Details

sample217.0ms

Algorithm

intervals

Results

57.0ms	178×	body	80	valid
40.0ms	360×	body	80	nan
39.0ms	56×	body	1280	valid
16.0ms	17×	body	2560	valid
7.0ms	18×	body	640	valid
4.0ms	12×	body	320	valid
2.0ms	8×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize35.0ms

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))))
23.8b	(cos (- y (/ (* z t) 3.0)))

rewrite88.0ms

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)
6.0ms	(/ a (* b 3.0))
48.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
22.0ms	(cos (- y (/ (* z t) 3.0)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* z t) 3.0)
34.0ms	(/ a (* b 3.0))
193.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
73.0ms	(cos (- y (/ (* z t) 3.0)))

simplify1.7s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	2919
1	711
0	327

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 13.6b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
27.3b	(sin (/ (* z t) 3.0))
27.5b	(cos (/ (* z t) 3.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `pow-prod-down` `associate-r/` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult`

Counts

4 → 66

Calls

4 calls:

10.0ms	(/ a (* b 3.0))
67.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
3.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (/ (* z t) 3.0))

series395.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ a (* b 3.0))
312.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
31.0ms	(sin (/ (* z t) 3.0))
23.0ms	(cos (/ (* z t) 3.0))

simplify2.0s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	2267
1	462
0	170

prune1.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 13.6b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
27.3b	(sin (/ (* z t) 3.0))
27.5b	(cos (/ (* z t) 3.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `associate-r` `pow-prod-down` `associate-r/`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult` `associate-/l`

Counts

4 → 66

Calls

4 calls:

13.0ms	(/ (* z t) 3.0)
54.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
3.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (/ (* z t) 3.0))

series441.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* z t) 3.0)
355.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
25.0ms	(sin (/ (* z t) 3.0))
24.0ms	(cos (/ (* z t) 3.0))

simplify1.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	2553
1	468
0	166

prune1.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 13.6b

localize116.0ms

Local error

Found 4 expressions with local error:

27.3b	(sin (/ (* z t) 3.0))
27.3b	(sin (/ (* z t) 3.0))
27.3b	(sin (/ (* z t) 3.0))
27.5b	(cos (/ (* z t) 3.0))

rewrite13.0ms

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sin (/ (* z t) 3.0))
37.0ms	(sin (/ (* z t) 3.0))
25.0ms	(sin (/ (* z t) 3.0))
15.0ms	(cos (/ (* z t) 3.0))

simplify1.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
8	2011
7	630
6	286
5	149
4	82
3	66
2	54
1	40
0	31

prune676.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 13.6b

regimes7.5s

Accuracy

30.6% (4.0b remaining)

Error of 18.4b against oracle of 14.5b and baseline of 20.2b

bsearch407.0ms

Steps

Iters	Range		Point
6	5.634629578742766e-21	4.015166101451561e-20	1.1505339337432292e-20
6	-2643088734.669235	-514313515.2214791	-519168038.2262618

