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

Percentage Accurate: 99.9% → 99.9%

Time: 12.2s

Alternatives: 13

Speedup: 1.0×

• 26.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= z -5.5e+22) t_1 (if (<= z 8.2e+135) (/ 0.5 (/ t (+ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -5.5e+22) {
		tmp = t_1;
	} else if (z <= 8.2e+135) {
		tmp = 0.5 / (t / (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    if (z <= (-5.5d+22)) then
        tmp = t_1
    else if (z <= 8.2d+135) then
        tmp = 0.5d0 / (t / (x + y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -5.5e+22) {
		tmp = t_1;
	} else if (z <= 8.2e+135) {
		tmp = 0.5 / (t / (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	tmp = 0
	if z <= -5.5e+22:
		tmp = t_1
	elif z <= 8.2e+135:
		tmp = 0.5 / (t / (x + y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (z <= -5.5e+22)
		tmp = t_1;
	elseif (z <= 8.2e+135)
		tmp = Float64(0.5 / Float64(t / Float64(x + y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	tmp = 0.0;
	if (z <= -5.5e+22)
		tmp = t_1;
	elseif (z <= 8.2e+135)
		tmp = 0.5 / (t / (x + y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -5.5e+22], t$95$1, If[LessEqual[z, 8.2e+135], N[(0.5 / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000021e22 or 8.2e135 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 73.3%

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

   5. Simplified 73.3%

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

   if -5.50000000000000021e22 < z < 8.2e135

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/l/ N/A

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

      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. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0

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

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

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

      2. +-lowering-+.f64 89.0%

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

   7. Simplified 89.0%

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

Alternative 3: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e+31)
   (/ (* x 0.5) t)
   (if (<= x -1.6e-239) (/ (* z -0.5) t) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e+31) {
		tmp = (x * 0.5) / t;
	} else if (x <= -1.6e-239) {
		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 <= (-5.8d+31)) then
        tmp = (x * 0.5d0) / t
    else if (x <= (-1.6d-239)) 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 <= -5.8e+31) {
		tmp = (x * 0.5) / t;
	} else if (x <= -1.6e-239) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e+31:
		tmp = (x * 0.5) / t
	elif x <= -1.6e-239:
		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 <= -5.8e+31)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (x <= -1.6e-239)
		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 <= -5.8e+31)
		tmp = (x * 0.5) / t;
	elseif (x <= -1.6e-239)
		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, -5.8e+31], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -1.6e-239], 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 < -5.8000000000000001e31

   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 69.7%

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

   5. Simplified 69.7%

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

   if -5.8000000000000001e31 < x < -1.6e-239

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.6%

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

   5. Simplified 50.6%

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

   if -1.6e-239 < 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 37.7%

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

   5. Simplified 37.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -1.44 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.4e+35)
   (/ (* x 0.5) t)
   (if (<= x -1.44e-241) (* z (/ -0.5 t)) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.4e+35) {
		tmp = (x * 0.5) / t;
	} else if (x <= -1.44e-241) {
		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 <= (-6.4d+35)) then
        tmp = (x * 0.5d0) / t
    else if (x <= (-1.44d-241)) 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 <= -6.4e+35) {
		tmp = (x * 0.5) / t;
	} else if (x <= -1.44e-241) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.4e+35:
		tmp = (x * 0.5) / t
	elif x <= -1.44e-241:
		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 <= -6.4e+35)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (x <= -1.44e-241)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.4e+35)
		tmp = (x * 0.5) / t;
	elseif (x <= -1.44e-241)
		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, -6.4e+35], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -1.44e-241], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.39999999999999965e35

   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 69.7%

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

   5. Simplified 69.7%

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

   if -6.39999999999999965e35 < x < -1.44000000000000006e-241

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.6%

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

   5. Simplified 50.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. distribute-rgt-neg-in N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 50.5%

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

   7. Applied egg-rr 50.5%

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

   if -1.44000000000000006e-241 < 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 37.7%

