Details

sample469.0ms

Algorithm

intervals

Results

99.0ms	144×	body	80	valid
92.0ms	46×	body	1280	valid
69.0ms	19×	body	320	valid
48.0ms	38×	body	640	valid
5.0ms	9×	body	160	valid

simplify113.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	42
5	42
4	37
3	29
2	22
1	13
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 128

Calls

4 calls:

31.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
12.0ms	(- 1 (* (tan x) (tan x)))
29.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
57.0ms	(- 1 (* (tan x) (tan x)))
73.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify4.7s

Counts

140 → 140

Iterations

Iter	Nodes
3	2924
2	989
1	381
0	157

prune971.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite670.0ms

Algorithm

rewrite-expression-head

Rules

240×	`pow1`
74×	`pow-prod-up`
72×	`tan-quot`
48×	`pow-prod-down`
46×	`pow-sqr`
38×	`pow-plus`
36×	`frac-times`
32×	`add-cbrt-cube` `add-exp-log`
28×	`pow2`
24×	`associate-l/` `associate-r/`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))
535.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
89.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))
68.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
74.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.1s

Counts

236 → 236

Iterations

Iter	Nodes
3	2206
2	896
1	299
0	112

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.6b	(expm1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16`
3×	`fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`expm1-log1p` `sub-neg` `flip3--` `diff-log` `flip--` `expm1-udef`

Counts

4 → 97

Calls

4 calls:

14.0ms	(- 1 (* (tan x) (tan x)))
28.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))
0.0ms	(expm1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1 (* (tan x) (tan x)))
53.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
179.0ms	(expm1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

simplify11.1s

Counts

109 → 109

Iterations

Iter	Nodes
4	4269
3	1468
2	609
1	265
0	116

prune781.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (tan x))
0.6b	(expm1 (/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`prod-diff`
12×	`times-frac`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`tan-quot` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `div-inv`
3×	`associate-/r` `fma-neg` `swap-sqr` `associate-r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`pow2` `frac-times` `expm1-log1p` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `associate-r/` `pow-sqr` `-commutative` `pow-prod-up` `flip--` `associate-/l*` `distribute-lft-out--` `expm1-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

24.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
30.0ms	(/ (* (tan x) (sin x)) (cos x))
28.0ms	(* (tan x) (tan x))
1.0ms	(expm1 (/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x)))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
107.0ms	(/ (* (tan x) (sin x)) (cos x))
62.0ms	(* (tan x) (tan x))
224.0ms	(expm1 (/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x)))))