simplify8.0s

Iterations

Iter	Nodes
done	5000
1223	4998
1222	4994
1221	4990
1220	4986
1219	4982
1218	4978
1217	4974
1216	4970
1215	4966
1214	4962
1213	4958
1212	4954
1211	4950
1210	4946
1209	4942
1208	4938
1207	4934
1206	4930
1205	4926
1204	4922
1203	4918
1202	4914
1201	4910
1200	4906
1199	4902
1198	4898
1197	4894
1196	4890
1195	4886
1194	4882
1193	4878
1192	4874
1191	4870
1190	4866
1189	4862
1188	4858
1187	4854
1186	4850
1185	4846
1184	4842
1183	4838
1182	4834
1181	4830
1180	4826
1179	4822
1178	4818
1177	4814
1176	4810
1175	4806
1174	4802
1173	4798
1172	4794
1171	4790
1170	4786
1169	4782
1168	4778
1167	4774
1166	4770
1165	4766
1164	4762
1163	4758
1162	4754
1161	4750
1160	4746
1159	4742
1158	4738
1157	4734
1156	4730
1155	4726
1154	4722
1153	4718
1152	4714
1151	4710
1150	4706
1149	4702
1148	4698
1147	4694
1146	4690
1145	4686
1144	4682
1143	4678
1142	4674
1141	4670
1140	4666
1139	4662
1138	4658
1137	4654
1136	4650
1135	4646
1134	4642
1133	4638
1132	4634
1131	4630
1130	4626
1129	4622
1128	4618
1127	4614
1126	4610
1125	4606
1124	4602
1123	4598
1122	4594
1121	4590
1120	4586
1119	4582
1118	4578
1117	4574
1116	4570
1115	4566
1114	4562
1113	4558
1112	4554
1111	4550
1110	4546
1109	4542
1108	4538
1107	4534
1106	4530
1105	4526
1104	4522
1103	4518
1102	4514
1101	4510
1100	4506
1099	4502
1098	4498
1097	4494
1096	4490
1095	4486
1094	4482
1093	4478
1092	4474
1091	4470
1090	4466
1089	4462
1088	4458
1087	4454
1086	4450
1085	4446
1084	4442
1083	4438
1082	4434
1081	4430
1080	4426
1079	4422
1078	4418
1077	4414
1076	4410
1075	4406
1074	4402
1073	4398
1072	4394
1071	4390
1070	4386
1069	4382
1068	4378
1067	4374
1066	4370
1065	4366
1064	4362
1063	4358
1062	4354
1061	4350
1060	4346
1059	4342
1058	4338
1057	4334
1056	4330
1055	4326
1054	4322
1053	4318
1052	4314
1051	4310
1050	4306
1049	4302
1048	4298
1047	4294
1046	4290
1045	4286
1044	4282
1043	4278
1042	4274
1041	4270
1040	4266
1039	4262
1038	4258
1037	4254
1036	4250
1035	4246
1034	4242
1033	4238
1032	4234
1031	4230
1030	4226
1029	4222
1028	4218
1027	4214
1026	4210
1025	4206
1024	4202
1023	4198
1022	4194
1021	4190
1020	4186
1019	4182
1018	4178
1017	4174
1016	4170
1015	4166
1014	4162
1013	4158
1012	4154
1011	4150
1010	4146
1009	4142
1008	4138
1007	4134
1006	4130
1005	4126
1004	4122
1003	4118
1002	4114
1001	4110
1000	4106
999	4102
998	4098
997	4094
996	4090
995	4086
994	4082
993	4078
992	4074
991	4070
990	4066
989	4062
988	4058
987	4054
986	4050
985	4046
984	4042
983	4038
982	4034
981	4030
980	4026
979	4022
978	4018
977	4014
976	4010
975	4006
974	4002
973	3998
972	3994
971	3990
970	3986
969	3982
968	3978
967	3974
966	3970
965	3966
964	3962
963	3958
962	3954
961	3950
960	3946
959	3942
958	3938
957	3934
956	3930
955	3926
954	3922
953	3918
952	3914
951	3910
950	3906
949	3902
948	3898
947	3894
946	3890
945	3886
944	3882
943	3878
942	3874
941	3870
940	3866
939	3862
938	3858
937	3854
936	3850
935	3846
934	3842
933	3838
932	3834
931	3830
930	3826
929	3822
928	3818
927	3814
926	3810
925	3806
924	3802
923	3798
922	3794
921	3790
920	3786
919	3782
918	3778
917	3774
916	3770
915	3766
914	3762
913	3758
912	3754
911	3750
910	3746
909	3742
908	3738
907	3734
906	3730
905	3726
904	3722
903	3718
902	3714
901	3710
900	3706
899	3702
898	3698
897	3694
896	3690
895	3686
894	3682
893	3678
892	3674
891	3670
890	3666
889	3662
888	3658
887	3654
886	3650
885	3646
884	3642
883	3638
882	3634
881	3630
880	3626
879	3622
878	3618
877	3614
876	3610
875	3606
874	3602
873	3598
872	3594
871	3590
870	3586
869	3582
868	3578
867	3574
866	3570
865	3566
864	3562
863	3558
862	3554
861	3550
860	3546
859	3542
858	3538
857	3534
856	3530
855	3526
854	3522
853	3518
852	3514
851	3510
850	3506
849	3502
848	3498
847	3494
846	3490
845	3486
844	3482
843	3478
842	3474
841	3470
840	3466
