Details

sample342.0ms

Algorithm

intervals

Results

175.0ms	112×	body	1280	valid
76.0ms	17×	body	2560	valid
47.0ms	49×	body	640	valid
14.0ms	21×	body	320	valid
10.0ms	22×	body	160	valid
7.0ms	35×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize23.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.3b	(tan (+ x eps))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

23.0ms	(- (tan (+ x eps)) (tan x))
9.0ms	(tan (+ x eps))

series195.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(- (tan (+ x eps)) (tan x))
77.0ms	(tan (+ x eps))

simplify1.5s

Counts

49 → 49

Iterations

Iter	Nodes
4	3838
3	1279
2	439
1	205
0	96

prune532.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
57×	`prod-diff`
49×	`times-frac`
21×	`fma-neg`
13×	`distribute-lft-out`
10×	`add-log-exp`
8×	`associate-/r/`
7×	`tan-quot`
6×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

6.0ms	(- 1 (* (tan x) (tan eps)))
8.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
105.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series954.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(- 1 (* (tan x) (tan eps)))
134.0ms	(+ (tan x) (tan eps))
124.0ms	(* (tan x) (tan eps))
534.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

167 → 167

Iterations

Iter	Nodes
3	4560
2	1435
1	565
0	243

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite686.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
100×	`times-frac`
90×	`prod-diff`
83×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/` `add-log-exp`
6×	`pow1`
5×	`flip3--` `tan-quot` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `-commutative` `frac-sub` `flip-+` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 205

Calls

4 calls:

11.0ms	(+ (tan x) (tan eps))
30.0ms	(/ (* (tan x) (sin eps)) (cos eps))
27.0ms	(* (tan x) (sin eps))
613.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series974.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (tan x) (tan eps))
133.0ms	(/ (* (tan x) (sin eps)) (cos eps))
97.0ms	(* (tan x) (sin eps))
620.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify3.1s

Counts

217 → 217

Iterations

Iter	Nodes
3	7010
2	1819
1	692
0	296

prune3.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.2b	(* (tan x) (sin eps))
0.2b	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
3.5b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-cbrt-cube` `add-exp-log`
22×	`add-sqr-sqrt`
17×	`prod-exp` `cbrt-unprod`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`pow1`
13×	`associate-r` `associate-l`
12×	`cbrt-undiv` `times-frac` `div-exp`
7×	`swap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `associate-l/` `-commutative` `unswap-sqr`
2×	`tan-quot`
1×	`pow2` `frac-times` `pow-plus` `associate-*r/` `pow-sqr` `pow-prod-up` `fma-udef`

Counts

4 → 114

Calls

4 calls:

14.0ms	(* (tan x) (sin eps))
20.0ms	(* (tan x) (sin eps))
60.0ms	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (tan x) (sin eps))
92.0ms	(* (tan x) (sin eps))
159.0ms	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
840.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))

simplify782.0ms

Counts

126 → 126

Iterations

Iter	Nodes
2	2242
1	550
0	190

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.5b

regimes405.0ms

Accuracy

89% (0.8b remaining)

Error of 15.4b against oracle of 14.6b and baseline of 22.1b

bsearch570.0ms

Steps

Iters	Range		Point
9	2.8247475806395485e-77	4.478245262004958e-68	4.367505480077063e-68
11	-511.55301347613675	-1.7758424453292816e-19	-7.812094276090538e-18

simplify7.3s

Iterations

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

end0.0ms

sample13.7s

Algorithm

intervals

Results

7.6s	3310×	body	1280	valid
2.6s	1902×	body	640	valid
2.1s	630×	body	2560	valid
727.0ms	755×	body	320	valid
302.0ms	1053×	body	80	valid
162.0ms	350×	body	160	valid