You can use:

• add +
• subtract –
• multiply *
• divide /
• x raised to the power n, xⁿ, shown as x^n, where you make x and n using the other rules
• parentheses ()

Use rules for 0 to 20, and:

1. factorial !, like 4! for 24
2. square root, like sqrt(4) for 2
3. .4~ for 0.444…

You cannot use:

1. %, like 44% for 0.44
2. .(anything), like .(4!) for 0.24
3. 1 directly, like 4^-1 or 1/4 for 0.25
4. functions like int(), ceil(), floor(), frac(), as these are approximations
5. log, which you could use to find every solution by nesting log and sqrt
6. constants other than 4, like π, or e