839	3462
838	3458
837	3454
836	3450
835	3446
834	3442
833	3438
832	3434
831	3430
830	3426
829	3422
828	3418
827	3414
826	3410
825	3406
824	3402
823	3398
822	3394
821	3390
820	3386
819	3382
818	3378
817	3374
816	3370
815	3366
814	3362
813	3358
812	3354
811	3350
810	3346
809	3342
808	3338
807	3334
806	3330
805	3326
804	3322
803	3318
802	3314
801	3310
800	3306
799	3302
798	3298
797	3294
796	3290
795	3286
794	3282
793	3278
792	3274
791	3270
790	3266
789	3262
788	3258
787	3254
786	3250
785	3246
784	3242
783	3238
782	3234
781	3230
780	3226
779	3222
778	3218
777	3214
776	3210
775	3206
774	3202
773	3198
772	3194
771	3190
770	3186
769	3182
768	3178
767	3174
766	3170
765	3166
764	3162
763	3158
762	3154
761	3150
760	3146
759	3142
758	3138
757	3134
756	3130
755	3126
754	3122
753	3118
752	3114
751	3110
750	3106
749	3102
748	3098
747	3094
746	3090
745	3086
744	3082
743	3078
742	3074
741	3070
740	3066
739	3062
738	3058
737	3054
736	3050
735	3046
734	3042
733	3038
732	3034
731	3030
730	3026
729	3022
728	3018
727	3014
726	3010
725	3006
724	3002
723	2998
722	2994
721	2990
720	2986
719	2982
718	2978
717	2974
716	2970
715	2966
714	2962
713	2958
712	2954
711	2950
710	2946
709	2942
708	2938
707	2934
706	2930
705	2926
704	2922
703	2918
702	2914
701	2910
700	2906
699	2902
698	2898
697	2894
696	2890
695	2886
694	2882
693	2878
692	2874
691	2870
690	2866
689	2862
688	2858
687	2854
686	2850
685	2846
684	2842
683	2838
682	2834
681	2830
680	2826
679	2822
678	2818
677	2814
676	2810
675	2806
674	2802
673	2798
672	2794
671	2790
670	2786
669	2782
668	2778
667	2774
666	2770
665	2766
664	2762
663	2758
662	2754
661	2750
660	2746
659	2742
658	2738
657	2734
656	2730
655	2726
654	2722
653	2718
652	2714
651	2710
650	2706
649	2702
648	2698
647	2694
646	2690
645	2686
644	2682
643	2678
642	2674
641	2670
640	2666
639	2662
638	2658
637	2654
636	2650
635	2646
634	2642
633	2638
632	2634
631	2630
630	2626
629	2622
628	2618
627	2614
626	2610
625	2606
624	2602
623	2598
622	2594
621	2590
620	2586
619	2582
618	2578
617	2574
616	2570
615	2566
614	2562
613	2558
612	2554
611	2550
610	2546
609	2542
608	2538
607	2534
606	2530
605	2526
604	2522
603	2518
602	2514
601	2510
600	2506
599	2502
598	2498
597	2494
596	2490
595	2486
594	2482
593	2478
592	2474
591	2470
590	2466
589	2462
588	2458
587	2454
586	2450
585	2446
584	2442
583	2438
582	2434
581	2430
580	2426
579	2422
578	2418
577	2414
576	2410
575	2406
574	2402
573	2398
572	2394
571	2390
570	2386
569	2382
568	2378
567	2374
566	2370
565	2366
564	2362
563	2358
562	2354
561	2350
560	2346
559	2342
558	2338
557	2334
556	2330
555	2326
554	2322
553	2318
552	2314
551	2310
550	2306
549	2302
548	2298
547	2294
546	2290
545	2286
544	2282
543	2278
542	2274
541	2270
540	2266
539	2262
538	2258
537	2254
536	2250
535	2246
534	2242
533	2238
532	2234
531	2230
530	2226
529	2222
528	2218
527	2214
526	2210
525	2206
524	2202
523	2198
522	2194
521	2190
520	2186
519	2182
518	2178
517	2174
516	2170
515	2166
514	2162
513	2158
512	2154
511	2150
510	2146
509	2142
508	2138
507	2134
506	2130
505	2126
504	2122
503	2118
502	2114
501	2110
500	2106
499	2102
498	2098
497	2094
496	2090
495	2086
494	2082
493	2078
492	2074
491	2070
490	2066
489	2062
488	2058
487	2054
486	2050
485	2046
484	2042
483	2038
482	2034
481	2030
480	2026
479	2022
478	2018
477	2014
476	2010
475	2006
474	2002
473	1998
472	1994
471	1990
470	1986
469	1982
468	1978
467	1974
466	1970
465	1966
464	1962
463	1958
462	1954
461	1950
460	1946
459	1942
458	1938
457	1934
456	1930
455	1926
454	1922
453	1918
452	1914
451	1910
450	1906
449	1902
448	1898
447	1894
446	1890
445	1886
444	1882
443	1878
442	1874
441	1870
440	1866
439	1862
438	1858
437	1854
436	1850
435	1846
434	1842
433	1838
432	1834
431	1830
430	1826
429	1822
428	1818
427	1814
426	1810
425	1806