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

   5. Simplified 37.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -1.44 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+34}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e+34)
   (/ (* x 0.5) t)
   (if (<= x -3.8e-240) (* z (/ -0.5 t)) (/ 0.5 (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e+34) {
		tmp = (x * 0.5) / t;
	} else if (x <= -3.8e-240) {
		tmp = z * (-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 <= (-2.3d+34)) then
        tmp = (x * 0.5d0) / t
    else if (x <= (-3.8d-240)) then
        tmp = z * ((-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 <= -2.3e+34) {
		tmp = (x * 0.5) / t;
	} else if (x <= -3.8e-240) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.3e+34:
		tmp = (x * 0.5) / t
	elif x <= -3.8e-240:
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.3e+34)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (x <= -3.8e-240)
		tmp = Float64(z * Float64(-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 <= -2.3e+34)
		tmp = (x * 0.5) / t;
	elseif (x <= -3.8e-240)
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.3e+34], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -3.8e-240], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998e34

   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 69.7%

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

   5. Simplified 69.7%

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

   if -2.2999999999999998e34 < x < -3.79999999999999988e-240

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.6%

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

   5. Simplified 50.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. distribute-rgt-neg-in N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 50.5%

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

   7. Applied egg-rr 50.5%

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

   if -3.79999999999999988e-240 < x

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/l/ N/A

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

      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. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.5%

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

   4. Applied egg-rr 99.5%

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

   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 37.6%

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

   7. Simplified 37.6%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+34}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-240}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e+35)
   (/ 0.5 (/ t x))
   (if (<= x -5.8e-239) (* z (/ -0.5 t)) (/ 0.5 (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+35) {
		tmp = 0.5 / (t / x);
	} else if (x <= -5.8e-239) {
		tmp = z * (-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 <= (-1.4d+35)) then
        tmp = 0.5d0 / (t / x)
    else if (x <= (-5.8d-239)) then
        tmp = z * ((-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 <= -1.4e+35) {
		tmp = 0.5 / (t / x);
	} else if (x <= -5.8e-239) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e+35:
		tmp = 0.5 / (t / x)
	elif x <= -5.8e-239:
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e+35)
		tmp = Float64(0.5 / Float64(t / x));
	elseif (x <= -5.8e-239)
		tmp = Float64(z * Float64(-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 <= -1.4e+35)
		tmp = 0.5 / (t / x);
	elseif (x <= -5.8e-239)
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e+35], N[(0.5 / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-239], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.39999999999999999e35

   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 69.7%

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

   5. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]
   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 69.5%

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

   7. Applied egg-rr 69.5%

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

   if -1.39999999999999999e35 < x < -5.8000000000000004e-239

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 50.6%

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

   5. Simplified 50.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. distribute-rgt-neg-in N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 50.5%

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

   7. Applied egg-rr 50.5%

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

   if -5.8000000000000004e-239 < x

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/l/ N/A

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

      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. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.5%

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

   4. Applied egg-rr 99.5%

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

   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 37.6%

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

   7. Simplified 37.6%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-239}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-230}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-230) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-230) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d-230)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-230) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-230:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-230)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e-230)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-230], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000005e-230

   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 64.2%

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

   5. Simplified 64.2%

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

   if -1.00000000000000005e-230 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 68.9%

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

   5. Simplified 68.9%

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

Alternative 8: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 5e+39) (/ (- x z) (* t 2.0)) (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 5e+39) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 5d+39) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (x + y) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 5e+39) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 5e+39:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 5e+39)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 5e+39)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+39], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5.00000000000000015e39

   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 69.0%

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

   5. Simplified 69.0%

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

   if 5.00000000000000015e39 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 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 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 5e+39) (/ 0.5 (/ t (- x z))) (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 5e+39) {
		tmp = 0.5 / (t / (x - z));
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 5d+39) then
        tmp = 0.5d0 / (t / (x - z))
    else
        tmp = (x + y) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 5e+39) {
		tmp = 0.5 / (t / (x - z));
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 5e+39:
		tmp = 0.5 / (t / (x - z))
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 5e+39)
		tmp = Float64(0.5 / Float64(t / Float64(x - z)));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 5e+39)
		tmp = 0.5 / (t / (x - z));
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+39], N[(0.5 / N[(t / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5.00000000000000015e39

