1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
use indexmap::{IndexMap, IndexSet};
use instant::{Duration, Instant};
use log::*;

use crate::{Analysis, EGraph, Id, Language, RecExpr, Rewrite, SearchMatches};

/** Faciliates running rewrites over an [`EGraph`].

One use for [`EGraph`]s is as the basis of a rewriting system.
Since an egraph never "forgets" state when applying a [`Rewrite`], you
can apply many rewrites many times quite efficiently.
After the egraph is "full" (the rewrites can no longer find new
equalities) or some other condition, the egraph compactly represents
many, many equivalent expressions.
At this point, the egraph is ready for extraction (see [`Extractor`])
which can pick the represented expression that's best according to
some cost function.

This technique is called
[equality saturation](https://www.cs.cornell.edu/~ross/publications/eqsat/)
in general.
However, there can be many challenges in implementing this "outer
loop" of applying rewrites, mostly revolving around which rules to run
and when to stop.

[`Runner`] is `egg`'s provided equality saturation engine that has
reasonable defaults and implements many useful things like saturation
checking, egraph size limits, and customizable rule
[scheduling](trait.RewriteScheduler.html).
Consider using [`Runner`] before rolling your own outer loop.

Here are some of the things [`Runner`] does for you:

- Saturation checking

  [`Runner`] checks to see if any of the rules added anything
  new to the [`EGraph`]. If none did, then it stops, returning
  [`StopReason::Saturated`](enum.StopReason.html#variant.Saturated).

- Iteration limits

  You can set a upper limit of iterations to do in case the search
  doesn't stop for some other reason. If this limit is hit, it stops with
  [`StopReason::IterationLimit`](enum.StopReason.html#variant.IterationLimit).

- [`EGraph`] size limit

  You can set a upper limit on the number of enodes in the egraph.
  If this limit is hit, it stops with
  [`StopReason::NodeLimit`](enum.StopReason.html#variant.NodeLimit).

- Time limit

  You can set a time limit on the runner.
  If this limit is hit, it stops with
  [`StopReason::TimeLimit`](enum.StopReason.html#variant.TimeLimit).

- Rule scheduling

  Some rules enable themselves, blowing up the [`EGraph`] and
  preventing other rewrites from running as many times.
  To prevent this, you can provide your own [`RewriteScheduler`] to
  govern when to run which rules.

  [`BackoffScheduler`] is the default scheduler.

[`Runner`] generates [`Iteration`]s that record some data about
each iteration.
You can add your own data to this by implementing the
[`IterationData`] trait.
[`Runner`] is generic over the [`IterationData`] that it will be in the
[`Iteration`]s, but by default it uses `()`.

[`Runner`]: struct.Runner.html
[`RewriteScheduler`]: trait.RewriteScheduler.html
[`Extractor`]: struct.Extractor.html
[`Rewrite`]: struct.Rewrite.html
[`BackoffScheduler`]: struct.BackoffScheduler.html
[`EGraph`]: struct.EGraph.html
[`Iteration`]: struct.Iteration.html
[`IterationData`]: trait.IterationData.html

# Example

```
use egg::{*, rewrite as rw};

define_language! {
    enum SimpleLanguage {
        Num(i32),
        "+" = Add([Id; 2]),
        "*" = Mul([Id; 2]),
        Symbol(Symbol),
    }
}

let rules: &[Rewrite<SimpleLanguage, ()>] = &[
    rw!("commute-add"; "(+ ?a ?b)" => "(+ ?b ?a)"),
    rw!("commute-mul"; "(* ?a ?b)" => "(* ?b ?a)"),

    rw!("add-0"; "(+ ?a 0)" => "?a"),
    rw!("mul-0"; "(* ?a 0)" => "0"),
    rw!("mul-1"; "(* ?a 1)" => "?a"),
];

pub struct MyIterData {
    smallest_so_far: usize,
}

type MyRunner = Runner<SimpleLanguage, (), MyIterData>;

impl IterationData<SimpleLanguage, ()> for MyIterData {
    fn make(runner: &MyRunner) -> Self {
        let root = runner.roots[0];
        let mut extractor = Extractor::new(&runner.egraph, AstSize);
        MyIterData {
            smallest_so_far: extractor.find_best(root).0,
        }
    }
}

let start = "(+ 0 (* 1 foo))".parse().unwrap();
// Runner is customizable in the builder pattern style.
let runner = MyRunner::new(Default::default())
    .with_iter_limit(10)
    .with_node_limit(10_000)
    .with_expr(&start)
    .with_scheduler(SimpleScheduler)
    .run(rules);

// Now we can check our iteration data to make sure that the cost only
// got better over time
for its in runner.iterations.windows(2) {
    assert!(its[0].data.smallest_so_far >= its[1].data.smallest_so_far);
}

println!(
    "Stopped after {} iterations, reason: {:?}",
    runner.iterations.len(),
    runner.stop_reason
);

