Details

sample43.0ms

Algorithm

intervals

Results

29.0ms

278×

body

valid

simplify12.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
952	1998
951	1996
950	1994
949	1992
948	1990
947	1988
946	1986
945	1984
944	1982
943	1980
942	1978
941	1976
940	1974
939	1972
938	1970
937	1968
936	1966
935	1964
934	1962
933	1960
932	1958
931	1956
930	1954
929	1952
928	1950
927	1948
926	1946
925	1944
924	1942
923	1940
922	1938
921	1936
920	1934
919	1932
918	1930
917	1928
916	1926
915	1924
914	1922
913	1920
912	1918
911	1916
910	1914
909	1912
908	1910
907	1908
906	1906
905	1904
904	1902
903	1900
902	1898
901	1896
900	1894
899	1892
898	1890
897	1888
896	1886
895	1884
894	1882
893	1880
892	1878
891	1876
890	1874
889	1872
888	1870
887	1868
886	1866
885	1864
884	1862
883	1860
882	1858
881	1856
880	1854
879	1852
878	1850
877	1848
876	1846
875	1844
874	1842
873	1840
872	1838
871	1836
870	1834
869	1832
868	1830
867	1828
866	1826
865	1824
864	1822
863	1820
862	1818
861	1816
860	1814
859	1812
858	1810
857	1808
856	1806
855	1804
854	1802
853	1800
852	1798
851	1796
850	1794
849	1792
848	1790
847	1788
846	1786
845	1784
844	1782
843	1780
842	1778
841	1776
840	1774
839	1772
838	1770
837	1768
836	1766
835	1764
834	1762
833	1760
832	1758
831	1756
830	1754
829	1752
828	1750
827	1748
826	1746
825	1744
824	1742
823	1740
822	1738
821	1736
820	1734
819	1732
818	1730
817	1728
816	1726
815	1724
814	1722
813	1720
812	1718
811	1716
810	1714
809	1712
808	1710
807	1708
806	1706
805	1704
804	1702
803	1700
802	1698
801	1696
800	1694
799	1692
798	1690
797	1688
796	1686
795	1684
794	1682
793	1680
792	1678
791	1676
790	1674
789	1672
788	1670
787	1668
786	1666
785	1664
784	1662
783	1660
782	1658
781	1656
780	1654
779	1652
778	1650
777	1648
776	1646
775	1644
774	1642
773	1640
772	1638
771	1636
770	1634
769	1632
768	1630
767	1628
766	1626
765	1624
764	1622
763	1620
762	1618
761	1616
760	1614
759	1612
758	1610
757	1608
756	1606
755	1604
754	1602
753	1600
752	1598
751	1596
750	1594
749	1592
748	1590
747	1588
746	1586
745	1584
744	1582
743	1580
742	1578
741	1576
740	1574
739	1572
738	1570
737	1568
736	1566
735	1564
734	1562
733	1560
732	1558
731	1556
730	1554
729	1552
728	1550
727	1548
726	1546
725	1544
724	1542
723	1540
722	1538
721	1536
720	1534
719	1532
718	1530
717	1528
716	1526
715	1524
714	1522
713	1520
712	1518
711	1516
710	1514
709	1512
708	1510
707	1508
706	1506
705	1504
704	1502
703	1500
702	1498
701	1496
700	1494
699	1492
698	1490
697	1488
696	1486
695	1484
694	1482
693	1480
692	1478
691	1476
690	1474
689	1472
688	1470
687	1468
686	1466
685	1464
684	1462
683	1460
682	1458
681	1456
680	1454
679	1452
678	1450
677	1448
676	1446
675	1444
674	1442
673	1440
672	1438
671	1436
670	1434
669	1432
668	1430
667	1428
666	1426
665	1424
