15

+

−

+ A + B + C

− (A − B) + C
A − (B + C)
∗ A ∗ (B + C)
(A ∗ B) + C
A/(B + C)
(A/B) + C

/

A + B − C
(A − B) − C
A − (B − C)
A ∗ (B − C)
(A ∗ B) − C
A/(B − C)
(A/B) − C

∗

(A + B) ∗ C
A + (B ∗ C)
(A − B) ∗ C
A − (B ∗ C)
A ∗ B ∗ C
(A/B) ∗ C
A/(B ∗ C)

/

(A + B)/C
A + (B/C)
(A − B)/C
A − (B/C)
(A ∗ B)/C
A ∗ (B/C)
(A/B)/C
A/(B/C)

Table 11: Two-operation formulae. All combinations of two-operation formulae, includ-
ing operator precedence where relevant. See Table 12 for the phrasings corresponding to
these formulae.

700 samples with a single operation were used for training the model, drawn ran-
domly from all operations, formats, and number of digits. The dev and test set
each included 210 samples drawn randomly for each of the 16 combinations of two
operation formulas, analyzed up to 7 digits.

16

What is the diﬀerence between A and the ratio between B and C?

What is the diﬀerence between A and the product of B and C?
How much is A times the diﬀerence between B and C?
MRKL Systems