```
*/
pub struct Runner<L: Language, N: Analysis<L>, IterData = ()> {
    /// The [`EGraph`](struct.EGraph.html) used.
    pub egraph: EGraph<L, N>,
    /// Data accumulated over each [`Iteration`](struct.Iteration.html).
    pub iterations: Vec<Iteration<IterData>>,
    /// The roots of expressions added by the
    /// [`with_expr`](#method.with_expr) method, in insertion order.
    pub roots: Vec<Id>,
    /// Why the `Runner` stopped. This will be `None` if it hasn't
    /// stopped yet.
    pub stop_reason: Option<StopReason>,

    /// The hooks added by the
    /// [`with_hook`](#method.with_hook) method, in insertion order.
    #[allow(clippy::type_complexity)]
    pub hooks: Vec<Box<dyn FnMut(&mut Self) -> Result<(), String>>>,

    // limits
    iter_limit: usize,
    node_limit: usize,
    time_limit: Duration,

    start_time: Option<Instant>,
    scheduler: Box<dyn RewriteScheduler<L, N>>,
}

impl<L, N> Default for Runner<L, N, ()>
where
    L: Language,
    N: Analysis<L> + Default,
{
    fn default() -> Self {
        Runner::new(N::default())
    }
}

/// Error returned by [`Runner`] when it stops.
///
/// [`Runner`]: struct.Runner.html
#[derive(Debug, Clone)]
#[cfg_attr(feature = "serde-1", derive(serde::Serialize))]
pub enum StopReason {
    /// The egraph saturated, i.e., there was an iteration where we
    /// didn't learn anything new from applying the rules.
    Saturated,
    /// The iteration limit was hit. The data is the iteration limit.
    IterationLimit(usize),
    /// The enode limit was hit. The data is the enode limit.
    NodeLimit(usize),
    /// The time limit was hit. The data is the time limit in seconds.
    TimeLimit(f64),
    /// Some other reason to stop.
    Other(String),
}

/// Data generated by running a [`Runner`] one iteration.
///
/// If the `serde-1` feature is enabled, this implements
/// [`serde::Serialize`][ser], which is useful if you want to output
/// this as a JSON or some other format.
///
/// [`Runner`]: struct.Runner.html
/// [ser]: https://docs.rs/serde/latest/serde/trait.Serialize.html
#[derive(Debug, Clone)]
#[cfg_attr(feature = "serde-1", derive(serde::Serialize))]
#[non_exhaustive]
pub struct Iteration<IterData> {
    /// The number of enodes in the egraph at the start of this
    /// iteration.
    pub egraph_nodes: usize,
    /// The number of eclasses in the egraph at the start of this
    /// iteration.
    pub egraph_classes: usize,
    /// A map from rule name to number of times it was _newly_ applied
    /// in this iteration.
    pub applied: IndexMap<String, usize>,
    /// Seconds spent running hooks.
    pub hook_time: f64,
    /// Seconds spent searching in this iteration.
    pub search_time: f64,
    /// Seconds spent applying rules in this iteration.
    pub apply_time: f64,
    /// Seconds spent [`rebuild`](struct.EGraph.html#method.rebuild)ing
    /// the egraph in this iteration.
    pub rebuild_time: f64,
    /// Total time spent in this iteration, including data generation time.
    pub total_time: f64,
    /// The user provided annotation for this iteration
    pub data: IterData,
    /// The number of rebuild iterations done after this iteration completed.
    pub n_rebuilds: usize,
    /// If the runner stopped on this iterations, this is the reason
    pub stop_reason: Option<StopReason>,
}

type RunnerResult<T> = std::result::Result<T, StopReason>;

impl<L, N, IterData> Runner<L, N, IterData>
where
    L: Language,
    N: Analysis<L>,
    IterData: IterationData<L, N>,
{
    /// Create a new `Runner` with the given analysis and default parameters.
    pub fn new(analysis: N) -> Self {
        Self {
            iter_limit: 30,
            node_limit: 10_000,
            time_limit: Duration::from_secs(5),

            egraph: EGraph::new(analysis),
            roots: vec![],
            iterations: vec![],
            stop_reason: None,
            hooks: vec![],

            start_time: None,
            scheduler: Box::new(BackoffScheduler::default()),
        }
    }