simplify11.4s

Counts

122 → 122

Iterations

Iter	Nodes
3	5576
2	1437
1	487
0	201

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.0b

regimes497.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.4s

Iterations

Iter	Nodes
987	2001
986	1999
985	1997
984	1995
983	1993
982	1991
981	1989
980	1987
979	1985
978	1983
977	1981
976	1979
975	1977
974	1975
973	1973
972	1971
971	1969
970	1967
969	1965
968	1963
967	1961
966	1959
965	1957
964	1955
963	1953
962	1951
961	1949
960	1947
959	1945
958	1943
957	1941
956	1939
955	1937
954	1935
953	1933
952	1931
951	1929
950	1927
949	1925
948	1923
947	1921
946	1919
945	1917
944	1915
943	1913
942	1911
941	1909
940	1907
939	1905
938	1903
937	1901
936	1899
935	1897
934	1895
933	1893
932	1891
931	1889
930	1887
929	1885
928	1883
927	1881
926	1879
925	1877
924	1875
923	1873
922	1871
921	1869
920	1867
919	1865
918	1863
917	1861
916	1859
915	1857
914	1855
913	1853
912	1851
911	1849
910	1847
909	1845
908	1843
907	1841
906	1839
905	1837
904	1835
903	1833
902	1831
901	1829
900	1827
899	1825
898	1823
897	1821
896	1819
895	1817
894	1815
893	1813
892	1811
891	1809
890	1807
889	1805
888	1803
887	1801
886	1799
885	1797
884	1795
883	1793
882	1791
881	1789
880	1787
879	1785
878	1783
877	1781
876	1779
875	1777
874	1775
873	1773
872	1771
871	1769
870	1767
869	1765
868	1763
867	1761
866	1759
865	1757
864	1755
863	1753
862	1751
861	1749
860	1747
859	1745
858	1743
857	1741
856	1739
855	1737
854	1735
853	1733
852	1731
851	1729
850	1727
849	1725
848	1723
847	1721
846	1719
845	1717
844	1715
843	1713
842	1711
841	1709
840	1707
839	1705
838	1703
837	1701
836	1699
835	1697
834	1695
833	1693
832	1691
831	1689
830	1687
829	1685
828	1683
827	1681
826	1679
825	1677
824	1675
823	1673
822	1671
821	1669
820	1667
819	1665
818	1663
817	1661
816	1659
815	1657
814	1655
813	1653
812	1651
811	1649
810	1647
809	1645
808	1643
807	1641
806	1639
805	1637
804	1635
803	1633
802	1631
801	1629
800	1627
799	1625
798	1623
797	1621
796	1619
795	1617
794	1615
793	1613
792	1611
791	1609
790	1607
789	1605
788	1603
787	1601
786	1599
785	1597
784	1595
783	1593
782	1591
781	1589
780	1587
779	1585
778	1583
777	1581
776	1579
775	1577
774	1575
773	1573
772	1571
771	1569
770	1567
769	1565
768	1563
767	1561
766	1559
765	1557
764	1555
763	1553
762	1551
761	1549
760	1547
759	1545
758	1543
757	1541
756	1539
755	1537
754	1535
753	1533
752	1531
751	1529
750	1527
749	1525
748	1523
747	1521
746	1519
745	1517
744	1515
743	1513
742	1511
741	1509
740	1507
739	1505
738	1503
737	1501
736	1499
735	1497
734	1495
733	1493
732	1491
731	1489
730	1487
729	1485
728	1483
727	1481
726	1479
725	1477
724	1475
723	1473
722	1471
721	1469
720	1467
719	1465
718	1463
717	1461
716	1459
715	1457
714	1455
713	1453
712	1451
711	1449
710	1447
709	1445
708	1443
707	1441
706	1439
705	1437
704	1435
703	1433
702	1431
701	1429
700	1427
699	1425
698	1423
697	1421
696	1419
695	1417
694	1415
693	1413
692	1411
691	1409
690	1407
689	1405
688	1403
687	1401
686	1399
685	1397
684	1395
683	1393
682	1391
681	1389
680	1387
679	1385
678	1383
677	1381
676	1379
675	1377
674	1375
673	1373
672	1371
671	1369
670	1367
669	1365
668	1363
667	1361
666	1359
665	1357
664	1355
663	1353
662	1351
661	1349
660	1347
659	1345
658	1343
657	1341
656	1339
655	1337
654	1335
653	1333
652	1331
651	1329
650	1327
649	1325
648	1323
647	1321
646	1319
645	1317
644	1315
643	1313
642	1311
641	1309
640	1307
639	1305
638	1303
637	1301
636	1299
635	1297
634	1295
633	1293
632	1291
631	1289
630	1287
629	1285
628	1283
627	1281
626	1279
625	1277
624	1275
623	1273
622	1271
621	1269
620	1267
619	1265
618	1263
617	1261
616	1259
615	1257
614	1255
613	1253
612	1251
611	1249
610	1247
609	1245
608	1243
607	1241
606	1239
605	1237
604	1235
603	1233
602	1231
601	1229
600	1227
599	1225
598	1223
597	1221
596	1219
595	1217
594	1215
593	1213
592	1211
591	1209
590	1207
589	1205
588	1203
587	1201
586	1199
585	1197
584	1195
583	1193
582	1191
581	1189
580	1187
579	1185
578	1183
577	1181
576	1179
575	1177
574	1175
573	1173
572	1171
571	1169
570	1167
569	1165
568	1163
567	1161
566	1159
565	1157
564	1155
563	1153
562	1151
561	1149
560	1147
559	1145
558	1143
557	1141
556	1139
555	1137
554	1135
553	1133
552	1131
551	1129
550	1127
549	1125
548	1123
547	1121
546	1119
545	1117
544	1115
543	1113
542	1111
541	1109
540	1107
539	1105
538	1103
537	1101
536	1099
535	1097
534	1095
533	1093
532	1091
