Details

sample202.0ms

Algorithm

intervals

Results

41.0ms	9×	body	2560	valid
35.0ms	296×	body	80	nan
34.0ms	50×	body	1280	valid
19.0ms	178×	body	80	valid
14.0ms	32×	body	640	valid
7.0ms	20×	body	320	valid
1.0ms	6×	body	160	valid

simplify119.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	110
6	110
5	108
4	100
3	82
2	58
1	33
0	18

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.2b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
26.5b	(cos (- y (/ (* z t) 3.0)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`prod-diff`
19×	`add-cbrt-cube` `add-exp-log`
15×	`times-frac`
9×	`pow1`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `div-exp` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`clear-num` `frac-2neg`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 101

Calls

4 calls:

8.0ms	(/ (* z t) 3.0)
9.0ms	(/ a (* b 3.0))
37.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
40.0ms	(cos (- y (/ (* z t) 3.0)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* z t) 3.0)
29.0ms	(/ a (* b 3.0))
150.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
72.0ms	(cos (- y (/ (* z t) 3.0)))

simplify1.7s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	2919
1	711
0	327

prune1.5s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 14.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos y) (cos (/ (* z t) 3.0))) (* 2.0 (sqrt x)))
2.0b	(* (* (sin y) (sin (/ (* z t) 3.0))) (* 2.0 (sqrt x)))
32.1b	(cos (/ (* z t) 3.0))
32.1b	(sin (/ (* z t) 3.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`associate-r` `associate-l` `associate-l/` `-commutative`
1×	`cos-mult` `sin-mult`

Counts

4 → 68

Calls

4 calls:

37.0ms	(* (* (cos y) (cos (/ (* z t) 3.0))) (* 2.0 (sqrt x)))
42.0ms	(* (* (sin y) (sin (/ (* z t) 3.0))) (* 2.0 (sqrt x)))
3.0ms	(cos (/ (* z t) 3.0))
3.0ms	(sin (/ (* z t) 3.0))

series469.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* (* (cos y) (cos (/ (* z t) 3.0))) (* 2.0 (sqrt x)))
192.0ms	(* (* (sin y) (sin (/ (* z t) 3.0))) (* 2.0 (sqrt x)))
15.0ms	(cos (/ (* z t) 3.0))
26.0ms	(sin (/ (* z t) 3.0))

simplify1.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1362
1	330
0	132

prune950.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 14.4b

localize159.0ms

Local error

Found 4 expressions with local error:

32.1b	(cos (/ (* z t) 3.0))
32.1b	(sin (/ (* z t) 3.0))
32.1b	(sin (/ (* z t) 3.0))
32.1b	(sin (/ (* z t) 3.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

3.0ms	(cos (/ (* z t) 3.0))
3.0ms	(sin (/ (* z t) 3.0))
3.0ms	(sin (/ (* z t) 3.0))
3.0ms	(sin (/ (* z t) 3.0))

series74.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cos (/ (* z t) 3.0))
19.0ms	(sin (/ (* z t) 3.0))
18.0ms	(sin (/ (* z t) 3.0))
19.0ms	(sin (/ (* z t) 3.0))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
8	2044
7	671
6	287
5	150
4	83
3	67
2	55
1	40
0	31

prune952.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 14.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))))
0.3b	(/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
26.3b	(cos (- y (/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

148×	`times-frac`
111×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
104×	`cos-sum`
102×	`prod-diff`
63×	`cbrt-prod`
32×	`add-exp-log`
30×	`div-inv`
23×	`add-cbrt-cube`
11×	`cbrt-undiv` `div-exp`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod` `associate-/l*`
7×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`clear-num` `frac-2neg`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

7.0ms	(/ a (* b 3.0))
46.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))))
18.0ms	(/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
100.0ms	(cos (- y (/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))))

series559.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ a (* b 3.0))
241.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))))
164.0ms	(/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
134.0ms	(cos (- y (/ (/ (* z t) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))))

simplify1.5s

Counts

235 → 235

Iterations

Iter	Nodes
done	5000
1	1970
0	964

prune2.8s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 14.2b

regimes10.7s

Accuracy

52.6% (3.0b remaining)

