Details

sample122.0ms

Algorithm

intervals

Results

45.0ms	45×	body	1280	valid
19.0ms	33×	body	640	valid
18.0ms	133×	body	80	valid
11.0ms	27×	body	320	valid
5.0ms	18×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5042
7	2651
6	720
5	277
4	165
3	112
2	68
1	34
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) J)
0.2b	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
7.2b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
17×	`pow1`
16×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`associate-l` `prod-exp`
8×	`sqrt-prod`
7×	`unpow-prod-down` `pow-prod-down` `cbrt-unprod`
4×	`sqrt-div` `associate-r` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (cos (/ K 2.0)) J)
39.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
326.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
112.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series748.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos (/ K 2.0)) J)
181.0ms	(pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0)
318.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
169.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1523
1	515
0	203

prune683.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.4b

localize87.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
7.2b	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite437.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

107.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
111.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
119.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
96.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

307.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
323.0ms	(sqrt (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)))
178.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
195.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify3.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5025
4	4734
3	1421
2	465
1	195
0	97

prune740.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.4b

localize126.0ms

Local error

Found 4 expressions with local error:

11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
17.0b	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
17.0b	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
17.0b	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`pow1/3`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

85.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
51.0ms	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
45.0ms	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
39.0ms	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

206.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
281.0ms	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
358.0ms	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
279.0ms	(cbrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify2.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5004
4	3420
3	1095
2	410
1	182
0	89

prune826.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.4b

localize112.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
11.3b	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`pow1` `sqrt-prod`
13×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-div`
7×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`flip3-+` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-*l/`
1×	`associate-r` `*-commutative`

Counts

4 → 75

Calls

4 calls:

248.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
79.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
98.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
122.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

series943.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (cos (/ K 2.0)) J) -2.0))
212.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
193.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))
214.0ms	(sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0))

simplify3.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5004
3	3267
2	852
1	262
0	103

prune677.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 10.4b

regimes845.0ms

Accuracy

6.7% (8.8b remaining)

Error of 17.3b against oracle of 8.5b and baseline of 18.0b

bsearch510.0ms

Steps

Iters	Range		Point
5	8.878003644028405e-176	2.748406799204312e-175	9.044065113033607e-176
8	-7.390816874604553e-253	-2.799211198675799e-257	-2.185755027344584e-254
10	-2.8377150508224685e-179	-1.0120612849820855e-196	-7.496155157232238e-180
6	-4.104200302208654e-68	-8.712999357163278e-69	-8.793677279707616e-69

