
| LA                           | original    | disjoint   | packed   | speedup ratio   |       |       |       |      |      |
|------------------------------|-------------|------------|----------|-----------------|-------|-------|-------|------|------|
| total                        | cmp         | exec       | total    | cmp             | exec  | net   | exec  |      |      |
| Regression,                  | 20 examples |            |          |                 |       |       |       |      |      |
| 0                            | 31.5        | 52.9       | 1.96     | 25.5            | 45.5  | 1.02  | 19.25 | 0.69 | 1.33 |
| 1                            | 194.99      | 248        | 55.9     | 109             | 1 07  | 1 2.6 | 16.6  | 1.82 | 6.53 |
| 2                            | 2193        | 3.0        | 2.4 6    |                 |       |       |       |      |      |
| 891                          | 192         |            |          |                 |       |       |       |      |      |
| Classification, 230 examples |             |            |          |                 |       |       |       |      |      |
| 0                            | 27.6        | 27. 3      | 1.83     | 4.71            | 25.4  | 1.13  | 3.42  | 1.09 | 1.38 |
| 1                            | 38.02       | 40. 3      | 7.55     | 9.09            | 3 0.6 | 3.11  | 3.65  | 1.24 | 2.49 |
| 2                            | 638         | 149        | 74.3     | 6.1 6           | 4. 2  |       |       |      |      |

Table 2: Timings of TILDE runs for Mutagenesis. A - in the table indicates that that run

ended prematurely.
according to our analysis, the speedup can in the limit approximate H if the complexity of clause c dominates over the complexity of the rest of the pack; such "early failing branes" in the pack cause the actual situation to approximate closer this ideal case.

We have also run experiments on the Mutagenesis data set (Table 2), both in a regression and a classification setting. Here, query packs are much larger than for the Bongard data set (there is a higher branching factor); with a lookahead of 2 the largest packs had over 20000 queries. For these large packs a significant amount of time is spent compiling the pack, but en then clear net speedups are obtained. 5 A comparison of execution times turned out infeasible because in the disjoint execution setting the pack structures consumed too much memory.

## 5.2 Warmr 5.2.1  U Sed  I M P L E M E N T A T I O N S

For WARMR we consider the following implementations:

1. No packs: the normal implementation of WARMR, where queries are generated, and for all examples the queries are evaluated one by one.

2. With packs: An implementation where first all queries for one level are generated and put into a pack, and then this pack is evaluated on each example.

## 5.2.2 Datasets

Mutagenesis   We used the Mutagenesis dataset of 230 molecules, where each example is repeated 10 times to make more accurate timings possible and to have a better idea of the effect on larger datasets. We used three different language biases. 'small' is a language