A set of binomials are multiplied together and must to be simplified to satisfy the win-conditions.
In Binomial Multiply the agent must learn to quickly distribute the binomial multiplications and factor out common terms to leave a simplified representation.
(4 + g^2)(9 + e^3)must be simplified to
36 + (4e^3 + (9g^2 + g^2 * e^3))
(a + a) * amust be simplified to
(c + 5) * cmust be simplified to
c^2 + 5c
(i^3 + 2)(i^3 + 9)must be simplified to
i^6 + (11i^3 + 18)
(3 + 12o)(10 + 8o)must be simplified to
30 + (144o + 96o^2)
A problem is considered solved when there are no remaining complex terms in the expression.
No Complex Terms¶
Terms are considered complex when there's a more concise way they could be expressed.
2 * 4xis complex because it has multiple coefficients which could be simplified to
4x * y * j^2is not complex despite being verbose because there is only a single coefficient and no matching variables
A trained agent learns to distribute and simplify binomial and monomial multiplications.
(k^4 + 7)(4 + h^2)
|initial||(k^4 + 7)(4 + h^2)|
|distributive multiply||(4 + h^2) * k^4 + (4 + h^2) * 7|
|distributive multiply||4k^4 + k^4 * h^2 + (4 + h^2) * 7|
|commutative swap||4k^4 + k^4 * h^2 + 7 * (4 + h^2)|
|distributive multiply||4k^4 + k^4 * h^2 + (7 * 4 + 7h^2)|
|constant arithmetic||4k^4 + k^4 * h^2 + (28 + 7h^2)|
|solution||4k^4 + k^4 * h^2 + 28 + 7h^2|
4k^4 + k^4 * h^2 + 28 + 7h^2