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/l/ N/A

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

      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. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around 0

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

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

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

      2. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

   if 5.00000000000000015e39 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 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 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x + y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 5e+39) (/ 0.5 (/ t (- x z))) (/ 0.5 (/ t (+ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 5e+39) {
		tmp = 0.5 / (t / (x - z));
	} else {
		tmp = 0.5 / (t / (x + 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 + y) <= 5d+39) then
        tmp = 0.5d0 / (t / (x - z))
    else
        tmp = 0.5d0 / (t / (x + y))
    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+39) {
		tmp = 0.5 / (t / (x - z));
	} else {
		tmp = 0.5 / (t / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 5e+39:
		tmp = 0.5 / (t / (x - z))
	else:
		tmp = 0.5 / (t / (x + y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 5e+39)
		tmp = Float64(0.5 / Float64(t / Float64(x - z)));
	else
		tmp = Float64(0.5 / Float64(t / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 5e+39)
		tmp = 0.5 / (t / (x - z));
	else
		tmp = 0.5 / (t / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+39], N[(0.5 / N[(t / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5.00000000000000015e39

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/l/ N/A

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

      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. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around 0

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

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

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

      2. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

   if 5.00000000000000015e39 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate-/r* N/A

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

      2. clear-num N/A

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

      3. associate-/l/ N/A

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

      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. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around 0

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

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

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

      2. +-lowering-+.f64 80.3%

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

   7. Simplified 80.3%

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

Alternative 11: 47.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.2e+34) (/ 0.5 (/ t x)) (* z (/ -0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.2e+34) {
		tmp = 0.5 / (t / x);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.2d+34)) then
        tmp = 0.5d0 / (t / x)
    else
        tmp = z * ((-0.5d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.2e+34) {
		tmp = 0.5 / (t / x);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.2e+34:
		tmp = 0.5 / (t / x)
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.2e+34)
		tmp = Float64(0.5 / Float64(t / x));
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.2e+34)
		tmp = 0.5 / (t / x);
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.2e+34], N[(0.5 / N[(t / x), $MachinePrecision]), $MachinePrecision], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999993e34

   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 69.7%

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

   5. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]
   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 69.5%

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

   7. Applied egg-rr 69.5%

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

   if -1.19999999999999993e34 < x

   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. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 40.6%

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

   5. Simplified 40.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. distribute-rgt-neg-in N/A

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

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

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

      9. distribute-rgt-neg-in N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. clear-num N/A

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

      14. /-lowering-/.f64 40.5%

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

   7. Applied egg-rr 40.5%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{0.5}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.6% accurate, 1.0× speedup

Math

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

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(x + Float64(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[(x + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-/r* N/A

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

   2. clear-num N/A

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

   3. associate-/l/ N/A

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

   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. associate--l+ N/A

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

   9. +-lowering-+.f64 N/A

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

   10. --lowering--.f64 99.6%

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

4. Applied egg-rr 99.6%

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

Alternative 13: 37.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf

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

   1. associate-*r/ N/A

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

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

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

   3. *-commutative N/A

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

   4. *-lowering-*.f64 37.3%

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

5. Simplified 37.3%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

   3. clear-num N/A

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

   4. div-inv N/A

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

   5. metadata-eval N/A

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

   6. metadata-eval N/A

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

   7. distribute-rgt-neg-in N/A

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

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

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

   9. distribute-rgt-neg-in N/A

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

   10. metadata-eval N/A

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

   11. metadata-eval N/A

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

   12. div-inv N/A

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

   13. clear-num N/A

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

   14. /-lowering-/.f64 37.2%

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

7. Applied egg-rr 37.2%

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

8. Final simplification 37.2%

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

Reproduce

herbie shell --seed 2024191 
(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)))