    /// Sets the iteration limit. Default: 30
    pub fn with_iter_limit(self, iter_limit: usize) -> Self {
        Self { iter_limit, ..self }
    }

    /// Sets the egraph size limit (in enodes). Default: 10,000
    pub fn with_node_limit(self, node_limit: usize) -> Self {
        Self { node_limit, ..self }
    }

    /// Sets the runner time limit. Default: 5 seconds
    pub fn with_time_limit(self, time_limit: Duration) -> Self {
        Self { time_limit, ..self }
    }

    /// Add a hook to instrument or modify the behavior of a [`Runner`].
    ///
    /// # Example
    /// ```
    /// # use egg::*;
    /// let rules: &[Rewrite<SymbolLang, ()>] = &[
    ///     rewrite!("commute-add"; "(+ ?a ?b)" => "(+ ?b ?a)"),
    ///     // probably some others ...
    /// ];
    ///
    /// Runner::<SymbolLang, ()>::default()
    ///     .with_expr(&"(+ 5 2)".parse().unwrap())
    ///     .with_hook(|runner| {
    ///          println!("Egraph is this big: {}", runner.egraph.total_size());
    ///          Ok(())
    ///     })
    ///     .run(rules);
    /// ```
    /// [`Runner`]: struct.Runner.html
    pub fn with_hook<F>(mut self, hook: F) -> Self
    where
        F: FnMut(&mut Self) -> Result<(), String> + 'static,
    {
        self.hooks.push(Box::new(hook));
        self
    }

    /// Change out the [`RewriteScheduler`] used by this [`Runner`].
    /// The default one is [`BackoffScheduler`].
    ///
    /// [`RewriteScheduler`]: trait.RewriteScheduler.html
    /// [`BackoffScheduler`]: struct.BackoffScheduler.html
    /// [`Runner`]: struct.Runner.html
    pub fn with_scheduler(self, scheduler: impl RewriteScheduler<L, N> + 'static) -> Self {
        let scheduler = Box::new(scheduler);
        Self { scheduler, ..self }
    }

    /// Add an expression to the egraph to be run.
    ///
    /// The eclass id of this addition will be recorded in the
    /// [`roots`](struct.Runner.html#structfield.roots) field, ordered by
    /// insertion order.
    pub fn with_expr(mut self, expr: &RecExpr<L>) -> Self {
        let id = self.egraph.add_expr(expr);
        self.roots.push(id);
        self
    }

    /// Replace the [`EGraph`](struct.EGraph.html) of this `Runner`.
    pub fn with_egraph(self, egraph: EGraph<L, N>) -> Self {
        Self { egraph, ..self }
    }

    /// Run this `Runner` until it stops.
    /// After this, the field
    /// [`stop_reason`](#structfield.stop_reason) is guaranteed to be
    /// set.
    pub fn run<'a, R>(mut self, rules: R) -> Self
    where
        R: IntoIterator<Item = &'a Rewrite<L, N>>,
        L: 'a,
        N: 'a,
    {
        let rules: Vec<&Rewrite<L, N>> = rules.into_iter().collect();
        check_rules(&rules);
        self.egraph.rebuild();
        // TODO check that we haven't
        loop {
            if let Err(stop_reason) = self.run_one(&rules) {
                info!("Stopping: {:?}", stop_reason);
                self.stop_reason = Some(stop_reason);
                // push on a final iteration to mark the end state
                self.iterations.push(Iteration {
                    stop_reason: self.stop_reason.clone(),
                    egraph_nodes: self.egraph.total_number_of_nodes(),
                    egraph_classes: self.egraph.number_of_classes(),
                    data: IterData::make(&self),
                    applied: Default::default(),
                    search_time: Default::default(),
                    hook_time: Default::default(),
                    apply_time: Default::default(),
                    rebuild_time: Default::default(),
                    total_time: Default::default(),
                    n_rebuilds: Default::default(),
                });
                break;
            }
        }