Error of 16.9b against oracle of 13.9b and baseline of 20.3b

bsearch9.0ms

simplify8.6s

Iterations

Iter	Nodes
done	5001
1220	4999
1219	4995
1218	4991
1217	4987
1216	4983
1215	4979
1214	4975
1213	4971
1212	4967
1211	4963
1210	4959
1209	4955
1208	4951
1207	4947
1206	4943
1205	4939
1204	4935
1203	4931
1202	4927
1201	4923
1200	4919
1199	4915
1198	4911
1197	4907
1196	4903
1195	4899
1194	4895
1193	4891
1192	4887
1191	4883
1190	4879
1189	4875
1188	4871
1187	4867
1186	4863
1185	4859
1184	4855
1183	4851
1182	4847
1181	4843
1180	4839
1179	4835
1178	4831
1177	4827
1176	4823
1175	4819
1174	4815
1173	4811
1172	4807
1171	4803
1170	4799
1169	4795
1168	4791
1167	4787
1166	4783
1165	4779
1164	4775
1163	4771
1162	4767
1161	4763
1160	4759
1159	4755
1158	4751
1157	4747
1156	4743
1155	4739
1154	4735
1153	4731
1152	4727
1151	4723
1150	4719
1149	4715
1148	4711
1147	4707
1146	4703
1145	4699
1144	4695
1143	4691
1142	4687
1141	4683
1140	4679
1139	4675
1138	4671
1137	4667
1136	4663
1135	4659
1134	4655
1133	4651
1132	4647
1131	4643
1130	4639
1129	4635
1128	4631
1127	4627
1126	4623
1125	4619
1124	4615
1123	4611
1122	4607
1121	4603
1120	4599
1119	4595
1118	4591
1117	4587
1116	4583
1115	4579
1114	4575
1113	4571
1112	4567
1111	4563
1110	4559
1109	4555
1108	4551
1107	4547
1106	4543
1105	4539
1104	4535
1103	4531
1102	4527
1101	4523
1100	4519
1099	4515
1098	4511
1097	4507
1096	4503
1095	4499
1094	4495
1093	4491
1092	4487
1091	4483
1090	4479
1089	4475
1088	4471
1087	4467
1086	4463
1085	4459
1084	4455
1083	4451
1082	4447
1081	4443
1080	4439
1079	4435
1078	4431
1077	4427
1076	4423
1075	4419
1074	4415
1073	4411
1072	4407
1071	4403
1070	4399
1069	4395
1068	4391
1067	4387
1066	4383
1065	4379
1064	4375
1063	4371
1062	4367
1061	4363
1060	4359
1059	4355
1058	4351
1057	4347
1056	4343
1055	4339
1054	4335
1053	4331
1052	4327
1051	4323
1050	4319
1049	4315
1048	4311
1047	4307
1046	4303
1045	4299
1044	4295
1043	4291
1042	4287
1041	4283
1040	4279
1039	4275
1038	4271
1037	4267
1036	4263
1035	4259
1034	4255
1033	4251
1032	4247
1031	4243
1030	4239
1029	4235
1028	4231
1027	4227
1026	4223
1025	4219
1024	4215
1023	4211
1022	4207
1021	4203
1020	4199
1019	4195
1018	4191
1017	4187
1016	4183
1015	4179
1014	4175
1013	4171
1012	4167
1011	4163
1010	4159
1009	4155
1008	4151
1007	4147
1006	4143
1005	4139
1004	4135
1003	4131
1002	4127
1001	4123
1000	4119
999	4115
998	4111
997	4107
996	4103
995	4099
994	4095
993	4091
992	4087
991	4083
990	4079
989	4075
988	4071
987	4067
986	4063
985	4059
984	4055
983	4051
982	4047
981	4043
980	4039
979	4035
978	4031
977	4027
976	4023
975	4019
974	4015
973	4011
972	4007
971	4003
970	3999
969	3995
968	3991
967	3987
966	3983
965	3979
964	3975
963	3971
962	3967
961	3963
960	3959
959	3955
958	3951
957	3947
956	3943
955	3939
954	3935
953	3931
952	3927
951	3923
950	3919
949	3915
948	3911
947	3907
