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

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 7

Speedup: 1.0×

• 25.7% 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. Final simplification 100.0%

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

Alternative 2: 46.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{t}\\ t_2 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-218}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x t))) (t_2 (/ (* z -0.5) t)))
   (if (<= x -5.8e+82)
     t_1
     (if (<= x -1.3e+53)
       t_2
       (if (<= x -2.2e+17) t_1 (if (<= x -9e-218) t_2 (/ (* y 0.5) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * (x / t);
	double t_2 = (z * -0.5) / t;
	double tmp;
	if (x <= -5.8e+82) {
		tmp = t_1;
	} else if (x <= -1.3e+53) {
		tmp = t_2;
	} else if (x <= -2.2e+17) {
		tmp = t_1;
	} else if (x <= -9e-218) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.5d0 * (x / t)
    t_2 = (z * (-0.5d0)) / t
    if (x <= (-5.8d+82)) then
        tmp = t_1
    else if (x <= (-1.3d+53)) then
        tmp = t_2
    else if (x <= (-2.2d+17)) then
        tmp = t_1
    else if (x <= (-9d-218)) then
        tmp = t_2
    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 t_1 = 0.5 * (x / t);
	double t_2 = (z * -0.5) / t;
	double tmp;
	if (x <= -5.8e+82) {
		tmp = t_1;
	} else if (x <= -1.3e+53) {
		tmp = t_2;
	} else if (x <= -2.2e+17) {
		tmp = t_1;
	} else if (x <= -9e-218) {
		tmp = t_2;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * (x / t)
	t_2 = (z * -0.5) / t
	tmp = 0
	if x <= -5.8e+82:
		tmp = t_1
	elif x <= -1.3e+53:
		tmp = t_2
	elif x <= -2.2e+17:
		tmp = t_1
	elif x <= -9e-218:
		tmp = t_2
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(x / t))
	t_2 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (x <= -5.8e+82)
		tmp = t_1;
	elseif (x <= -1.3e+53)
		tmp = t_2;
	elseif (x <= -2.2e+17)
		tmp = t_1;
	elseif (x <= -9e-218)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * (x / t);
	t_2 = (z * -0.5) / t;
	tmp = 0.0;
	if (x <= -5.8e+82)
		tmp = t_1;
	elseif (x <= -1.3e+53)
		tmp = t_2;
	elseif (x <= -2.2e+17)
		tmp = t_1;
	elseif (x <= -9e-218)
		tmp = t_2;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[x, -5.8e+82], t$95$1, If[LessEqual[x, -1.3e+53], t$95$2, If[LessEqual[x, -2.2e+17], t$95$1, If[LessEqual[x, -9e-218], t$95$2, N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8000000000000003e82 or -1.29999999999999999e53 < x < -2.2e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.8%

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

   if -5.8000000000000003e82 < x < -1.29999999999999999e53 or -2.2e17 < x < -8.99999999999999953e-218

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-*l/ 52.2%

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

   5. Simplified 52.2%

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

   if -8.99999999999999953e-218 < 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 44.2%

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

      1. associate-*r/ 44.2%

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

   5. Simplified 44.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-218}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00031 \lor \neg \left(y \leq 1.35 \cdot 10^{+45}\right) \land y \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 0.00031) (and (not (<= y 1.35e+45)) (<= y 1.55e+105)))
   (* 0.5 (/ (- x z) t))
   (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 0.00031) || (!(y <= 1.35e+45) && (y <= 1.55e+105))) {
		tmp = 0.5 * ((x - z) / 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 ((y <= 0.00031d0) .or. (.not. (y <= 1.35d+45)) .and. (y <= 1.55d+105)) then
        tmp = 0.5d0 * ((x - z) / 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 ((y <= 0.00031) || (!(y <= 1.35e+45) && (y <= 1.55e+105))) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= 0.00031) or (not (y <= 1.35e+45) and (y <= 1.55e+105)):
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 0.00031) || (!(y <= 1.35e+45) && (y <= 1.55e+105)))
		tmp = Float64(0.5 * Float64(Float64(x - z) / 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 ((y <= 0.00031) || (~((y <= 1.35e+45)) && (y <= 1.55e+105)))
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, 0.00031], And[N[Not[LessEqual[y, 1.35e+45]], $MachinePrecision], LessEqual[y, 1.55e+105]]], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.1e-4 or 1.34999999999999992e45 < y < 1.55000000000000002e105

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.2%

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

   if 3.1e-4 < y < 1.34999999999999992e45 or 1.55000000000000002e105 < 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 68.2%

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

      1. associate-*r/ 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00031 \lor \neg \left(y \leq 1.35 \cdot 10^{+45}\right) \land y \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-6} \lor \neg \left(z \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.6e-6) (not (<= z 2.4e+126)))
   (* 0.5 (/ (- x z) t))
   (* (+ x y) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.6e-6) || !(z <= 2.4e+126)) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (x + 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 ((z <= (-5.6d-6)) .or. (.not. (z <= 2.4d+126))) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = (x + 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 ((z <= -5.6e-6) || !(z <= 2.4e+126)) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = (x + y) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.6e-6) or not (z <= 2.4e+126):
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = (x + y) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.6e-6) || !(z <= 2.4e+126))
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.6e-6) || ~((z <= 2.4e+126)))
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = (x + y) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.6e-6], N[Not[LessEqual[z, 2.4e+126]], $MachinePrecision]], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999975e-6 or 2.40000000000000012e126 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.7%

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

   if -5.59999999999999975e-6 < z < 2.40000000000000012e126

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.7%

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

      1. associate-*r/ 92.7%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. +-commutative 92.4%

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

   5. Simplified 92.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-6} \lor \neg \left(z \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-134}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-134) (* 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 + y) <= -5e-134) {
		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 + y) <= (-5d-134)) 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 + y) <= -5e-134) {
		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 + y) <= -5e-134:
		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 (Float64(x + y) <= -5e-134)
		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 + y) <= -5e-134)
		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[N[(x + y), $MachinePrecision], -5e-134], 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 2 regimes

2. if (+.f64 x y) < -5.0000000000000003e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 66.9%

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

   if -5.0000000000000003e-134 < (+.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 74.9%

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

      1. associate-*r/ 74.9%

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

   5. Simplified 74.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-134}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-39}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e-39) (* 0.5 (/ x t)) (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-39) {
		tmp = 0.5 * (x / 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 <= (-6d-39)) then
        tmp = 0.5d0 * (x / 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 <= -6e-39) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e-39:
		tmp = 0.5 * (x / t)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e-39)
		tmp = Float64(0.5 * Float64(x / 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 <= -6e-39)
		tmp = 0.5 * (x / t);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e-39], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000055e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.8%

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

   if -6.00000000000000055e-39 < 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 44.5%

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

      1. associate-*r/ 44.5%

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

   5. Simplified 44.5%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-39}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 40.2%

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

4. Final simplification 40.2%

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

Reproduce

herbie shell --seed 2024075 
(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)))