        self
    }

    #[rustfmt::skip]
    /// Prints some information about a runners run.
    pub fn print_report(&self) {
        let search_time: f64 = self.iterations.iter().map(|i| i.search_time).sum();
        let apply_time: f64 = self.iterations.iter().map(|i| i.apply_time).sum();
        let rebuild_time: f64 = self.iterations.iter().map(|i| i.rebuild_time).sum();
        let total_time: f64 = self.iterations.iter().map(|i| i.total_time).sum();

        let iters = self.iterations.len();
        let rebuilds: usize = self.iterations.iter().map(|i| i.n_rebuilds).sum();

        let eg = &self.egraph;
        println!("Runner report");
        println!("=============");
        println!("  Stop reason: {:?}", self.stop_reason.as_ref().unwrap());
        println!("  Iterations: {}", iters);
        println!("  Egraph size: {} nodes, {} classes, {} memo", eg.total_number_of_nodes(), eg.number_of_classes(), eg.total_size());
        println!("  Rebuilds: {}, {:.2} per iter", rebuilds, (rebuilds as f64) / (iters as f64));
        println!("  Total time: {}", total_time);
        println!("    Search:  ({:.2}) {}", search_time / total_time, search_time);
        println!("    Apply:   ({:.2}) {}", apply_time / total_time, apply_time);
        println!("    Rebuild: ({:.2}) {}", rebuild_time / total_time, rebuild_time);
    }

    fn run_one(&mut self, rules: &[&Rewrite<L, N>]) -> RunnerResult<()> {
        assert!(self.stop_reason.is_none());

        info!("\nIteration {}", self.iterations.len());

        self.try_start();
        self.check_limits()?;

        let hook_time = Instant::now();
        let mut hooks = std::mem::take(&mut self.hooks);
        for hook in &mut hooks {
            hook(self).map_err(StopReason::Other)?
        }
        self.hooks = hooks;
        let hook_time = hook_time.elapsed().as_secs_f64();

        let i = self.iterations.len();
        let egraph_nodes = self.egraph.total_size();
        let egraph_classes = self.egraph.number_of_classes();
        trace!("EGraph {:?}", self.egraph.dump());

        let start_time = Instant::now();

        let mut matches = Vec::new();
        for rule in rules {
            let ms = self.scheduler.search_rewrite(i, &self.egraph, rule);
            matches.push(ms);
            if self.check_limits().is_err() {
                // bail on searching, make sure applying doesn't do anything
                matches.clear();
                break;
            }
        }

        let search_time = start_time.elapsed().as_secs_f64();
        info!("Search time: {}", search_time);

        let apply_time = Instant::now();

        let mut applied = IndexMap::new();
        for (rw, ms) in rules.iter().zip(matches) {
            let total_matches: usize = ms.iter().map(|m| m.substs.len()).sum();
            if total_matches == 0 {
                continue;
            }

            debug!("Applying {} {} times", rw.name(), total_matches);

            let actually_matched = self.scheduler.apply_rewrite(i, &mut self.egraph, rw, ms);
            if actually_matched > 0 {
                if let Some(count) = applied.get_mut(rw.name()) {
                    *count += actually_matched;
                } else {
                    applied.insert(rw.name().to_owned(), actually_matched);
                }
                debug!("Applied {} {} times", rw.name(), actually_matched);
            }

            if self.check_limits().is_err() {
                break;
            }
        }

        let apply_time = apply_time.elapsed().as_secs_f64();
        info!("Apply time: {}", apply_time);

        let rebuild_time = Instant::now();
        let n_rebuilds = self.egraph.rebuild();

        let rebuild_time = rebuild_time.elapsed().as_secs_f64();
        info!("Rebuild time: {}", rebuild_time);
        info!(
            "Size: n={}, e={}",
            self.egraph.total_size(),
            self.egraph.number_of_classes()
        );

        let saturated = applied.is_empty() && self.scheduler.can_stop(i);

        self.iterations.push(Iteration {
            applied,
            egraph_nodes,
            egraph_classes,
            hook_time,
            search_time,
            apply_time,
            rebuild_time,
            n_rebuilds,
            data: IterData::make(&self),
            total_time: start_time.elapsed().as_secs_f64(),
            stop_reason: None,
        });

        if saturated {
            Err(StopReason::Saturated)
        } else {
            Ok(())
        }
    }

    fn try_start(&mut self) {
        self.start_time.get_or_insert_with(Instant::now);
    }

    fn check_limits(&self) -> RunnerResult<()> {
        let elapsed = self.start_time.unwrap().elapsed();
        if elapsed > self.time_limit {
            return Err(StopReason::TimeLimit(elapsed.as_secs_f64()));
        }

        let size = self.egraph.total_size();
        if size > self.node_limit {
            return Err(StopReason::NodeLimit(size));
        }

        if self.iterations.len() >= self.iter_limit {
            return Err(StopReason::IterationLimit(self.iterations.len()));
        }

