y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+57) || !(z <= 5.2e+180)) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e+57) or not (z <= 5.2e+180):
		tmp = (-0.5 * z) / t
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e+57) || !(z <= 5.2e+180))
		tmp = Float64(Float64(-0.5 * z) / t);
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e+57) || ~((z <= 5.2e+180)))
		tmp = (-0.5 * z) / t;
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e+57], N[Not[LessEqual[z, 5.2e+180]], $MachinePrecision]], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000006e57 or 5.20000000000000042e180 < 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 76.7%

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

      1. *-commutative 76.7%

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

      2. associate-*l/ 76.7%

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

   5. Simplified 76.7%

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

   if -7.5000000000000006e57 < z < 5.20000000000000042e180

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.7%

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

      1. +-commutative 84.7%

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

   5. Simplified 84.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+57} \lor \neg \left(z \leq 5.2 \cdot 10^{+180}\right):\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -200000:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e+186)
   (* 0.5 (/ (+ x y) t))
   (if (<= x -200000.0) (* 0.5 (/ (- x z) t)) (* (- y z) (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e+186) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -200000.0) {
		tmp = 0.5 * ((x - z) / t);
	} 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 <= (-3.6d+186)) then
        tmp = 0.5d0 * ((x + y) / t)
    else if (x <= (-200000.0d0)) then
        tmp = 0.5d0 * ((x - z) / t)
    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 <= -3.6e+186) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -200000.0) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e+186:
		tmp = 0.5 * ((x + y) / t)
	elif x <= -200000.0:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e+186)
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	elseif (x <= -200000.0)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	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 <= -3.6e+186)
		tmp = 0.5 * ((x + y) / t);
	elseif (x <= -200000.0)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e+186], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -200000.0], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6000000000000002e186

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.6000000000000002e186 < x < -2e5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.3%

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

   if -2e5 < 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 81.6%

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

      1. associate-*r/ 81.6%

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

      2. associate-*l/ 81.4%

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

      3. *-commutative 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -200000:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+187}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -0.102:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.9e+187)
   (* 0.5 (/ (+ x y) t))
   (if (<= x -0.102) (* 0.5 (/ (- x z) t)) (/ (* 0.5 (- y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+187) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -0.102) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (0.5 * (y - z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.9d+187)) then
        tmp = 0.5d0 * ((x + y) / t)
    else if (x <= (-0.102d0)) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = (0.5d0 * (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+187) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -0.102) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (0.5 * (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.9e+187:
		tmp = 0.5 * ((x + y) / t)
	elif x <= -0.102:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (0.5 * (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.9e+187)
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	elseif (x <= -0.102)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(Float64(0.5 * Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.9e+187)
		tmp = 0.5 * ((x + y) / t);
	elseif (x <= -0.102)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (0.5 * (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.9e+187], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -0.102], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9000000000000001e187

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -2.9000000000000001e187 < x < -0.101999999999999993

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.3%

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

   if -0.101999999999999993 < 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 81.6%

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

      1. associate-*r/ 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+187}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -0.102:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9.2e+60) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.2e+60) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 9.2d+60) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * ((x + y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.2e+60) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.2e+60:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.2e+60)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 9.2e+60)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.2e+60], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.20000000000000068e60

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.3%

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

   if 9.20000000000000068e60 < 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 87.1%

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

      1. +-commutative 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -140000:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -140000.0) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -140000.0) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-140000.0d0)) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -140000.0) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -140000.0:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -140000.0)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -140000.0)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -140000.0], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.0%

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

   if -1.4e5 < 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 48.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -140000:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.5d0 / (t / (y + (x - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(0.5 / N[(t / N[(y + N[(x - z), $MachinePrecision]), $MachinePrecision]), $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 99.6%

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

   2. inv-pow 99.6%

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

   3. *-commutative 99.6%

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

   4. *-un-lft-identity 99.6%

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

   5. times-frac 99.6%

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

   6. metadata-eval 99.6%

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

   7. associate--l+ 99.6%

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

4. Applied egg-rr 99.6%

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

   1. unpow-1 99.6%

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

   2. associate-/r* 99.6%

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

   3. metadata-eval 99.6%

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

   4. associate-+r- 99.6%

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

   5. +-commutative 99.6%

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

   6. associate--l+ 99.6%

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

6. Applied egg-rr 99.6%

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

7. Final simplification 99.6%

   \[\leadsto \frac{0.5}{\frac{t}{y + \left(x - z\right)}} \]
8. Add Preprocessing

Alternative 10: 37.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.5d0 * (x / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(0.5 * N[(x / 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 inf 33.2%

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

4. Final simplification 33.2%

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

Reproduce

herbie shell --seed 2024034 
(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)))