946	3903
945	3899
944	3895
943	3891
942	3887
941	3883
940	3879
939	3875
938	3871
937	3867
936	3863
935	3859
934	3855
933	3851
932	3847
931	3843
930	3839
929	3835
928	3831
927	3827
926	3823
925	3819
924	3815
923	3811
922	3807
921	3803
920	3799
919	3795
918	3791
917	3787
916	3783
915	3779
914	3775
913	3771
912	3767
911	3763
910	3759
909	3755
908	3751
907	3747
906	3743
905	3739
904	3735
903	3731
902	3727
901	3723
900	3719
899	3715
898	3711
897	3707
896	3703
895	3699
894	3695
893	3691
892	3687
891	3683
890	3679
889	3675
888	3671
887	3667
886	3663
885	3659
884	3655
883	3651
882	3647
881	3643
880	3639
879	3635
878	3631
877	3627
876	3623
875	3619
874	3615
873	3611
872	3607
871	3603
870	3599
869	3595
868	3591
867	3587
866	3583
865	3579
864	3575
863	3571
862	3567
861	3563
860	3559
859	3555
858	3551
857	3547
856	3543
855	3539
854	3535
853	3531
852	3527
851	3523
850	3519
849	3515
848	3511
847	3507
846	3503
845	3499
844	3495
843	3491
842	3487
841	3483
840	3479
839	3475
838	3471
837	3467
836	3463
835	3459
834	3455
833	3451
832	3447
831	3443
830	3439
829	3435
828	3431
827	3427
826	3423
825	3419
824	3415
823	3411
822	3407
821	3403
820	3399
819	3395
818	3391
817	3387
816	3383
815	3379
814	3375
813	3371
812	3367
811	3363
810	3359
809	3355
808	3351
807	3347
806	3343
805	3339
804	3335
803	3331
802	3327
801	3323
800	3319
799	3315
798	3311
797	3307
796	3303
795	3299
794	3295
793	3291
792	3287
791	3283
790	3279
789	3275
788	3271
787	3267
786	3263
785	3259
784	3255
783	3251
782	3247
781	3243
780	3239
779	3235
778	3231
777	3227
776	3223
775	3219
774	3215
773	3211
772	3207
771	3203
770	3199
769	3195
768	3191
767	3187
766	3183
765	3179
764	3175
763	3171
762	3167
761	3163
760	3159
759	3155
758	3151
757	3147
756	3143
755	3139
754	3135
753	3131
752	3127
751	3123
750	3119
749	3115
748	3111
747	3107
746	3103
745	3099
744	3095
743	3091
742	3087
741	3083
740	3079
739	3075
738	3071
737	3067
736	3063
735	3059
734	3055
733	3051
732	3047
731	3043
730	3039
729	3035
728	3031
727	3027
726	3023
725	3019
724	3015
723	3011
722	3007
721	3003
720	2999
719	2995
718	2991
717	2987
716	2983
715	2979
714	2975
713	2971
712	2967
711	2963
710	2959
709	2955
708	2951
707	2947
706	2943
705	2939
704	2935
703	2931
702	2927
701	2923
700	2919
699	2915
698	2911
697	2907
696	2903
695	2899
694	2895
693	2891
692	2887
691	2883
690	2879
689	2875
688	2871
687	2867
686	2863
685	2859
684	2855
683	2851
682	2847
681	2843
680	2839
679	2835
678	2831
677	2827
676	2823
675	2819
674	2815
673	2811
672	2807
671	2803
670	2799
669	2795
668	2791
667	2787
666	2783
665	2779
664	2775
663	2771
662	2767
661	2763
660	2759
659	2755
658	2751
657	2747
656	2743
655	2739
654	2735
653	2731
652	2727
651	2723
650	2719
649	2715
648	2711
647	2707
646	2703
645	2699
644	2695
643	2691
642	2687
641	2683
640	2679
639	2675
638	2671
637	2667
636	2663
635	2659