        Ok(())
    }
}

fn check_rules<L, N>(rules: &[&Rewrite<L, N>]) {
    let mut name_counts = IndexMap::new();
    for rw in rules {
        *name_counts.entry(rw.name()).or_default() += 1
    }

    name_counts.retain(|_, count: &mut usize| *count > 1);
    if !name_counts.is_empty() {
        eprintln!("WARNING: Duplicated rule names may affect rule reporting and scheduling.");
        log::warn!("Duplicated rule names may affect rule reporting and scheduling.");
        for (name, &count) in name_counts.iter() {
            assert!(count > 1);
            eprintln!("Rule '{}' appears {} times", name, count);
            log::warn!("Rule '{}' appears {} times", name, count);
        }
    }
}

/** A way to customize how a [`Runner`] runs [`Rewrite`]s.

This gives you a way to prevent certain [`Rewrite`]s from exploding
the [`EGraph`] and dominating how much time is spent while running the
[`Runner`].

[`EGraph`]: struct.EGraph.html
[`Runner`]: struct.Runner.html
[`Rewrite`]: struct.Rewrite.html
*/
#[allow(unused_variables)]
pub trait RewriteScheduler<L, N>
where
    L: Language,
    N: Analysis<L>,
{
    /// Whether or not the [`Runner`](struct.Runner.html) is allowed
    /// to say it has saturated.
    ///
    /// This is only called when the runner is otherwise saturated.
    /// Default implementation just returns `true`.
    fn can_stop(&mut self, iteration: usize) -> bool {
        true
    }

    /// A hook allowing you to customize rewrite searching behavior.
    /// Useful to implement rule management.
    ///
    /// Default implementation just calls
    /// [`Rewrite::search`](struct.Rewrite.html#method.search).
    fn search_rewrite(
        &mut self,
        iteration: usize,
        egraph: &EGraph<L, N>,
        rewrite: &Rewrite<L, N>,
    ) -> Vec<SearchMatches> {
        rewrite.search(egraph)
    }

    /// A hook allowing you to customize rewrite application behavior.
    /// Useful to implement rule management.
    ///
    /// Default implementation just calls
    /// [`Rewrite::apply`](struct.Rewrite.html#method.apply)
    /// and returns number of new applications.
    fn apply_rewrite(
        &mut self,
        iteration: usize,
        egraph: &mut EGraph<L, N>,
        rewrite: &Rewrite<L, N>,
        matches: Vec<SearchMatches>,
    ) -> usize {
        rewrite.apply(egraph, &matches).len()
    }
}

/// A very simple [`RewriteScheduler`] that runs every rewrite every
/// time.
///
/// Using this is basically turning off rule scheduling.
/// It uses the default implementation for all [`RewriteScheduler`]
/// methods.
///
/// This is not the default scheduler; choose it with the
/// [`with_scheduler`](struct.Runner.html#method.with_scheduler)
/// method.
///
/// [`RewriteScheduler`]: trait.RewriteScheduler.html
pub struct SimpleScheduler;

impl<L, N> RewriteScheduler<L, N> for SimpleScheduler
where
    L: Language,
    N: Analysis<L>,
{
}

/// A [`RewriteScheduler`] that implements exponentional rule backoff.
///
/// For each rewrite, there exists a configurable initial match limit.
/// If a rewrite search yield more than this limit, then we ban this
/// rule for number of iterations, double its limit, and double the time
/// it will be banned next time.
///
/// This seems effective at preventing explosive rules like
/// associativity from taking an unfair amount of resources.
///
/// [`BackoffScheduler`] is configurable in the builder-pattern style.
///
/// [`RewriteScheduler`]: trait.RewriteScheduler.html
/// [`BackoffScheduler`]: struct.BackoffScheduler.html
pub struct BackoffScheduler {
    initial_match_limit: usize,
    ban_length: usize,
    stats: IndexMap<String, RuleStats>,
    dont_ban: IndexSet<String>,
}

struct RuleStats {
    times_applied: usize,
    banned_until: usize,
    times_banned: usize,
}

impl BackoffScheduler {
    /// Set the initial match limit after which a rule will be banned.
    /// Default: 1,000
    pub fn with_initial_match_limit(self, initial_match_limit: usize) -> Self {
        Self {
            initial_match_limit,
            ..self
        }
    }

