Poly Simplify

Core to working with algebra problems is the ability to combine like terms in polynomials, and Mathy provides an environment that generates problems that require simplification to satisfy the win-conditions.

Challenge

In Poly Simplify the agent must learn to quickly combine and simplify all the like terms in the generated input expression.

Examples

  • 4x + 2y + 2x must be simplified to 6x + 2y
  • 23j + 7 + 12x + 2j must be simplified to 25j + 7 + 12x
  • 1.3j + 2j - 7 must be simplified to 3.3j - 7

Win Conditions

A problem is considered solved when there are no remaining like terms in the expression, and all terms are expressed in a simple way.

No Like Terms

Terms are like when they share a common variable and exponent and are connected by an addition or subtraction.

Examples

  • 4x + 2y there are no like terms because x and y are different variables
  • 2x^2 + 4x there are no like terms because x^2 and x have different exponents
  • 82x + 14x the terms are like because x and x are the same
  • 12x + 12y there are no like terms because x and y different variables

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 to 8x
  • 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 combine multiple low-level actions into higher-level ones that combine like terms

Input

1k + 210r + 7z + 11k + 10z

1 k * 210 r * + 7 z * + 11 k * + 10 z * +

Steps

Step Text
input 1k + 210r + 7z + 11k + 10z
commutative swap 11k + (1k + 210r + 7z) + 10z
distributive factoring 11k + (1k + 210r) + (7 + 10) * z
distributive factoring (11 + 1) * k + 210r + (7 + 10) * z
constant arithmetic (11 + 1) * k + 210r + 17z
constant arithmetic 12k + 210r + 17z
solution 12k + 210r + 17z

Solution

12k + 210r + 17z

12 k * 210 r * + 17 z * +