664	1422
663	1420
662	1418
661	1416
660	1414
659	1412
658	1410
657	1408
656	1406
655	1404
654	1402
653	1400
652	1398
651	1396
650	1394
649	1392
648	1390
647	1388
646	1386
645	1384
644	1382
643	1380
642	1378
641	1376
640	1374
639	1372
638	1370
637	1368
636	1366
635	1364
634	1362
633	1360
632	1358
631	1356
630	1354
629	1352
628	1350
627	1348
626	1346
625	1344
624	1342
623	1340
622	1338
621	1336
620	1334
619	1332
618	1330
617	1328
616	1326
615	1324
614	1322
613	1320
612	1318
611	1316
610	1314
609	1312
608	1310
607	1308
606	1306
605	1304
604	1302
603	1300
602	1298
601	1296
600	1294
599	1292
598	1290
597	1288
596	1286
595	1284
594	1282
593	1280
592	1278
591	1276
590	1274
589	1272
588	1270
587	1268
586	1266
585	1264
584	1262
583	1260
582	1258
581	1256
580	1254
579	1252
578	1250
577	1248
576	1246
575	1244
574	1242
573	1240
572	1238
571	1236
570	1234
569	1232
568	1230
567	1228
566	1226
565	1224
564	1222
563	1220
562	1218
561	1216
560	1214
559	1212
558	1210
557	1208
556	1206
555	1204
554	1202
553	1200
552	1198
551	1196
550	1194
549	1192
548	1190
547	1188
546	1186
545	1184
544	1182
543	1180
542	1178
541	1176
540	1174
539	1172
538	1170
537	1168
536	1166
535	1164
534	1162
533	1160
532	1158
531	1156
530	1154
529	1152
528	1150
527	1148
526	1146
525	1144
524	1142
523	1140
522	1138
521	1136
520	1134
519	1132
518	1130
517	1128
516	1126
515	1124
514	1122
513	1120
512	1118
511	1116
510	1114
509	1112
508	1110
507	1108
506	1106
505	1104
504	1102
503	1100
502	1098
501	1096
500	1094
499	1092
498	1090
497	1088
496	1086
495	1084
494	1082
493	1080
492	1078
491	1076
490	1074
489	1072
488	1070
487	1068
486	1066
485	1064
484	1062
483	1060
482	1058
481	1056
480	1054
479	1052
478	1050
477	1048
476	1046
475	1044
474	1042
473	1040
472	1038
471	1036
470	1034
469	1032
468	1030
467	1028
466	1026
465	1024
464	1022
463	1020
462	1018
461	1016
460	1014
459	1012
458	1010
457	1008
456	1006
455	1004
454	1002
453	1000
452	998
451	996
450	994
449	992
448	990
447	988
446	986
445	984
444	982
443	980
442	978
441	976
440	974
439	972
438	970
437	968
436	966
435	964
434	962
433	960
432	958
431	956
430	954
429	952
428	950
427	948
426	946
425	944
424	942
423	940
422	938
421	936
420	934
419	932
418	930
417	928
416	926
415	924
414	922
413	920
412	918
411	916
410	914
409	912
408	910
407	908
406	906
405	904
404	902
403	900
402	898
401	896
400	894
399	892
398	890
397	888
396	886
395	884
394	882
393	880
392	878
391	876
390	874
389	872
388	870
387	868
386	866
385	864
384	862
383	860
382	858
381	856
380	854
379	852
378	850
377	848
376	846
375	844
374	842
373	840
372	838
371	836
370	834
369	832
368	830
367	828
366	826
365	824
364	822
363	820
362	818
361	816
360	814
359	812
358	810
357	808
356	806
355	804
354	802
353	800
352	798
351	796
350	794
349	792
