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$$\frac{44}{\left\lfloor\sqrt{\sqrt{(4+4)!}}\right\rfloor}$$

is equal to

the common approximation $22/7$

and scores

$$\frac{-\log_{10}\left(\frac{22}7-\pi\right)}6$$

which is $\approx0.483$.

Edit: Better yet is

$$\sqrt{\frac{44-4}4}$$

which scores

$$\frac{-\log_{10}\left(\sqrt{10}-\pi\right)}3$$

, or $\approx0.5614$.

$$\frac{44}{\left\lfloor\sqrt{\sqrt{(4+4)!}}\right\rfloor}$$

is equal to

the common approximation $22/7$

and scores

$$\frac{-\log_{10}\left(\frac{22}7-\pi\right)}6$$

which is $\approx0.4830$.

Edit: Better yet is

$$\sqrt{\frac{44-4}4}$$

which scores

$$\frac{-\log_{10}\left(\sqrt{10}-\pi\right)}3$$

, or $\approx0.5614$.

$$\frac{44}{\left\lfloor\sqrt{\sqrt{(4+4)!}}\right\rfloor}$$

is equal to

the common approximation $22/7$

and scores

$$\frac{-\log_{10}\left(\frac{22}7-\pi\right)}6$$

which is $\approx0.483$.

$$\frac{44}{\left\lfloor\sqrt{\sqrt{(4+4)!}}\right\rfloor}$$

is equal to

the common approximation $22/7$

and scores

$$\frac{-\log_{10}\left(\frac{22}7-\pi\right)}6$$

which is $\approx0.483$.

Edit: Better yet is

$$\sqrt{\frac{44-4}4}$$

which scores

$$\frac{-\log_{10}\left(\sqrt{10}-\pi\right)}3$$

, or $\approx0.5614$.

$\frac{44}{\left\lfloor\sqrt{\sqrt{(4+4)!}}\right\rfloor}$

scores $\approx0.483$

$$\frac{44}{\left\lfloor\sqrt{\sqrt{(4+4)!}}\right\rfloor}$$

is equal to

the common approximation $22/7$

and scores

$$\frac{-\log_{10}\left(\frac{22}7-\pi\right)}6$$

which is $\approx0.483$.