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

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 12

Speedup: 1.0×

• 26.4% 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. Add Preprocessing

Alternative 2: 46.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-307}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.7e+90)
   (/ (* x 0.5) t)
   (if (<= x -1.65e-307) (/ (* z -0.5) t) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+90) {
		tmp = (x * 0.5) / t;
	} else if (x <= -1.65e-307) {
		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 <= (-1.7d+90)) then
        tmp = (x * 0.5d0) / t
    else if (x <= (-1.65d-307)) 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 <= -1.7e+90) {
		tmp = (x * 0.5) / t;
	} else if (x <= -1.65e-307) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.7e+90:
		tmp = (x * 0.5) / t
	elif x <= -1.65e-307:
		tmp = (z * -0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.7e+90)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (x <= -1.65e-307)
		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 <= -1.7e+90)
		tmp = (x * 0.5) / t;
	elseif (x <= -1.65e-307)
		tmp = (z * -0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.7e+90], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -1.65e-307], 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 x < -1.70000000000000009e90

   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

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 80.7%

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

   if -1.70000000000000009e90 < x < -1.65e-307

   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

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

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{1}{2} \cdot -1\right) \cdot z}{t} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(-1 \cdot z\right)}{t} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)}{t} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(\mathsf{neg}\left(z\right)\right)\right), \color{blue}{t}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left(-1 \cdot z\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{1}{2} \cdot -1\right) \cdot z\right), t\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot z\right), t\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \frac{-1}{2}\right), t\right) \]

      10. *-lowering-*.f64 68.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), t\right) \]

   5. Simplified 68.5%

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

   if -1.65e-307 < 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

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot y\right), t\right) \]

      5. *-lowering-*.f64 42.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, y\right), t\right) \]

   5. Simplified 42.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-307}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e+56) (/ (- 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 <= -5.8e+56) {
		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 <= (-5.8d+56)) 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 <= -5.8e+56) {
		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 <= -5.8e+56:
		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 (x <= -5.8e+56)
		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 <= -5.8e+56)
		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[x, -5.8e+56], 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 x < -5.80000000000000014e56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 98.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 98.3%

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

   if -5.80000000000000014e56 < 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

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(y - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 81.3%

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

Alternative 4: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e+55) (/ (- x z) (* t 2.0)) (/ 0.5 (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+55) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	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 <= (-4.5d+55)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = 0.5d0 / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+55) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e+55:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = 0.5 / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e+55)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(0.5 / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e+55)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = 0.5 / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e+55], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999998e55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x - z\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 98.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 98.3%

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

   if -4.49999999999999998e55 < x

   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 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y - z}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(y - z\right)}\right)\right) \]

      2. --lowering--.f64 81.0%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 81.0%

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

Alternative 5: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e+100) (/ (+ x y) (* t 2.0)) (/ 0.5 (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+100) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	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 <= (-5.5d+100)) then
        tmp = (x + y) / (t * 2.0d0)
    else
        tmp = 0.5d0 / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+100) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e+100:
		tmp = (x + y) / (t * 2.0)
	else:
		tmp = 0.5 / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e+100)
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	else
		tmp = Float64(0.5 / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e+100)
		tmp = (x + y) / (t * 2.0);
	else
		tmp = 0.5 / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e+100], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000002e100

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + y\right)}, \mathsf{*.f64}\left(t, 2\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y + x\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

      2. +-lowering-+.f64 84.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, x\right), \mathsf{*.f64}\left(\color{blue}{t}, 2\right)\right) \]

   5. Simplified 84.5%

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

   if -5.5000000000000002e100 < x

   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 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y - z}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(y - z\right)}\right)\right) \]

      2. --lowering--.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 80.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+103}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.4e+103) (/ (* x 0.5) t) (/ 0.5 (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.4e+103) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	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 <= (-5.4d+103)) then
        tmp = (x * 0.5d0) / t
    else
        tmp = 0.5d0 / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.4e+103) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 0.5 / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.4e+103:
		tmp = (x * 0.5) / t
	else:
		tmp = 0.5 / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.4e+103)
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(0.5 / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.4e+103)
		tmp = (x * 0.5) / t;
	else
		tmp = 0.5 / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.4e+103], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(0.5 / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999985e103