348	790
347	788
346	786
345	784
344	782
343	780
342	778
341	776
340	774
339	772
338	770
337	768
336	766
335	764
334	762
333	760
332	758
331	756
330	754
329	752
328	750
327	748
326	746
325	744
324	742
323	740
322	738
321	736
320	734
319	732
318	730
317	728
316	726
315	724
314	722
313	720
312	718
311	716
310	714
309	712
308	710
307	708
306	706
305	704
304	702
303	700
302	698
301	696
300	694
299	692
298	690
297	688
296	686
295	684
294	682
293	680
292	678
291	676
290	674
289	672
288	670
287	668
286	666
285	664
284	662
283	660
282	658
281	656
280	654
279	652
278	650
277	648
276	646
275	644
274	642
273	640
272	638
271	636
270	634
269	632
268	630
267	628
266	626
265	624
264	622
263	620
262	618
261	616
260	614
259	612
258	610
257	608
256	606
255	604
254	602
253	600
252	598
251	596
250	594
249	592
248	590
247	588
246	586
245	584
244	582
243	580
242	578
241	576
240	574
239	572
238	570
237	568
236	566
235	564
234	562
233	560
232	558
231	556
230	554
229	552
228	550
227	548
226	546
225	544
224	542
223	540
222	538
221	536
220	534
219	532
218	530
217	528
216	526
215	524
214	522
213	520
212	518
211	516
210	514
209	512
208	510
207	508
206	506
205	504
204	502
203	500
202	498
201	496
200	494
199	492
198	490
197	488
196	486
195	484
194	482
193	480
192	478
191	476
190	474
189	472
188	470
187	468
186	466
185	464
184	462
183	460
182	458
181	456
180	454
179	452
178	450
177	448
176	446
175	444
174	442
173	440
172	438
171	436
170	434
169	432
168	430
167	428
166	426
165	424
164	422
163	420
162	418
161	416
160	414
159	412
158	410
157	408
156	406
155	404
154	402
153	400
152	398
151	396
150	394
149	392
148	390
147	388
146	386
145	384
144	382
143	380
142	378
141	376
140	374
139	372
138	370
137	368
136	366
135	364
134	362
133	360
132	358
131	356
130	354
129	352
128	350
127	348
126	346
125	344
124	342
123	340
122	338
121	336
120	334
119	332
118	330
117	328
116	326
115	324
114	322
113	320
112	318
111	316
110	314
109	312
108	310
107	308
106	306
105	304
104	302
103	300
102	298
101	296
100	294
99	292
98	290
97	288
96	286
95	284
94	282
93	280
92	278
91	276
90	274
89	272
88	270
87	268
86	266
85	264
84	262
83	260
82	258
81	256
80	254
79	252
78	250
77	248
76	246
75	244
74	242
73	240
72	238
71	236
70	234
69	232
68	230
67	228
66	226
65	224
64	222
63	220
62	218
61	216
60	214
59	212
58	210
57	208
56	206
55	204
54	202
53	200
52	198
51	196
50	194
49	192
48	190
47	188
46	186
45	184
44	182
43	180
42	178
41	176
40	174
39	172
38	170
37	168
36	166
35	164
34	162
33	160
32	158
31	156
30	154
29	152
28	150
27	148
26	146
25	144
24	142
23	140
22	138
21	136
20	134
19	132
18	130
17	128
16	126
15	124
14	122
13	120
12	118
11	116
10	114
9	112
8	110
7	108
6	106
5	103
4	84
3	55
2	37
1	21
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize21.0ms