    /// Set the initial ban length.
    /// Default: 5 iterations
    pub fn with_ban_length(self, ban_length: usize) -> Self {
        Self { ban_length, ..self }
    }

    /// Never ban a particular rule.
    pub fn do_not_ban(mut self, name: impl Into<String>) -> Self {
        self.dont_ban.insert(name.into());
        self
    }
}

impl Default for BackoffScheduler {
    fn default() -> Self {
        Self {
            dont_ban: Default::default(),
            stats: Default::default(),
            initial_match_limit: 1_000,
            ban_length: 5,
        }
    }
}

impl<L, N> RewriteScheduler<L, N> for BackoffScheduler
where
    L: Language,
    N: Analysis<L>,
{
    fn can_stop(&mut self, iteration: usize) -> bool {
        let n_stats = self.stats.len();

        let mut banned: Vec<_> = self
            .stats
            .iter_mut()
            .filter(|(_, s)| s.banned_until > iteration)
            .collect();

        if banned.is_empty() {
            true
        } else {
            let min_ban = banned
                .iter()
                .map(|(_, s)| s.banned_until)
                .min()
                .expect("banned cannot be empty here");

            assert!(min_ban >= iteration);
            let delta = min_ban - iteration;

            let mut unbanned = vec![];
            for (name, s) in &mut banned {
                s.banned_until -= delta;
                if s.banned_until == iteration {
                    unbanned.push(name.as_str());
                }
            }

            assert!(!unbanned.is_empty());
            info!(
                "Banned {}/{}, fast-forwarded by {} to unban {}",
                banned.len(),
                n_stats,
                delta,
                unbanned.join(", "),
            );

            false
        }
    }

    fn search_rewrite(
        &mut self,
        iteration: usize,
        egraph: &EGraph<L, N>,
        rewrite: &Rewrite<L, N>,
    ) -> Vec<SearchMatches> {
        if let Some(limit) = self.stats.get_mut(rewrite.name()) {
            if iteration < limit.banned_until {
                debug!(
                    "Skipping {} ({}-{}), banned until {}...",
                    rewrite.name(),
                    limit.times_applied,
                    limit.times_banned,
                    limit.banned_until,
                );
                return vec![];
            }

            let matches = rewrite.search(egraph);
            let total_len: usize = matches.iter().map(|m| m.substs.len()).sum();
            let threshold = self.initial_match_limit << limit.times_banned;
            if total_len > threshold {
                let ban_length = self.ban_length << limit.times_banned;
                limit.times_banned += 1;
                limit.banned_until = iteration + ban_length;
                info!(
                    "Banning {} ({}-{}) for {} iters: {} < {}",
                    rewrite.name(),
                    limit.times_applied,
                    limit.times_banned,
                    ban_length,
                    threshold,
                    total_len,
                );
                vec![]
            } else {
                limit.times_applied += 1;
                matches
            }
        } else {
            if !self.dont_ban.contains(rewrite.name()) {
                self.stats.insert(
                    rewrite.name().into(),
                    RuleStats {
                        times_applied: 0,
                        banned_until: 0,
                        times_banned: 0,
                    },
                );
            }
            rewrite.search(egraph)
        }
    }
}

/// Custom data to inject into the [`Iteration`]s recorded by a [`Runner`]
///
/// This trait allows you to add custom data to the [`Iteration`]s
/// recorded as a [`Runner`] applies rules.
///
/// See the [`Runner`] docs for an example.
///
/// [`Runner`] is generic over the [`IterationData`] that it will be in the
/// [`Iteration`]s, but by default it uses `()`.
///
/// [`Runner`]: struct.Runner.html
/// [`Iteration`]: struct.Iteration.html
/// [`IterationData`]: trait.IterationData.html
pub trait IterationData<L, N>: Sized
where
    L: Language,
    N: Analysis<L>,
{
    /// Given the current [`Runner`](struct.Runner.html), make the
    /// data to be put in this [`Iteration`](struct.Iteration.html).
    fn make(runner: &Runner<L, N, Self>) -> Self;
}

impl<L, N> IterationData<L, N> for ()
where
    L: Language,
    N: Analysis<L>,
{
    fn make(_: &Runner<L, N, Self>) -> Self {}
}