424	1802
423	1798
422	1794
421	1790
420	1786
419	1782
418	1778
417	1774
416	1770
415	1766
414	1762
413	1758
412	1754
411	1750
410	1746
409	1742
408	1738
407	1734
406	1730
405	1726
404	1722
403	1718
402	1714
401	1710
400	1706
399	1702
398	1698
397	1694
396	1690
395	1686
394	1682
393	1678
392	1674
391	1670
390	1666
389	1662
388	1658
387	1654
386	1650
385	1646
384	1642
383	1638
382	1634
381	1630
380	1626
379	1622
378	1618
377	1614
376	1610
375	1606
374	1602
373	1598
372	1594
371	1590
370	1586
369	1582
368	1578
367	1574
366	1570
365	1566
364	1562
363	1558
362	1554
361	1550
360	1546
359	1542
358	1538
357	1534
356	1530
355	1526
354	1522
353	1518
352	1514
351	1510
350	1506
349	1502
348	1498
347	1494
346	1490
345	1486
344	1482
343	1478
342	1474
341	1470
340	1466
339	1462
338	1458
337	1454
336	1450
335	1446
334	1442
333	1438
332	1434
331	1430
330	1426
329	1422
328	1418
327	1414
326	1410
325	1406
324	1402
323	1398
322	1394
321	1390
320	1386
319	1382
318	1378
317	1374
316	1370
315	1366
314	1362
313	1358
312	1354
311	1350
310	1346
309	1342
308	1338
307	1334
306	1330
305	1326
304	1322
303	1318
302	1314
301	1310
300	1306
299	1302
298	1298
297	1294
296	1290
295	1286
294	1282
293	1278
292	1274
291	1270
290	1266
289	1262
288	1258
287	1254
286	1250
285	1246
284	1242
283	1238
282	1234
281	1230
280	1226
279	1222
278	1218
277	1214
276	1210
275	1206
274	1202
273	1198
272	1194
271	1190
270	1186
269	1182
268	1178
267	1174
266	1170
265	1166
264	1162
263	1158
262	1154
261	1150
260	1146
259	1142
258	1138
257	1134
256	1130
255	1126
254	1122
253	1118
252	1114
251	1110
250	1106
249	1102
248	1098
247	1094
246	1090
245	1086
244	1082
243	1078
242	1074
241	1070
240	1066
239	1062
238	1058
237	1054
236	1050
235	1046
234	1042
233	1038
232	1034
231	1030
230	1026
229	1022
228	1018
227	1014
226	1010
225	1006
224	1002
223	998
222	994
221	990
220	986
219	982
218	978
217	974
216	970
215	966
214	962
213	958
212	954
211	950
210	946
209	942
208	938
207	934
206	930
205	926
204	922
203	918
202	914
201	910
200	906
199	902
198	898
197	894
196	890
195	886
194	882
193	878
192	874
191	870
190	866
189	862
188	858
187	854
186	850
185	846
184	842
183	838
182	834
181	830
180	826
179	822
178	818
177	814
176	810
175	806
174	802
173	798
172	794
171	790
170	786
169	782
168	778
167	774
166	770
165	766
164	762
163	758
162	754
161	750
160	746
159	742
158	738
157	734
156	730
155	726
154	722
153	718
152	714
151	710
150	706
149	702
148	698
147	694
146	690
145	686
144	682
143	678
142	674
141	670
140	666
139	662
138	658
137	654
136	650
135	646
134	642
133	638
132	634
131	630
130	626
129	622
128	618
127	614
126	610
125	606
124	602
123	598
122	594
121	590
120	586
119	582
118	578
117	574
116	570
115	566
114	562
113	558
112	554
111	550
110	546
109	542
108	538
107	534
106	530
105	526
104	522
103	518
102	514
101	510
100	506
99	502
98	498
97	494
96	490
95	486
94	482
93	478
92	474
91	470
90	466
89	462
88	458
87	454
86	450
85	446
84	442
83	438
82	434
81	430
80	426
79	422
78	418
77	414
76	410
75	406
74	402
73	398
72	394
71	390
70	386
69	382
68	378
67	374
66	370
65	366
64	362
63	358
62	354
61	350
60	346
59	342
58	338
57	334
56	330
55	326
54	322
53	318
52	314
51	310
50	306
49	302
48	298
47	294
46	290
45	286
44	282
43	278
42	274
41	270
40	266
39	262
38	258
37	254
36	250
35	246
34	242
33	238
32	234
31	230
30	226
29	222
28	218
27	214
26	210
25	206
24	202
23	198
22	194
21	190
20	186
19	182
18	178
17	174
16	170
15	166
14	162
13	158
12	154
11	150
10	146
9	142
8	138
7	134
6	130
5	126
4	122
3	117
2	99
1	84
0	63

end0.0ms

sample7.5s

Algorithm

intervals

Results

1.8s	9043×	body	80	nan
1.8s	1552×	body	1280	valid
1.0s	5611×	body	80	valid
936.0ms	866×	body	640	valid
559.0ms	400×	body	2560	valid
250.0ms	466×	body	320	valid
53.0ms	201×	body	160	valid