Details

sample389.0ms

Algorithm

intervals

Results

93.0ms	358×	body	80	nan
19.0ms	157×	body	80	valid
19.0ms	34×	body	640	valid
17.0ms	32×	body	1280	valid
9.0ms	18×	body	1280	nan
8.0ms	21×	body	640	nan
6.0ms	20×	body	320	valid
3.0ms	11×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3799
6	1449
5	797
4	423
3	199
2	93
1	39
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

69.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms	(* (sqrt 2.0) t)
33.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
53.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

564.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
53.0ms	(* (sqrt 2.0) t)
387.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	2619
1	455
0	167

prune702.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

localize43.0ms

Local error

Found 4 expressions with local error:

4.4b	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
6.4b	(/ (* l l) x)
8.6b	(/ x (* t t))
25.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `flip3-+` `sqrt-div` `div-exp` `frac-add` `associate-r/` `flip-+` `associate-/l*`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 74

Calls

4 calls:

49.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
15.0ms	(/ (* l l) x)
13.0ms	(/ x (* t t))
76.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
33.0ms	(/ (* l l) x)
25.0ms	(/ x (* t t))
403.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	3089
1	509
0	168

prune690.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.3b

localize78.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ 4.0 (/ x (* t t)))
4.4b	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t))))
8.6b	(/ x (* t t))
25.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `associate-*r/` `flip-+`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-/r/`

Counts

4 → 101

Calls

4 calls:

10.0ms	(/ 4.0 (/ x (* t t)))
40.0ms	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t))))
6.0ms	(/ x (* t t))
112.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 4.0 (/ x (* t t)))
92.0ms	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t))))
42.0ms	(/ x (* t t))
387.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

simplify2.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	3194
1	585
0	206

prune931.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.3b

localize106.0ms

Local error

Found 4 expressions with local error:

8.6b	(/ x (* t t))
8.6b	(/ x (* t t))
25.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))
25.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`pow1` `times-frac` `sqrt-prod` `associate-/l*`
4×	`cbrt-undiv` `flip3-+` `div-exp` `frac-add` `associate-*r/` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

7.0ms	(/ x (* t t))
7.0ms	(/ x (* t t))
72.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))
81.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ x (* t t))
45.0ms	(/ x (* t t))
364.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))
363.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (/ 4.0 (/ x (* t t)))))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1644
1	346
0	120

prune758.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.3b

regimes1.0s

Accuracy

77.2% (5.5b remaining)

Error of 9.5b against oracle of 4.0b and baseline of 28.1b

bsearch1.1s

Steps

Iters	Range		Point
9	8.029604051112713e+47	4.771574953324125e+55	4.214549585149478e+55
10	3.1913228427846884e-157	3.080469255526081e-145	3.2479806443803153e-157
10	7.396249846299801e-250	6.414192999540213e-240	1.8396588411989053e-241
9	-2.2008797770019196e+94	-2.884593901536308e+87	-1.940005881918409e+94

