Details

sample64.0ms

Algorithm

intervals

Results

29.0ms	81×	body	1280	valid
9.0ms	47×	body	640	valid
6.0ms	163×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	16×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5028
8	3392
7	883
6	221
5	93
4	44
3	23
2	16
1	11
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.6b	(- (exp (* a x)) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 24

Calls

2 calls:

6.0ms	(exp (* a x))
19.0ms	(- (exp (* a x)) 1.0)

series60.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
45.0ms	(- (exp (* a x)) 1.0)

simplify2.8s

Counts

30 → 30

Iterations

Iter	Nodes
done	5002
4	4038
3	1117
2	310
1	116
0	53

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* (* x a) 1/2))
4.4b	(+ (* x a) (* (* x a) (* (* x a) 1/2)))
12.1b	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

64×	`pow1`
37×	`add-cbrt-cube` `add-exp-log`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
2×	`+-commutative` `flip3-+` `pow-plus` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`pow2` `associate-+r+` `swap-sqr`

Counts

4 → 86

Calls

4 calls:

42.0ms	(* (* x a) (* x a))
86.0ms	(* (* x a) (* (* x a) 1/2))
8.0ms	(+ (* x a) (* (* x a) (* (* x a) 1/2)))
317.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* x a) (* x a))
51.0ms	(* (* x a) (* (* x a) 1/2))
91.0ms	(+ (* x a) (* (* x a) (* (* x a) 1/2)))
162.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* x a) (* (* x a) (* (* x a) 1/2))))

simplify1.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1633
1	368
0	123

prune296.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.2b	(* x (* 3 a))
4.5b	(- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--`

Counts

4 → 50

Calls

4 calls:

3.0ms	(exp (* a x))
3.0ms	(exp (* a x))
21.0ms	(* x (* 3 a))
33.0ms	(- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(exp (* a x))
21.0ms	(exp (* a x))
28.0ms	(* x (* 3 a))
60.0ms	(- (exp (* x (* 3 a))) (* 1.0 (* 1.0 1.0)))

simplify2.3s

Counts

62 → 62

Iterations

Iter	Nodes
done	5003
3	3498
2	711
1	223
0	90

prune292.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* 9 a))
0.2b	(* (* a x) 3)
0.2b	(* (* a x) 3)
4.4b	(- (exp (* x (* 9 a))) (* (* (* (* 1.0 1.0) (* 1.0 1.0)) 1.0) (* (* 1.0 1.0) (* 1.0 1.0))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
3×	`*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 66

Calls

4 calls:

12.0ms	(* x (* 9 a))
13.0ms	(* (* a x) 3)
17.0ms	(* (* a x) 3)
17.0ms	(- (exp (* x (* 9 a))) (* (* (* (* 1.0 1.0) (* 1.0 1.0)) 1.0) (* (* 1.0 1.0) (* 1.0 1.0))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* x (* 9 a))
35.0ms	(* (* a x) 3)
23.0ms	(* (* a x) 3)
54.0ms	(- (exp (* x (* 9 a))) (* (* (* (* 1.0 1.0) (* 1.0 1.0)) 1.0) (* (* 1.0 1.0) (* 1.0 1.0))))

simplify1.5s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1184
1	297
0	109

prune645.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

37.4% (13.9b remaining)

Error of 14.0b against oracle of 0.1b and baseline of 22.3b

bsearch436.0ms

Steps

Iters	Range		Point
9	1.4933560481619722e+96	2.1498767242488486e+105	1.61596322380751e+101
5	-2.639018161482553e-43	-8.703467406804623e-44	-2.2530088269998953e-43
9	-1.5217483354069433e-28	-2.593318257876323e-34	-2.7735030981717545e-34
9	-1.2225730314059041e+79	-1.8599689544989674e+74	-4.7697460024798494e+75

