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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 8

Speedup: 1.0×

• 26.8% 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. Final simplification 100.0%

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

Alternative 2: 47.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.5}{\frac{t}{x}}\\ t_2 := 0.5 \cdot \frac{y}{t}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-284}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 0.5 (/ t x))) (t_2 (* 0.5 (/ y t))))
   (if (<= x -6.8e+166)
     t_1
     (if (<= x -5.5e+139)
       t_2
       (if (<= x -2.9e+25) t_1 (if (<= x 3.1e-284) (* (/ z t) -0.5) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 / (t / x);
	double t_2 = 0.5 * (y / t);
	double tmp;
	if (x <= -6.8e+166) {
		tmp = t_1;
	} else if (x <= -5.5e+139) {
		tmp = t_2;
	} else if (x <= -2.9e+25) {
		tmp = t_1;
	} else if (x <= 3.1e-284) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = t_2;
	}
	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 / (t / x)
    t_2 = 0.5d0 * (y / t)
    if (x <= (-6.8d+166)) then
        tmp = t_1
    else if (x <= (-5.5d+139)) then
        tmp = t_2
    else if (x <= (-2.9d+25)) then
        tmp = t_1
    else if (x <= 3.1d-284) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 / (t / x);
	double t_2 = 0.5 * (y / t);
	double tmp;
	if (x <= -6.8e+166) {
		tmp = t_1;
	} else if (x <= -5.5e+139) {
		tmp = t_2;
	} else if (x <= -2.9e+25) {
		tmp = t_1;
	} else if (x <= 3.1e-284) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 / (t / x)
	t_2 = 0.5 * (y / t)
	tmp = 0
	if x <= -6.8e+166:
		tmp = t_1
	elif x <= -5.5e+139:
		tmp = t_2
	elif x <= -2.9e+25:
		tmp = t_1
	elif x <= 3.1e-284:
		tmp = (z / t) * -0.5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 / Float64(t / x))
	t_2 = Float64(0.5 * Float64(y / t))
	tmp = 0.0
	if (x <= -6.8e+166)
		tmp = t_1;
	elseif (x <= -5.5e+139)
		tmp = t_2;
	elseif (x <= -2.9e+25)
		tmp = t_1;
	elseif (x <= 3.1e-284)
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 / (t / x);
	t_2 = 0.5 * (y / t);
	tmp = 0.0;
	if (x <= -6.8e+166)
		tmp = t_1;
	elseif (x <= -5.5e+139)
		tmp = t_2;
	elseif (x <= -2.9e+25)
		tmp = t_1;
	elseif (x <= 3.1e-284)
		tmp = (z / t) * -0.5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 / N[(t / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+166], t$95$1, If[LessEqual[x, -5.5e+139], t$95$2, If[LessEqual[x, -2.9e+25], t$95$1, If[LessEqual[x, 3.1e-284], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000001e166 or -5.4999999999999996e139 < x < -2.8999999999999999e25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.0%

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

      1. associate-*r/ 75.0%

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

      2. associate-/l* 75.0%

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

   4. Simplified 75.0%

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

   if -6.8000000000000001e166 < x < -5.4999999999999996e139 or 3.0999999999999998e-284 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 44.7%

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

   if -2.8999999999999999e25 < x < 3.0999999999999998e-284

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

   4. Simplified 55.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+139}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+25}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-284}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 0.5}{t}\\ t_2 := 0.5 \cdot \frac{y}{t}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-284}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 0.5) t)) (t_2 (* 0.5 (/ y t))))
   (if (<= x -6.8e+166)
     t_1
     (if (<= x -5.5e+132)
       t_2
       (if (<= x -2.3e+25) t_1 (if (<= x 1.55e-284) (* (/ z t) -0.5) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) / t;
	double t_2 = 0.5 * (y / t);
	double tmp;
	if (x <= -6.8e+166) {
		tmp = t_1;
	} else if (x <= -5.5e+132) {
		tmp = t_2;
	} else if (x <= -2.3e+25) {
		tmp = t_1;
	} else if (x <= 1.55e-284) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = t_2;
	}
	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 = (x * 0.5d0) / t
    t_2 = 0.5d0 * (y / t)
    if (x <= (-6.8d+166)) then
        tmp = t_1
    else if (x <= (-5.5d+132)) then
        tmp = t_2
    else if (x <= (-2.3d+25)) then
        tmp = t_1
    else if (x <= 1.55d-284) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) / t;
	double t_2 = 0.5 * (y / t);
	double tmp;
	if (x <= -6.8e+166) {
		tmp = t_1;
	} else if (x <= -5.5e+132) {
		tmp = t_2;
	} else if (x <= -2.3e+25) {
		tmp = t_1;
	} else if (x <= 1.55e-284) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 0.5) / t
	t_2 = 0.5 * (y / t)
	tmp = 0
	if x <= -6.8e+166:
		tmp = t_1
	elif x <= -5.5e+132:
		tmp = t_2
	elif x <= -2.3e+25:
		tmp = t_1
	elif x <= 1.55e-284:
		tmp = (z / t) * -0.5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 0.5) / t)
	t_2 = Float64(0.5 * Float64(y / t))
	tmp = 0.0
	if (x <= -6.8e+166)
		tmp = t_1;
	elseif (x <= -5.5e+132)
		tmp = t_2;
	elseif (x <= -2.3e+25)
		tmp = t_1;
	elseif (x <= 1.55e-284)
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 0.5) / t;
	t_2 = 0.5 * (y / t);
	tmp = 0.0;
	if (x <= -6.8e+166)
		tmp = t_1;
	elseif (x <= -5.5e+132)
		tmp = t_2;
	elseif (x <= -2.3e+25)
		tmp = t_1;
	elseif (x <= 1.55e-284)
		tmp = (z / t) * -0.5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+166], t$95$1, If[LessEqual[x, -5.5e+132], t$95$2, If[LessEqual[x, -2.3e+25], t$95$1, If[LessEqual[x, 1.55e-284], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000001e166 or -5.5e132 < x < -2.2999999999999998e25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.0%

