Details

sample427.0ms

Algorithm

intervals

Results

175.0ms	95×	body	1280	valid
105.0ms	29×	body	2560	valid
99.0ms	55×	body	640	valid
21.0ms	27×	body	320	valid
11.0ms	44×	body	80	valid
4.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize18.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

17.0ms	(- (tan (+ x eps)) (tan x))
31.0ms	(tan (+ x eps))

series221.0ms

Counts

2 → 6

Calls

2 calls:

157.0ms	(- (tan (+ x eps)) (tan x))
64.0ms	(tan (+ x eps))

simplify1.2s

Counts

49 → 49

Iterations

Iter	Nodes
done	2002
4	2002
3	1357
2	454
1	205
0	96

prune507.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

24.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
74.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

342.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
149.0ms	(+ (tan x) (tan eps))
143.0ms	(* (tan x) (tan eps))
478.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.4s

Counts

185 → 185

Iterations

Iter	Nodes
done	2007
3	2007
2	1631
1	580
0	242

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))
3.9b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

2638×	`times-frac`
1961×	`add-sqr-sqrt`
1951×	`*-un-lft-identity`
1394×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
28×	`associate-/r/`
17×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`quot-tan` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `diff-log` `associate-*r/` `frac-sub` `associate-/l/`

Counts

4 → 1290

Calls

4 calls:

27.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
15.0ms	(/ (sin x) (cos x))
8.0ms	(/ (sin x) (cos x))
166.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
37.0ms	(/ (sin x) (cos x))
36.0ms	(/ (sin x) (cos x))
341.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify3.0s

Counts

1302 → 1302

Iterations

Iter	Nodes
done	2000
1	2000
0	1296

prune23.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))
0.2b	(* (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)) (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))
3.9b	(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)) (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (+ 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))) (- (/ (sin x) (cos x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-cbrt-cube` `add-exp-log`
34×	`cbrt-undiv` `div-exp`
32×	`prod-exp` `cbrt-unprod`
30×	`add-sqr-sqrt` `times-frac`
28×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`associate-/r` `div-inv` `associate-/l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`quot-tan` `clear-num` `frac-2neg`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

8.0ms	(/ (sin x) (cos x))
8.0ms	(/ (sin x) (cos x))
45.0ms	(* (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)) (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))
0.0ms	(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)) (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (+ 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))) (- (/ (sin x) (cos x))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (sin x) (cos x))
19.0ms	(/ (sin x) (cos x))
122.0ms	(* (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)) (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))
423.0ms	(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)) (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (+ 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))) (- (/ (sin x) (cos x))))

simplify1.0s

Counts

158 → 158

Iterations

Iter	Nodes
done	2004
2	2004
1	661
0	222

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.3b

regimes159.0ms

Accuracy

0% (0.3b remaining)