simplify49.2s

Iterations

Iter	Nodes
done	5001
660	4996
659	4989
658	4981
657	4974
656	4966
655	4959
654	4951
653	4944
652	4936
651	4929
650	4921
649	4914
648	4906
647	4899
646	4891
645	4884
644	4876
643	4869
642	4861
641	4854
640	4846
639	4839
638	4831
637	4824
636	4816
635	4809
634	4801
633	4794
632	4786
631	4779
630	4771
629	4764
628	4756
627	4749
626	4741
625	4734
624	4726
623	4719
622	4711
621	4704
620	4696
619	4689
618	4681
617	4674
616	4666
615	4659
614	4651
613	4644
612	4636
611	4629
610	4621
609	4614
608	4606
607	4599
606	4591
605	4584
604	4576
603	4569
602	4561
601	4554
600	4546
599	4539
598	4531
597	4524
596	4516
595	4509
594	4501
593	4494
592	4486
591	4479
590	4471
589	4464
588	4456
587	4449
586	4441
585	4434
584	4426
583	4419
582	4411
581	4404
580	4396
579	4389
578	4381
577	4374
576	4366
575	4359
574	4351
573	4344
572	4336
571	4329
570	4321
569	4314
568	4306
567	4299
566	4291
565	4284
564	4276
563	4269
562	4261
561	4254
560	4246
559	4239
558	4231
557	4224
556	4216
555	4209
554	4201
553	4194
552	4186
551	4179
550	4171
549	4164
548	4156
547	4149
546	4141
545	4134
544	4126
543	4119
542	4111
541	4104
540	4096
539	4089
538	4081
537	4074
536	4066
535	4059
534	4051
533	4044
532	4036
531	4029
530	4021
529	4014
528	4006
527	3999
526	3991
525	3984
524	3976
523	3969
522	3961
521	3954
520	3946
519	3939
518	3931
517	3924
516	3916
515	3909
514	3901
513	3894
512	3886
511	3879
510	3871
509	3864
508	3856
507	3849
506	3841
505	3834
504	3826
503	3819
502	3811
501	3804
500	3796
499	3789
498	3781
497	3774
496	3766
495	3759
494	3751
493	3744
492	3736
491	3729
490	3721
489	3714
488	3706
487	3699
486	3691
485	3684
484	3676
483	3669
482	3661
481	3654
480	3646
479	3639
478	3631
477	3624
476	3616
475	3609
474	3601
473	3594
472	3586
471	3579
470	3571
469	3564
468	3556
467	3549
466	3541
465	3534
464	3526
463	3519
462	3511
461	3504
460	3496
459	3489
458	3481
457	3474
456	3466
455	3459
454	3451
453	3444
452	3436
451	3429
450	3421
449	3414
448	3406
447	3399
446	3391
445	3384
444	3376
443	3369
442	3361
441	3354
440	3346
439	3339
438	3331
437	3324
436	3316
435	3309
434	3301
433	3294
432	3286
431	3279
430	3271
429	3264
428	3256
427	3249
426	3241
425	3234
424	3226
423	3219
422	3211
421	3204
420	3196
419	3189
418	3181
417	3174
416	3166
415	3159
414	3151
413	3144
412	3136
411	3129
410	3121
409	3114
408	3106
407	3099
406	3091
405	3084
404	3076
403	3069
402	3061
401	3054
400	3046
399	3039
398	3031
397	3024
396	3016
395	3009
394	3001
393	2994
392	2986
391	2979
390	2971
389	2964
388	2956
387	2949
386	2941
385	2934
384	2926
383	2919
382	2911
381	2904
380	2896
379	2889
378	2881
377	2874
376	2866
375	2859
374	2851
373	2844
372	2836
371	2829
370	2821
369	2814
368	2806
367	2799
366	2791
365	2784
364	2776
363	2769
362	2761
361	2754
360	2746
359	2739
358	2731
357	2724
356	2716
355	2709
354	2701
353	2694
352	2686
351	2679
350	2671
349	2664
348	2656
347	2649
346	2641
345	2634
344	2626
343	2619
342	2611
341	2604
340	2596
339	2589
338	2581
337	2574
336	2566