simplify4.9s

Iterations

Iter	Nodes
done	5000
820	4998
819	4992
818	4986
817	4980
816	4974
815	4968
814	4962
813	4956
812	4950
811	4944
810	4938
809	4932
808	4926
807	4920
806	4914
805	4908
804	4902
803	4896
802	4890
801	4884
800	4878
799	4872
798	4866
797	4860
796	4854
795	4848
794	4842
793	4836
792	4830
791	4824
790	4818
789	4812
788	4806
787	4800
786	4794
785	4788
784	4782
783	4776
782	4770
781	4764
780	4758
779	4752
778	4746
777	4740
776	4734
775	4728
774	4722
773	4716
772	4710
771	4704
770	4698
769	4692
768	4686
767	4680
766	4674
765	4668
764	4662
763	4656
762	4650
761	4644
760	4638
759	4632
758	4626
757	4620
756	4614
755	4608
754	4602
753	4596
752	4590
751	4584
750	4578
749	4572
748	4566
747	4560
746	4554
745	4548
744	4542
743	4536
742	4530
741	4524
740	4518
739	4512
738	4506
737	4500
736	4494
735	4488
734	4482
733	4476
732	4470
731	4464
730	4458
729	4452
728	4446
727	4440
726	4434
725	4428
724	4422
723	4416
722	4410
721	4404
720	4398
719	4392
718	4386
717	4380
716	4374
715	4368
714	4362
713	4356
712	4350
711	4344
710	4338
709	4332
708	4326
707	4320
706	4314
705	4308
704	4302
703	4296
702	4290
701	4284
700	4278
699	4272
698	4266
697	4260
696	4254
695	4248
694	4242
693	4236
692	4230
691	4224
690	4218
689	4212
688	4206
687	4200
686	4194
685	4188
684	4182
683	4176
682	4170
681	4164
680	4158
679	4152
678	4146
677	4140
676	4134
675	4128
674	4122
673	4116
672	4110
671	4104
670	4098
669	4092
668	4086
667	4080
666	4074
665	4068
664	4062
663	4056
662	4050
661	4044
660	4038
659	4032
658	4026
657	4020
656	4014
655	4008
654	4002
653	3996
652	3990
651	3984
650	3978
649	3972
648	3966
647	3960
646	3954
645	3948
644	3942
643	3936
642	3930
641	3924
640	3918
639	3912
638	3906
637	3900
636	3894
635	3888
634	3882
633	3876
632	3870
631	3864
630	3858
629	3852
628	3846
627	3840
626	3834
625	3828
624	3822
623	3816
622	3810
621	3804
620	3798
619	3792
618	3786
617	3780
616	3774
615	3768
614	3762
613	3756
612	3750
611	3744
610	3738
609	3732
608	3726
607	3720
606	3714
605	3708
604	3702
603	3696
602	3690
601	3684
600	3678
599	3672
598	3666
597	3660
596	3654
595	3648
594	3642
593	3636
592	3630
591	3624
590	3618
589	3612
588	3606
587	3600
586	3594
585	3588
584	3582
583	3576
582	3570
581	3564
580	3558
579	3552
578	3546
577	3540
576	3534
575	3528
574	3522
573	3516
572	3510
571	3504
570	3498
569	3492
568	3486
567	3480
566	3474
565	3468
564	3462
563	3456
562	3450
561	3444
560	3438
559	3432
558	3426
557	3420
556	3414
555	3408
554	3402
553	3396
552	3390
551	3384
550	3378
549	3372
548	3366
547	3360
546	3354
545	3348
544	3342
543	3336
542	3330
541	3324
540	3318
539	3312
538	3306
537	3300
536	3294
535	3288
534	3282
533	3276
532	3270
531	3264
530	3258
529	3252
528	3246
527	3240
526	3234
525	3228
524	3222
523	3216
522	3210
521	3204
520	3198
519	3192
518	3186
517	3180
516	3174
515	3168
514	3162
513	3156
512	3150
511	3144
510	3138
509	3132
508	3126
507	3120
506	3114
505	3108
504	3102
503	3096
502	3090
501	3084
500	3078
499	3072
498	3066
497	3060
496	3054
495	3048
494	3042
493	3036
492	3030
491	3024
490	3018
489	3012
488	3006
487	3000
486	2994
485	2988
484	2982
483	2976
482	2970
481	2964
480	2958
479	2952
478	2946
477	2940
476	2934
475	2928
474	2922
473	2916
472	2910
471	2904
470	2898
469	2892
468	2886
467	2880
466	2874
465	2868
464	2862
463	2856
462	2850
461	2844
460	2838
459	2832
458	2826
457	2820
456	2814
455	2808
454	2802
453	2796
452	2790
451	2784
450	2778
449	2772
448	2766
447	2760
446	2754
445	2748
444	2742
443	2736
442	2730
441	2724
440	2718
439	2712
438	2706
437	2700
436	2694
435	2688
434	2682
433	2676
432	2670
431	2664
430	2658
429	2652
428	2646
427	2640
426	2634
425	2628
424	2622
423	2616
422	2610
421	2604
420	2598
419	2592
418	2586
417	2580
416	2574
415	2568
414	2562
413	2556
412	2550
411	2544
410	2538