531	1089
530	1087
529	1085
528	1083
527	1081
526	1079
525	1077
524	1075
523	1073
522	1071
521	1069
520	1067
519	1065
518	1063
517	1061
516	1059
515	1057
514	1055
513	1053
512	1051
511	1049
510	1047
509	1045
508	1043
507	1041
506	1039
505	1037
504	1035
503	1033
502	1031
501	1029
500	1027
499	1025
498	1023
497	1021
496	1019
495	1017
494	1015
493	1013
492	1011
491	1009
490	1007
489	1005
488	1003
487	1001
486	999
485	997
484	995
483	993
482	991
481	989
480	987
479	985
478	983
477	981
476	979
475	977
474	975
473	973
472	971
471	969
470	967
469	965
468	963
467	961
466	959
465	957
464	955
463	953
462	951
461	949
460	947
459	945
458	943
457	941
456	939
455	937
454	935
453	933
452	931
451	929
450	927
449	925
448	923
447	921
446	919
445	917
444	915
443	913
442	911
441	909
440	907
439	905
438	903
437	901
436	899
435	897
434	895
433	893
432	891
431	889
430	887
429	885
428	883
427	881
426	879
425	877
424	875
423	873
422	871
421	869
420	867
419	865
418	863
417	861
416	859
415	857
414	855
413	853
412	851
411	849
410	847
409	845
408	843
407	841
406	839
405	837
404	835
403	833
402	831
401	829
400	827
399	825
398	823
397	821
396	819
395	817
394	815
393	813
392	811
391	809
390	807
389	805
388	803
387	801
386	799
385	797
384	795
383	793
382	791
381	789
380	787
379	785
378	783
377	781
376	779
375	777
374	775
373	773
372	771
371	769
370	767
369	765
368	763
367	761
366	759
365	757
364	755
363	753
362	751
361	749
360	747
359	745
358	743
357	741
356	739
355	737
354	735
353	733
352	731
351	729
350	727
349	725
348	723
347	721
346	719
345	717
344	715
343	713
342	711
341	709
340	707
339	705
338	703
337	701
336	699
335	697
334	695
333	693
332	691
331	689
330	687
329	685
328	683
327	681
326	679
325	677
324	675
323	673
322	671
321	669
320	667
319	665
318	663
317	661
316	659
315	657
314	655
313	653
312	651
311	649
310	647
309	645
308	643
307	641
306	639
305	637
304	635
303	633
302	631
301	629
300	627
299	625
298	623
297	621
296	619
295	617
294	615
293	613
292	611
291	609
290	607
289	605
288	603
287	601
286	599
285	597
284	595
283	593
282	591
281	589
280	587
279	585
278	583
277	581
276	579
275	577
274	575
273	573
272	571
271	569
270	567
269	565
268	563
267	561
266	559
265	557
264	555
263	553
262	551
261	549
260	547
259	545
258	543
257	541
256	539
255	537
254	535
253	533
252	531
251	529
250	527
249	525
248	523
247	521
246	519
245	517
244	515
243	513
242	511
241	509
240	507
239	505
238	503
237	501
236	499
235	497
234	495
233	493
232	491
231	489
230	487
229	485
228	483
227	481
226	479
225	477
224	475
223	473
222	471
221	469
220	467
219	465
218	463
217	461
216	459
215	457
214	455
213	453
212	451
211	449
210	447
209	445
208	443
207	441
206	439
205	437
204	435
203	433
202	431
201	429
200	427
199	425
198	423
197	421
196	419
195	417
194	415
193	413
192	411
191	409
190	407
189	405
188	403
187	401
186	399
185	397
184	395
183	393
182	391
181	389
180	387
179	385
178	383
177	381
176	379
175	377
174	375
173	373
172	371
171	369
170	367
169	365
168	363
167	361
166	359
165	357
164	355
163	353
162	351
161	349
160	347
159	345
158	343
157	341
156	339
155	337
154	335
153	333
152	331
151	329
150	327
149	325
148	323
147	321
146	319
145	317
144	315
143	313
142	311
141	309
140	307
139	305
138	303
137	301
136	299
135	297
134	295
133	293
132	291
131	289
130	287
129	285
128	283
127	281
126	279
125	277
124	275
123	273
122	271
121	269
120	267
119	265
118	263
117	261
116	259
115	257
114	255
113	253
112	251
111	249
110	247
109	245
108	243
107	241
106	239
105	237
104	235
103	233
102	231
101	229
100	227
99	225
98	223
97	221
96	219
95	217
94	215
93	213
92	211
91	209
90	207
89	205
88	203
87	201
86	199
85	197
84	195
83	193
82	191
81	189
80	187
79	185
78	183
77	181
76	179
75	177
74	175
73	173
72	171
71	169
70	167
69	165
68	163
67	161
66	159
65	157
64	155
63	153
62	151
61	149
60	147
59	145
58	143
57	141
56	139
55	137
54	135
53	133
52	131
51	129
50	127
49	125
48	123
47	121
46	119
45	117
44	115
43	113
42	111
41	109
40	107
39	105
38	103
37	101
36	99
35	97
34	95
33	93
32	91
31	89
30	87
29	85
28	83
27	81
26	79
25	77
24	75
23	73
22	71
21	69
20	67
19	65
18	63
17	61
16	59
15	57
14	55
13	53
12	51
11	49
10	47
9	45
8	43
7	41
6	39
5	37
4	35
3	33
2	31
1	27
0	18

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.8s	1552×	body	1280	valid
1.5s	1239×	body	640	valid
957.0ms	4318×	body	80	valid
489.0ms	588×	body	320	valid
131.0ms	303×	body	160	valid