335	2559
334	2551
333	2544
332	2536
331	2529
330	2521
329	2514
328	2506
327	2499
326	2491
325	2484
324	2476
323	2469
322	2461
321	2454
320	2446
319	2439
318	2431
317	2424
316	2416
315	2409
314	2401
313	2394
312	2386
311	2379
310	2371
309	2364
308	2356
307	2349
306	2341
305	2334
304	2326
303	2319
302	2311
301	2304
300	2296
299	2289
298	2281
297	2274
296	2266
295	2259
294	2251
293	2244
292	2236
291	2229
290	2221
289	2214
288	2206
287	2199
286	2191
285	2184
284	2176
283	2169
282	2161
281	2154
280	2146
279	2139
278	2131
277	2124
276	2116
275	2109
274	2101
273	2094
272	2086
271	2079
270	2071
269	2064
268	2056
267	2049
266	2041
265	2034
264	2026
263	2019
262	2011
261	2004
260	1996
259	1989
258	1981
257	1974
256	1966
255	1959
254	1951
253	1944
252	1936
251	1929
250	1921
249	1914
248	1906
247	1899
246	1891
245	1884
244	1876
243	1869
242	1861
241	1854
240	1846
239	1839
238	1831
237	1824
236	1816
235	1809
234	1801
233	1794
232	1786
231	1779
230	1771
229	1764
228	1756
227	1749
226	1741
225	1734
224	1726
223	1719
222	1711
221	1704
220	1696
219	1689
218	1681
217	1674
216	1666
215	1659
214	1651
213	1644
212	1636
211	1629
210	1621
209	1614
208	1606
207	1599
206	1591
205	1584
204	1576
203	1569
202	1561
201	1554
200	1546
199	1539
198	1531
197	1524
196	1516
195	1509
194	1501
193	1494
192	1486
191	1479
190	1471
189	1464
188	1456
187	1449
186	1441
185	1434
184	1426
183	1419
182	1411
181	1404
180	1396
179	1389
178	1381
177	1374
176	1366
175	1359
174	1351
173	1344
172	1336
171	1329
170	1321
169	1314
168	1306
167	1299
166	1291
165	1284
164	1276
163	1269
162	1261
161	1254
160	1246
159	1239
158	1231
157	1224
156	1216
155	1209
154	1201
153	1194
152	1186
151	1179
150	1171
149	1164
148	1156
147	1149
146	1141
145	1134
144	1126
143	1119
142	1111
141	1104
140	1096
139	1089
138	1081
137	1074
136	1066
135	1059
134	1051
133	1044
132	1036
131	1029
130	1021
129	1014
128	1006
127	999
126	991
125	984
124	976
123	969
122	961
121	954
120	946
119	939
118	931
117	924
116	916
115	909
114	901
113	894
112	886
111	879
110	871
109	864
108	856
107	849
106	841
105	834
104	826
103	819
102	811
101	804
100	796
99	789
98	781
97	774
96	766
95	759
94	751
93	744
92	736
91	729
90	721
89	714
88	706
87	699
86	691
85	684
84	676
83	669
82	661
81	654
80	646
79	639
78	631
77	624
76	616
75	609
74	601
73	594
72	586
71	579
70	571
69	564
68	556
67	549
66	541
65	534
64	526
63	519
62	511
61	504
60	496
59	489
58	481
57	474
56	466
55	459
54	451
53	444
52	436
51	429
50	421
49	414
48	406
47	399
46	391
45	384
44	376
43	369
42	361
41	354
40	346
39	339
38	331
37	324
36	316
35	309
34	301
33	294
32	286
31	279
30	271
29	264
28	256
27	249
26	241
25	234
24	226
23	219
22	211
21	204
20	196
19	189
18	181
17	174
16	166
15	159
14	151
13	144
12	136
11	129
10	121
9	114
8	104
7	103
6	100
5	99
4	96
3	93
2	87
1	84
0	59

end0.0ms

sample1.2s

Algorithm

intervals

Results

555.0ms	2713×	body	1280	valid
196.0ms	5565×	body	80	valid
133.0ms	1249×	body	640	valid
56.0ms	749×	body	320	valid
17.0ms	361×	body	160	valid