409	2532
408	2526
407	2520
406	2514
405	2508
404	2502
403	2496
402	2490
401	2484
400	2478
399	2472
398	2466
397	2460
396	2454
395	2448
394	2442
393	2436
392	2430
391	2424
390	2418
389	2412
388	2406
387	2400
386	2394
385	2388
384	2382
383	2376
382	2370
381	2364
380	2358
379	2352
378	2346
377	2340
376	2334
375	2328
374	2322
373	2316
372	2310
371	2304
370	2298
369	2292
368	2286
367	2280
366	2274
365	2268
364	2262
363	2256
362	2250
361	2244
360	2238
359	2232
358	2226
357	2220
356	2214
355	2208
354	2202
353	2196
352	2190
351	2184
350	2178
349	2172
348	2166
347	2160
346	2154
345	2148
344	2142
343	2136
342	2130
341	2124
340	2118
339	2112
338	2106
337	2100
336	2094
335	2088
334	2082
333	2076
332	2070
331	2064
330	2058
329	2052
328	2046
327	2040
326	2034
325	2028
324	2022
323	2016
322	2010
321	2004
320	1998
319	1992
318	1986
317	1980
316	1974
315	1968
314	1962
313	1956
312	1950
311	1944
310	1938
309	1932
308	1926
307	1920
306	1914
305	1908
304	1902
303	1896
302	1890
301	1884
300	1878
299	1872
298	1866
297	1860
296	1854
295	1848
294	1842
293	1836
292	1830
291	1824
290	1818
289	1812
288	1806
287	1800
286	1794
285	1788
284	1782
283	1776
282	1770
281	1764
280	1758
279	1752
278	1746
277	1740
276	1734
275	1728
274	1722
273	1716
272	1710
271	1704
270	1698
269	1692
268	1686
267	1680
266	1674
265	1668
264	1662
263	1656
262	1650
261	1644
260	1638
259	1632
258	1626
257	1620
256	1614
255	1608
254	1602
253	1596
252	1590
251	1584
250	1578
249	1572
248	1566
247	1560
246	1554
245	1548
244	1542
243	1536
242	1530
241	1524
240	1518
239	1512
238	1506
237	1500
236	1494
235	1488
234	1482
233	1476
232	1470
231	1464
230	1458
229	1452
228	1446
227	1440
226	1434
225	1428
224	1422
223	1416
222	1410
221	1404
220	1398
219	1392
218	1386
217	1380
216	1374
215	1368
214	1362
213	1356
212	1350
211	1344
210	1338
209	1332
208	1326
207	1320
206	1314
205	1308
204	1302
203	1296
202	1290
201	1284
200	1278
199	1272
198	1266
197	1260
196	1254
195	1248
194	1242
193	1236
192	1230
191	1224
190	1218
189	1212
188	1206
187	1200
186	1194
185	1188
184	1182
183	1176
182	1170
181	1164
180	1158
179	1152
178	1146
177	1140
176	1134
175	1128
174	1122
173	1116
172	1110
171	1104
170	1098
169	1092
168	1086
167	1080
166	1074
165	1068
164	1062
163	1056
162	1050
161	1044
160	1038
159	1032
158	1026
157	1020
156	1014
155	1008
154	1002
153	996
152	990
151	984
150	978
149	972
148	966
147	960
146	954
145	948
144	942
143	936
142	930
141	924
140	918
139	912
138	906
137	900
136	894
135	888
134	882
133	876
132	870
131	864
130	858
129	852
128	846
127	840
126	834
125	828
124	822
123	816
122	810
121	804
120	798
119	792
118	786
117	780
116	774
115	768
114	762
113	756
112	750
111	744
110	738
109	732
108	726
107	720
106	714
105	708
104	702
103	696
102	690
101	684
100	678
99	672
98	666
97	660
96	654
95	648
94	642
93	636
92	630
91	624
90	618
89	612
88	606
87	600
86	594
85	588
84	582
83	576
82	570
81	564
80	558
79	552
78	546
77	540
76	534
75	528
74	522
73	516
72	510
71	504
70	498
69	492
68	486
67	480
66	474
65	468
64	462
63	456
62	450
61	444
60	438
59	432
58	426
57	420
56	414
55	408
54	402
53	396
52	390
51	384
50	378
49	372
48	366
47	360
46	354
45	348
44	342
43	336
42	330
41	324
40	318
39	312
38	306
37	300
36	294
35	288
34	282
33	276
32	270
31	264
30	258
29	252
28	246
27	240
26	234
25	228
24	222
23	216
22	210
21	204
20	198
19	192
18	186
17	180
16	174
15	168
14	162
13	156
12	150
11	144
10	138
9	132
8	126
7	120
6	109
5	99
4	93
3	91
2	86
1	79
0	57

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.7s	9922×	body	80	nan
993.0ms	1060×	body	640	valid
739.0ms	5112×	body	80	valid
561.0ms	819×	body	1280	valid
304.0ms	625×	body	640	nan
301.0ms	599×	body	1280	nan
269.0ms	644×	body	320	valid
98.0ms	335×	body	320	nan
73.0ms	365×	body	160	valid
69.0ms	191×	body	160	nan