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

      1. associate-*r/ 75.0%

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

   4. Simplified 75.0%

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

   if -6.8000000000000001e166 < x < -5.5e132 or 1.5499999999999999e-284 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 44.7%

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

   if -2.2999999999999998e25 < x < 1.5499999999999999e-284

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

   4. Simplified 55.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+132}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-284}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 77.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-46}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.7e+14)
   (/ 0.5 (/ t (+ x y)))
   (if (<= x -1.25e-46) (* 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 <= -2.7e+14) {
		tmp = 0.5 / (t / (x + y));
	} else if (x <= -1.25e-46) {
		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 <= (-2.7d+14)) then
        tmp = 0.5d0 / (t / (x + y))
    else if (x <= (-1.25d-46)) 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 <= -2.7e+14) {
		tmp = 0.5 / (t / (x + y));
	} else if (x <= -1.25e-46) {
		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 <= -2.7e+14:
		tmp = 0.5 / (t / (x + y))
	elif x <= -1.25e-46:
		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 <= -2.7e+14)
		tmp = Float64(0.5 / Float64(t / Float64(x + y)));
	elseif (x <= -1.25e-46)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.7e+14)
		tmp = 0.5 / (t / (x + y));
	elseif (x <= -1.25e-46)
		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, -2.7e+14], N[(0.5 / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.25e-46], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e14

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 94.4%

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

      1. associate-*r/ 94.4%

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

      2. +-commutative 94.4%

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

      3. associate-/l* 94.3%

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

      4. +-commutative 94.3%

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

   4. Simplified 94.3%

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

   if -2.7e14 < x < -1.24999999999999998e-46

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.0%

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

   if -1.24999999999999998e-46 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.7%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-46}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 5: 57.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+64} \lor \neg \left(z \leq 4.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.5e+64) (not (<= z 4.6e+88)))
   (* (/ z t) -0.5)
   (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+64) || !(z <= 4.6e+88)) {
		tmp = (z / t) * -0.5;
	} 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 ((z <= (-6.5d+64)) .or. (.not. (z <= 4.6d+88))) then
        tmp = (z / t) * (-0.5d0)
    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 ((z <= -6.5e+64) || !(z <= 4.6e+88)) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.5e+64) or not (z <= 4.6e+88):
		tmp = (z / t) * -0.5
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.5e+64) || !(z <= 4.6e+88))
		tmp = Float64(Float64(z / t) * -0.5);
	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 ((z <= -6.5e+64) || ~((z <= 4.6e+88)))
		tmp = (z / t) * -0.5;
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.5e+64], N[Not[LessEqual[z, 4.6e+88]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000007e64 or 4.6000000000000003e88 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 77.1%

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

      1. *-commutative 77.1%

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

   4. Simplified 77.1%

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

   if -6.50000000000000007e64 < z < 4.6000000000000003e88

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 50.3%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+64} \lor \neg \left(z \leq 4.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.75e+20) (* 0.5 (/ (- x z) t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.75e+20) {
		tmp = 0.5 * ((x - 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 (y <= 1.75d+20) then
        tmp = 0.5d0 * ((x - 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 (y <= 1.75e+20) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.75e+20:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.75e+20)
		tmp = Float64(0.5 * Float64(Float64(x - 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 (y <= 1.75e+20)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.75e+20], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.75e20

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.9%

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

   if 1.75e20 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e-45) (* 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 <= -1.1e-45) {
		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 <= (-1.1d-45)) 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 <= -1.1e-45) {
		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 <= -1.1e-45:
		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 <= -1.1e-45)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.1e-45)
		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, -1.1e-45], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.09999999999999997e-45

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.5%

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

   if -1.09999999999999997e-45 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 8: 37.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 40.2%

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

3. Final simplification 40.2%

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

Reproduce

herbie shell --seed 2023268 
(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)))