634	2655
633	2651
632	2647
631	2643
630	2639
629	2635
628	2631
627	2627
626	2623
625	2619
624	2615
623	2611
622	2607
621	2603
620	2599
619	2595
618	2591
617	2587
616	2583
615	2579
614	2575
613	2571
612	2567
611	2563
610	2559
609	2555
608	2551
607	2547
606	2543
605	2539
604	2535
603	2531
602	2527
601	2523
600	2519
599	2515
598	2511
597	2507
596	2503
595	2499
594	2495
593	2491
592	2487
591	2483
590	2479
589	2475
588	2471
587	2467
586	2463
585	2459
584	2455
583	2451
582	2447
581	2443
580	2439
579	2435
578	2431
577	2427
576	2423
575	2419
574	2415
573	2411
572	2407
571	2403
570	2399
569	2395
568	2391
567	2387
566	2383
565	2379
564	2375
563	2371
562	2367
561	2363
560	2359
559	2355
558	2351
557	2347
556	2343
555	2339
554	2335
553	2331
552	2327
551	2323
550	2319
549	2315
548	2311
547	2307
546	2303
545	2299
544	2295
543	2291
542	2287
541	2283
540	2279
539	2275
538	2271
537	2267
536	2263
535	2259
534	2255
533	2251
532	2247
531	2243
530	2239
529	2235
528	2231
527	2227
526	2223
525	2219
524	2215
523	2211
522	2207
521	2203
520	2199
519	2195
518	2191
517	2187
516	2183
515	2179
514	2175
513	2171
512	2167
511	2163
510	2159
509	2155
508	2151
507	2147
506	2143
505	2139
504	2135
503	2131
502	2127
501	2123
500	2119
499	2115
498	2111
497	2107
496	2103
495	2099
494	2095
493	2091
492	2087
491	2083
490	2079
489	2075
488	2071
487	2067
486	2063
485	2059
484	2055
483	2051
482	2047
481	2043
480	2039
479	2035
478	2031
477	2027
476	2023
475	2019
474	2015
473	2011
472	2007
471	2003
470	1999
469	1995
468	1991
467	1987
466	1983
465	1979
464	1975
463	1971
462	1967
461	1963
460	1959
459	1955
458	1951
457	1947
456	1943
455	1939
454	1935
453	1931
452	1927
451	1923
450	1919
449	1915
448	1911
447	1907
446	1903
445	1899
444	1895
443	1891
442	1887
441	1883
440	1879
439	1875
438	1871
437	1867
436	1863
435	1859
434	1855
433	1851
432	1847
431	1843
430	1839
429	1835
428	1831
427	1827
426	1823
425	1819
424	1815
423	1811
422	1807
421	1803
420	1799
419	1795
418	1791
417	1787
416	1783
415	1779
414	1775
413	1771
412	1767
411	1763
410	1759
409	1755
408	1751
407	1747
406	1743
405	1739
404	1735
403	1731
402	1727
401	1723
400	1719
399	1715
398	1711
397	1707
396	1703
395	1699
394	1695
393	1691
392	1687
391	1683
390	1679
389	1675
388	1671
387	1667
386	1663
385	1659
384	1655
383	1651
382	1647
381	1643
380	1639
379	1635
378	1631
377	1627
376	1623
375	1619
374	1615
373	1611
372	1607
371	1603
370	1599
369	1595
368	1591
367	1587
366	1583
365	1579
364	1575
363	1571
362	1567
361	1563
360	1559
359	1555
358	1551
357	1547
356	1543
355	1539
354	1535
353	1531
352	1527
351	1523
350	1519
349	1515
348	1511
347	1507
346	1503
345	1499
344	1495
343	1491
342	1487
341	1483
340	1479
339	1475
338	1471
337	1467
336	1463
335	1459
334	1455
333	1451
332	1447
331	1443
330	1439
329	1435
328	1431
327	1427
326	1423
325	1419
324	1415
323	1411
322	1407