   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

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 82.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 82.5%

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

   if -5.39999999999999985e103 < x

   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 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y - z}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(y - z\right)}\right)\right) \]

      2. --lowering--.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 80.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+103}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.42e+51) (/ (* x 0.5) t) (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.42e+51) {
		tmp = (x * 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 <= (-1.42d+51)) then
        tmp = (x * 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 <= -1.42e+51) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.42e+51:
		tmp = (x * 0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.42e+51)
		tmp = Float64(Float64(x * 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 <= -1.42e+51)
		tmp = (x * 0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.42e+51], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.41999999999999998e51

   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

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 74.8%

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

   if -1.41999999999999998e51 < 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

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot y\right), t\right) \]

      5. *-lowering-*.f64 40.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, y\right), t\right) \]

   5. Simplified 40.1%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e+52) (/ (* x 0.5) t) (/ 0.5 (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+52) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 0.5 / (t / y);
	}
	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 <= (-6.8d+52)) then
        tmp = (x * 0.5d0) / t
    else
        tmp = 0.5d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+52) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e+52:
		tmp = (x * 0.5) / t
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e+52)
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(0.5 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.8e+52)
		tmp = (x * 0.5) / t;
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e+52], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8e52

   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

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 74.8%

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

   if -6.8e52 < x

   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 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 40.0%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 40.0%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.2e+50) (/ 0.5 (/ t x)) (/ 0.5 (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.2e+50) {
		tmp = 0.5 / (t / x);
	} else {
		tmp = 0.5 / (t / y);
	}
	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 <= (-5.2d+50)) then
        tmp = 0.5d0 / (t / x)
    else
        tmp = 0.5d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.2e+50) {
		tmp = 0.5 / (t / x);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.2e+50:
		tmp = 0.5 / (t / x)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.2e+50)
		tmp = Float64(0.5 / Float64(t / x));
	else
		tmp = Float64(0.5 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.2e+50)
		tmp = 0.5 / (t / x);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.2e+50], N[(0.5 / N[(t / x), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000004e50

   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

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

      2. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

      5. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

   5. Simplified 74.8%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{x}\right)}\right) \]

      5. /-lowering-/.f64 74.6%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 74.6%

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

   if -5.2000000000000004e50 < x

   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 N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

      9. +-lowering-+.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 40.0%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 40.0%

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

Alternative 10: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. *-commutative N/A

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

   3. associate-/l* N/A

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

   4. associate-/r* N/A

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

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{t}{\left(x + y\right) - z}\right)}\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \left(\frac{\color{blue}{t}}{\left(x + y\right) - z}\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{\left(\left(x + y\right) - z\right)}\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\left(x + y\right), \color{blue}{z}\right)\right)\right) \]

   9. +-lowering-+.f64 99.7%

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right)\right)\right) \]

4. Applied egg-rr 99.7%

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

Alternative 11: 37.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

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

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

   5. *-lowering-*.f64 35.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

5. Simplified 35.6%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{t}{x}\right)}\right) \]

   5. /-lowering-/.f64 35.5%

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{/.f64}\left(t, \color{blue}{x}\right)\right) \]

7. Applied egg-rr 35.5%

   \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{x}}} \]
8. Add Preprocessing

Alternative 12: 37.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * 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 x around inf

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

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

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \color{blue}{t}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), t\right) \]

   5. *-lowering-*.f64 35.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), t\right) \]

5. Simplified 35.6%

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

   1. clear-num N/A

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

   2. associate-/r/ N/A

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

   3. associate-*r* N/A

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

   4. metadata-eval N/A

      \[\leadsto \left(\frac{1}{t} \cdot \frac{1}{2}\right) \cdot x \]

   5. div-inv N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{t}}{2}\right), \color{blue}{x}\right) \]

   7. associate-/l/ N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot t}\right), x\right) \]

   8. associate-/r* N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), x\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{t}\right), x\right) \]

   10. /-lowering-/.f64 35.4%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, t\right), x\right) \]

7. Applied egg-rr 35.4%

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

8. Final simplification 35.4%

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

Reproduce

herbie shell --seed 2024161 
(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)))