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Predicting SMT Solver Performance for Software Verification

Andrew Healy, Rosemary Monahan, James, F. Power

Principles of Programming Research Group, Dept. of Computer Science, Maynooth University, Ireland

F-IDE 2016 support data

This repository contains data measuring 8 SMT solvers' performance on the Why3 examples dataset. We record the result returned by Alt-Ergo (versions 0.95.2 and 1.01), CVC3, CVC4, veriT, Yices, and Z3 (versions 4.3.2 and 4.4.1). We also measure the time taken by the solver to return the result.

Python libraries we use: Pandas, Numpy, Sci-kit Learn, Matplotlib. All Python files can be run on the command line in the usual way: eg python <>


Folder containing latex source files and images for the paper itself


This folder contains a subfolder for each file in the examples repository. Each folder contains:

  • <name>.mlw the WhyML file sent to Why3
  • <name>.json a JSON dictionary containing timings and results for various timeout values
  • stats.json the syntacic features statically extracted from <name>.mlw (used as independent variables for prediction)
  • split/ folder containing the resultant goals after applying the Why3 transformation split_goal_wp to each file .mlw. file. Created by


Python interface to the Benchexec measurement framework. See LICENCE_benchexec.txt for licence.

A collection of short, commonly-used constants and functions used by many of the other Python scripts.

Python script to collect data from the JSON files. Results printed for Table 1 and saved to fig1_data.csv to be read in by

Make the first figure (stacked barcharts - 60 second timeout). Uses fig1_data.csv. Renders barcharts.pdf to paper folder

Collect data from the JSON files and combine it with the syntax metrics. Save the data as whygoal_stats.csv

Use the entire dataset to plot the cumulative time taken for Valid/Invalid/Unknown answers to be returned. Renders line_graph.pdf to paper folder and prints values for the 99th percentile.

whygoal_test.csv, whygoal_valid_test.csv

Disjoint partitions of whygoal_stats.csv for testing (25%) and training/validation (75%) respectively

Perform KFold cross-validation on the training set to compare a number of regressor implementations from Sci-kit Learn. Renders compare_regressors.pdf which is the full version of Table 2 in the paper.

Find values for the 'Random' strategy (either train or test) by averaging values for all possible rankings. Is slow because it has 8! rankings to get through.

Outputs several data files used in the Evaluation section:

  • forest.json: a JSON representation of the trained random forest - suitable for use when compiling the OCaml binary
  • data_for_second_barchart.csv: results for each prover and strategy for the test goals
  • data_for_second_linegraph.csv: how long each strategy took to return a Valid/Invalid answer for the test set
  • feature_importances.txt: These relevance metrics are computed by Sci-kit Learn's Random Forest implementation: they describe the proportion of decisions based on each input variable across all decision trees in Where4's random forest.

Renders barcharts2.pdf to the paper folder. Similar to but reads from data_for_second_barchart.csv and includes theoretical strategies and Where4 results (result of choosing the first solver in each ranking).

The cumulative time taken for the three theoretical strategies and Where to find an answer to the goals in the test dataset. Uses data stored in data_for_second_linegraph.csv - particularly important for the time-consuming 'Random' calculations. Renders line_graph_eval_provers.pdf to the paper folder. Also prints the average times File/Theory/Goal times used in Table 3.

Parameterise Where4's performance by using a threshold, reading data from data_for_second_linegraph.csv. Renders thresholds.pdf to paper folder. These plots show the effect of the threshold on the time taken for a response (top) and number of goals which can be proved (bottom).

An example of how the Benchexec framework is used to measure the CPU time consumed by each SMT solver.

An application of the Why3 transformation split_goal_wp applied to every .mlw in order to count the number of simplified goals which could be created by this tactic.


data and code to complement the paper "Predicting SMT Solver Performance for Software Verification"




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