Binomial Multiply
A set of binomials are multiplied together and must to be simplified to satisfy the win-conditions.
Challenge¶
In Binomial Multiply the agent must learn to quickly distribute the binomial multiplications and factor out common terms to leave a simplified representation.
Examples
(4 + g^2)(9 + e^3)
must be simplified to36 + (4e^3 + (9g^2 + g^2 * e^3))
(a + a) * a
must be simplified to2a^2
(c + 5) * c
must be simplified toc^2 + 5c
(i^3 + 2)(i^3 + 9)
must be simplified toi^6 + (11i^3 + 18)
(3 + 12o)(10 + 8o)
must be simplified to30 + (144o + 96o^2)
Win Conditions¶
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.
Examples
2 * 4x
is complex because it has multiple coefficients which could be simplified to8x
4x * y * j^2
is not complex despite being verbose because there is only a single coefficient and no matching variables
Example Episode¶
A trained agent learns to distribute and simplify binomial and monomial multiplications.
Input¶
(k^4 + 7)(4 + h^2)
Steps¶
Step | Text |
---|---|
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 |
Solution¶
4k^4 + k^4 * h^2 + 28 + 7h^2
Last update: November 28, 2019