321	1403
320	1399
319	1395
318	1391
317	1387
316	1383
315	1379
314	1375
313	1371
312	1367
311	1363
310	1359
309	1355
308	1351
307	1347
306	1343
305	1339
304	1335
303	1331
302	1327
301	1323
300	1319
299	1315
298	1311
297	1307
296	1303
295	1299
294	1295
293	1291
292	1287
291	1283
290	1279
289	1275
288	1271
287	1267
286	1263
285	1259
284	1255
283	1251
282	1247
281	1243
280	1239
279	1235
278	1231
277	1227
276	1223
275	1219
274	1215
273	1211
272	1207
271	1203
270	1199
269	1195
268	1191
267	1187
266	1183
265	1179
264	1175
263	1171
262	1167
261	1163
260	1159
259	1155
258	1151
257	1147
256	1143
255	1139
254	1135
253	1131
252	1127
251	1123
250	1119
249	1115
248	1111
247	1107
246	1103
245	1099
244	1095
243	1091
242	1087
241	1083
240	1079
239	1075
238	1071
237	1067
236	1063
235	1059
234	1055
233	1051
232	1047
231	1043
230	1039
229	1035
228	1031
227	1027
226	1023
225	1019
224	1015
223	1011
222	1007
221	1003
220	999
219	995
218	991
217	987
216	983
215	979
214	975
213	971
212	967
211	963
210	959
209	955
208	951
207	947
206	943
205	939
204	935
203	931
202	927
201	923
200	919
199	915
198	911
197	907
196	903
195	899
194	895
193	891
192	887
191	883
190	879
189	875
188	871
187	867
186	863
185	859
184	855
183	851
182	847
181	843
180	839
179	835
178	831
177	827
176	823
175	819
174	815
173	811
172	807
171	803
170	799
169	795
168	791
167	787
166	783
165	779
164	775
163	771
162	767
161	763
160	759
159	755
158	751
157	747
156	743
155	739
154	735
153	731
152	727
151	723
150	719
149	715
148	711
147	707
146	703
145	699
144	695
143	691
142	687
141	683
140	679
139	675
138	671
137	667
136	663
135	659
134	655
133	651
132	647
131	643
130	639
129	635
128	631
127	627
126	623
125	619
124	615
123	611
122	607
121	603
120	599
119	595
118	591
117	587
116	583
115	579
114	575
113	571
112	567
111	563
110	559
109	555
108	551
107	547
106	543
105	539
104	535
103	531
102	527
101	523
100	519
99	515
98	511
97	507
96	503
95	499
94	495
93	491
92	487
91	483
90	479
89	475
88	471
87	467
86	463
85	459
84	455
83	451
82	447
81	443
80	439
79	435
78	431
77	427
76	423
75	419
74	415
73	411
72	407
71	403
70	399
69	395
68	391
67	387
66	383
65	379
64	375
63	371
62	367
61	363
60	359
59	355
58	351
57	347
56	343
55	339
54	335
53	331
52	327
51	323
50	319
49	315
48	311
47	307
46	303
45	299
44	295
43	291
42	287
41	283
40	279
39	275
38	271
37	267
36	263
35	259
34	255
33	251
32	247
31	243
30	239
29	235
28	231
27	227
26	223
25	219
24	215
23	211
22	207
21	203
20	199
19	195
18	191
17	187
16	183
15	179
14	175
13	171
12	167
11	163
10	159
9	155
8	151
7	147
6	143
5	139
4	135
3	130
2	111
1	91
0	67

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.0s	8978×	body	80	nan
1.8s	1555×	body	1280	valid
844.0ms	5654×	body	80	valid
628.0ms	918×	body	640	valid
533.0ms	349×	body	2560	valid
180.0ms	451×	body	320	valid
53.0ms	196×	body	160	valid