simplify1.0m

Iterations

Iter	Nodes
done	5001
666	4999
665	4992
664	4984
663	4977
662	4969
661	4962
660	4954
659	4947
658	4939
657	4932
656	4924
655	4917
654	4909
653	4902
652	4894
651	4887
650	4879
649	4872
648	4864
647	4857
646	4849
645	4842
644	4834
643	4827
642	4819
641	4812
640	4804
639	4797
638	4789
637	4782
636	4774
635	4767
634	4759
633	4752
632	4744
631	4737
630	4729
629	4722
628	4714
627	4707
626	4699
625	4692
624	4684
623	4677
622	4669
621	4662
620	4654
619	4647
618	4639
617	4632
616	4624
615	4617
614	4609
613	4602
612	4594
611	4587
610	4579
609	4572
608	4564
607	4557
606	4549
605	4542
604	4534
603	4527
602	4519
601	4512
600	4504
599	4497
598	4489
597	4482
596	4474
595	4467
594	4459
593	4452
592	4444
591	4437
590	4429
589	4422
588	4414
587	4407
586	4399
585	4392
584	4384
583	4377
582	4369
581	4362
580	4354
579	4347
578	4339
577	4332
576	4324
575	4317
574	4309
573	4302
572	4294
571	4287
570	4279
569	4272
568	4264
567	4257
566	4249
565	4242
564	4234
563	4227
562	4219
561	4212
560	4204
559	4197
558	4189
557	4182
556	4174
555	4167
554	4159
553	4152
552	4144
551	4137
550	4129
549	4122
548	4114
547	4107
546	4099
545	4092
544	4084
543	4077
542	4069
541	4062
540	4054
539	4047
538	4039
537	4032
536	4024
535	4017
534	4009
533	4002
532	3994
531	3987
530	3979
529	3972
528	3964
527	3957
526	3949
525	3942
524	3934
523	3927
522	3919
521	3912
520	3904
519	3897
518	3889
517	3882
516	3874
515	3867
514	3859
513	3852
512	3844
511	3837
510	3829
509	3822
508	3814
507	3807
506	3799
505	3792
504	3784
503	3777
502	3769
501	3762
500	3754
499	3747
498	3739
497	3732
496	3724
495	3717
494	3709
493	3702
492	3694
491	3687
490	3679
489	3672
488	3664
487	3657
486	3649
485	3642
484	3634
483	3627
482	3619
481	3612
480	3604
479	3597
478	3589
477	3582
476	3574
475	3567
474	3559
473	3552
472	3544
471	3537
470	3529
469	3522
468	3514
467	3507
466	3499
465	3492
464	3484
463	3477
462	3469
461	3462
460	3454
459	3447
458	3439
457	3432
456	3424
455	3417
454	3409
453	3402
452	3394
451	3387
450	3379
449	3372
448	3364
447	3357
446	3349
445	3342
444	3334
443	3327
442	3319
441	3312
440	3304
439	3297
438	3289
437	3282
436	3274
435	3267
434	3259
433	3252
432	3244
431	3237
430	3229
429	3222
428	3214
427	3207
426	3199
425	3192
424	3184
423	3177
422	3169
421	3162
420	3154
419	3147
418	3139
417	3132
416	3124
415	3117
414	3109
413	3102
412	3094
411	3087
410	3079
409	3072
408	3064
407	3057
406	3049
405	3042
404	3034
403	3027
402	3019
401	3012
400	3004
399	2997
398	2989
397	2982
396	2974
395	2967
394	2959
393	2952
392	2944
391	2937
390	2929
389	2922
388	2914
387	2907
386	2899
385	2892
384	2884
383	2877
382	2869
381	2862
380	2854
379	2847
378	2839
377	2832
376	2824
375	2817
374	2809
373	2802
372	2794
371	2787
370	2779
369	2772
368	2764
367	2757
366	2749
365	2742
364	2734
363	2727
362	2719
361	2712
360	2704
359	2697
358	2689
357	2682
356	2674
355	2667
354	2659
353	2652
352	2644
351	2637
350	2629
349	2622
348	2614
347	2607
346	2599
345	2592
344	2584
343	2577
342	2569
341	2562
340	2554
339	2547
338	2539
337	2532
336	2524
335	2517
334	2509
333	2502
332	2494
331	2487
330	2479
329	2472
328	2464
327	2457
326	2449
325	2442
324	2434
323	2427
322	2419
321	2412
320	2404
319	2397
318	2389
317	2382
316	2374
315	2367
314	2359
313	2352
312	2344
311	2337
310	2329
309	2322
308	2314
307	2307
306	2299
305	2292
304	2284
303	2277
302	2269
301	2262
300	2254
299	2247
298	2239
297	2232
296	2224
295	2217
294	2209
293	2202
292	2194
291	2187
290	2179
289	2172
288	2164
287	2157
286	2149
285	2142
284	2134
283	2127
282	2119
281	2112
280	2104
279	2097
278	2089
277	2082
276	2074
275	2067
274	2059
273	2052
272	2044
271	2037
270	2029
269	2022
268	2014
267	2007
266	1999
265	1992
264	1984
263	1977
262	1969
261	1962
260	1954
259	1947
258	1939
257	1932
256	1924
255	1917
254	1909
253	1902
252	1894
251	1887
250	1879
249	1872
248	1864
247	1857
246	1849
245	1842
244	1834
243	1827
242	1819
241	1812
240	1804
239	1797
238	1789
237	1782
236	1774
235	1767
234	1759
233	1752
232	1744
231	1737
230	1729
229	1722
228	1714
227	1707
226	1699
225	1692
224	1684
223	1677
222	1669
221	1662
220	1654
219	1647
218	1639
217	1632
216	1624
215	1617
214	1609
213	1602
212	1594
211	1587
210	1579
209	1572
208	1564
207	1557
206	1549
205	1542
204	1534
203	1527
202	1519
201	1512
200	1504
199	1497
198	1489
197	1482
196	1474
195	1467
194	1459
193	1452
192	1444
191	1437
190	1429
189	1422
188	1414
187	1407
186	1399
185	1392
184	1384
183	1377
182	1369
181	1362
180	1354
179	1347
178	1339
177	1332
176	1324
175	1317
174	1309
173	1302
172	1294
171	1287
170	1279
169	1272
168	1264
167	1257
166	1249
165	1242
164	1234
163	1227
162	1219
161	1212
160	1204
159	1197
158	1189
157	1182
156	1174
155	1167
154	1159
153	1152
152	1144
151	1137
150	1129
149	1122
148	1114
147	1107
146	1099
145	1092
144	1084
143	1077
142	1069
141	1062
140	1054
139	1047
138	1039
137	1032
136	1024
135	1017
134	1009
133	1002
132	994
131	987
130	979
129	972
128	964
127	957
126	949
125	942
124	934
123	927
122	919
121	912
120	904
119	897
118	889
117	882
116	874
115	867
114	859
113	852
112	844
111	837
110	829
109	822
108	814
107	807
106	799
105	792
104	784
103	777
102	769
101	762
100	754
99	747
98	739
97	732
96	724
95	717
94	709
93	702
92	694
91	687
90	679
89	672
88	664
87	657
86	649
85	642
84	634
83	627
82	619
81	612
80	604
79	597
78	589
77	582
76	574
75	567
74	559
73	552
72	544
71	537
70	529
69	522
68	514
67	507
66	499
65	492
64	484
63	477
62	469
61	462
60	454
59	447
58	439
57	432
56	424
55	417
54	409
53	402
52	394
51	387
50	379
49	372
48	364
47	357
46	349
45	342
44	334
43	327
42	319
41	312
40	304
39	297
38	289
37	282
36	274
35	267
34	259
33	252
32	244
31	237
30	229
29	222
28	214
27	207
26	199
25	192
24	184
23	177
22	169
21	162
20	154
19	147
18	139
17	132
16	124
15	117
14	109
13	102
12	94
11	87
10	79
9	72
8	62
7	61
6	58
5	57
4	54
3	51
2	45
1	42
0	32

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	4339×	body	80	valid
1.1s	1456×	body	1280	valid
710.0ms	1210×	body	640	valid
358.0ms	668×	body	320	valid
85.0ms	330×	body	160	valid