Local error

Found 2 expressions with local error:

3.9b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.5b	(* y (+ 1.0 (* z z)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `pow-prod-down` `-commutative` `unswap-sqr` `associate-/l/`

Counts

2 → 72

Calls

2 calls:

26.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
19.0ms	(* y (+ 1.0 (* z z)))

series135.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
57.0ms	(* y (+ 1.0 (* z z)))

simplify816.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2129
2	1606
1	426
0	158

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize20.0ms

Local error

Found 2 expressions with local error:

4.1b	(/ (/ 1 x) (+ 1.0 (* z z)))
4.3b	(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
114×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
86×	`add-cube-cbrt`
46×	`add-exp-log`
45×	`associate-r`
28×	`add-cbrt-cube`
23×	`div-exp`
13×	`associate-l` `associate-/l*`
12×	`cbrt-undiv`
10×	`prod-exp` `div-inv`
8×	`unswap-sqr`
6×	`cbrt-unprod`
4×	`pow1` `associate-/r/`
3×	`rec-exp` `associate-/r*` `1-exp`
2×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

2 → 170

Calls

2 calls:

11.0ms	(/ (/ 1 x) (+ 1.0 (* z z)))
28.0ms	(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))

series138.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (/ 1 x) (+ 1.0 (* z z)))
70.0ms	(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))

simplify662.0ms

Counts

176 → 176

Iterations

Iter	Nodes
done	2004
1	892
0	294

prune734.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize26.0ms

Local error

Found 2 expressions with local error:

4.1b	(/ (/ 1 x) (+ 1.0 (* z z)))
4.3b	(/ (* 1.0 (/ (/ 1 x) (+ 1.0 (* z z)))) y)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
33×	`add-exp-log`
21×	`add-cbrt-cube`
18×	`div-exp`
14×	`associate-/l*`
10×	`cbrt-undiv`
6×	`associate-/r*` `div-inv`
5×	`prod-exp`
3×	`cbrt-unprod`
2×	`pow1` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/r/` `insert-posit16` `add-log-exp` `associate-/l/`
1×	`flip3-+` `associate-*r/` `flip-+`

Counts

2 → 104

Calls

2 calls:

11.0ms	(/ (/ 1 x) (+ 1.0 (* z z)))
25.0ms	(/ (* 1.0 (/ (/ 1 x) (+ 1.0 (* z z)))) y)

series146.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (/ 1 x) (+ 1.0 (* z z)))
90.0ms	(/ (* 1.0 (/ (/ 1 x) (+ 1.0 (* z z)))) y)

simplify619.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
1	644
0	240

prune312.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (sqrt (+ 1.0 (* z z))) x))
4.3b	(* (/ 1.0 y) (* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ 1 (* (sqrt (+ 1.0 (* z z))) x))))
17.7b	(sqrt (+ 1.0 (* z z)))
17.7b	(sqrt (+ 1.0 (* z z)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

270×	`add-exp-log`
141×	`prod-exp`
93×	`div-exp`
74×	`add-cbrt-cube`
32×	`rec-exp` `1-exp`
31×	`cbrt-unprod`
23×	`cbrt-undiv`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
13×	`associate-l`
12×	`times-frac`
6×	`frac-times` `sqrt-div` `associate-*r/` `sqrt-prod`
5×	`associate-*l/`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `un-div-inv` `div-inv` `pow-flip`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `inv-pow`

Counts

4 → 169

Calls

4 calls:

18.0ms	(/ 1 (* (sqrt (+ 1.0 (* z z))) x))
124.0ms	(* (/ 1.0 y) (* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ 1 (* (sqrt (+ 1.0 (* z z))) x))))
4.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1 (* (sqrt (+ 1.0 (* z z))) x))
68.0ms	(* (/ 1.0 y) (* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ 1 (* (sqrt (+ 1.0 (* z z))) x))))
45.0ms	(sqrt (+ 1.0 (* z z)))
52.0ms	(sqrt (+ 1.0 (* z z)))

simplify585.0ms

Counts

181 → 181

Iterations

Iter	Nodes
done	2000
1	806
0	319

prune638.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.7b

regimes421.0ms

Accuracy

64.4% (1.5b remaining)

Error of 3.9b against oracle of 2.4b and baseline of 6.7b

bsearch120.0ms

Steps

Iters	Range		Point
10	5.347915437316568e+158	4.664738124958666e+171	5.440139318875033e+158
8	-1.9286510901543454e+44	-9.111130320209477e+39	-9.275971739486716e+43

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

968.0ms

8646×

body

valid