Error of 12.7b against oracle of 12.4b and baseline of 12.7b

bsearch0.0ms

simplify634.0ms

Iterations

Iter	Nodes
done	2000
562	2000
561	1997
560	1993
559	1990
558	1986
557	1983
556	1979
555	1976
554	1972
553	1969
552	1965
551	1962
550	1958
549	1955
548	1951
547	1948
546	1944
545	1941
544	1937
543	1934
542	1930
541	1927
540	1923
539	1920
538	1916
537	1913
536	1909
535	1906
534	1902
533	1899
532	1895
531	1892
530	1888
529	1885
528	1881
527	1878
526	1874
525	1871
524	1867
523	1864
522	1860
521	1857
520	1853
519	1850
518	1846
517	1843
516	1839
515	1836
514	1832
513	1829
512	1825
511	1822
510	1818
509	1815
508	1811
507	1808
506	1804
505	1801
504	1797
503	1794
502	1790
501	1787
500	1783
499	1780
498	1776
497	1773
496	1769
495	1766
494	1762
493	1759
492	1755
491	1752
490	1748
489	1745
488	1741
487	1738
486	1734
485	1731
484	1727
483	1724
482	1720
481	1717
480	1713
479	1710
478	1706
477	1703
476	1699
475	1696
474	1692
473	1689
472	1685
471	1682
470	1678
469	1675
468	1671
467	1668
466	1664
465	1661
464	1657
463	1654
462	1650
461	1647
460	1643
459	1640
458	1636
457	1633
456	1629
455	1626
454	1622
453	1619
452	1615
451	1612
450	1608
449	1605
448	1601
447	1598
446	1594
445	1591
444	1587
443	1584
442	1580
441	1577
440	1573
439	1570
438	1566
437	1563
436	1559
435	1556
434	1552
433	1549
432	1545
431	1542
430	1538
429	1535
428	1531
427	1528
426	1524
425	1521
424	1517
423	1514
422	1510
421	1507
420	1503
419	1500
418	1496
417	1493
416	1489
415	1486
414	1482
413	1479
412	1475
411	1472
410	1468
409	1465
408	1461
407	1458
406	1454
405	1451
404	1447
403	1444
402	1440
401	1437
400	1433
399	1430
398	1426
397	1423
396	1419
395	1416
394	1412
393	1409
392	1405
391	1402
390	1398
389	1395
388	1391
387	1388
386	1384
385	1381
384	1377
383	1374
382	1370
381	1367
380	1363
379	1360
378	1356
377	1353
376	1349
375	1346
374	1342
373	1339
372	1335
371	1332
370	1328
369	1325
368	1321
367	1318
366	1314
365	1311
364	1307
363	1304
362	1300
361	1297
360	1293
359	1290
358	1286
357	1283
356	1279
355	1276
354	1272
353	1269
352	1265
351	1262
350	1258
349	1255
348	1251
347	1248
346	1244
345	1241
344	1237
343	1234
342	1230
341	1227
340	1223
339	1220
338	1216
337	1213
336	1209
335	1206
334	1202
333	1199
332	1195
331	1192
330	1188
329	1185
328	1181
327	1178
326	1174
325	1171
324	1167
323	1164
322	1160
321	1157
320	1153
319	1150
318	1146
317	1143
316	1139
315	1136
314	1132
313	1129
312	1125
311	1122
310	1118
309	1115
308	1111
307	1108
306	1104
305	1101
304	1097
303	1094
302	1090
301	1087
300	1083
299	1080
298	1076
297	1073
296	1069
295	1066
294	1062
293	1059
292	1055
291	1052
290	1048
289	1045
288	1041
287	1038
286	1034
285	1031
284	1027
283	1024
282	1020
281	1017
280	1013
279	1010
278	1006
277	1003
276	999
275	996
274	992
273	989
272	985
271	982
270	978
269	975
268	971
267	968
266	964
265	961
264	957
263	954
262	950
261	947
260	943
259	940
258	936
257	933
256	929
255	926
254	922
253	919
252	915
251	912
250	908
249	905
248	901
247	898
246	894
245	891
244	887
243	884
242	880
241	877
240	873
239	870
238	866
237	863
236	859
235	856
234	852
233	849
232	845
231	842
230	838
229	835
228	831
227	828
226	824
225	821
224	817
223	814
222	810
221	807
220	803
219	800
218	796
217	793
216	789
215	786
214	782
213	779
212	775
211	772
210	768
209	765
208	761
207	758
206	754
205	751
204	747
203	744
202	740
201	737
200	733
199	730
198	726
197	723
196	719
195	716
194	712
193	709
192	705
191	702
190	698
189	695
188	691
187	688
186	684
185	681
184	677
183	674
182	670
181	667
180	663
179	660
178	656
177	653
176	649
175	646
174	642
173	639
172	635
171	632
170	628
169	625
168	621
167	618
166	614
165	611
164	607
163	604
162	600
161	597
160	593
159	590
158	586
157	583
156	579
155	576
154	572
153	569
152	565
151	562
150	558
149	555
148	551
147	548
146	544
145	541
144	537
143	534
142	530
141	527
140	523
139	520
138	516
137	513
136	509
135	506
134	502
133	499
132	495
131	492
130	488
129	485
128	481
127	478
126	474
125	471
124	467
123	464
122	460
121	457
120	453
119	450
118	446
117	443
116	439
115	436
114	432
113	429
112	425
111	422
110	418
109	415
108	411
107	408
106	404
105	401
104	397
103	394
102	390
101	387
100	383
99	380
98	376
97	373
96	369
95	366
94	362
93	359
92	355
91	352
90	348
89	345
88	341
87	338
86	334
85	331
84	327
83	324
82	320
81	317
80	313
79	310
78	306
77	303
76	299
75	296
74	292
73	289
72	285
71	282
70	278
69	275
68	271
67	268
66	264
65	261
64	257
63	254
62	250
61	247
60	243
59	240
58	236
57	233
56	229
55	226
54	222
53	219
52	215
51	212
50	208
49	205
48	201
47	198
46	194
45	191
44	187
43	184
42	180
41	177
40	173
39	170
38	166
37	163
36	159
35	156
34	152
33	149
32	145
31	142
30	138
29	135
28	131
27	128
26	124
25	121
24	117
23	114
22	110
21	107
20	103
19	100
18	96
17	93
16	89
15	86
14	82
13	79
12	75
11	72
10	68
9	65
8	61
7	58
6	54
5	51
4	47
3	44
2	39
1	34
0	22

end0.0ms

sample9.6s

Algorithm

intervals

Results

4.8s	3248×	body	1280	valid
2.2s	1886×	body	640	valid
1.6s	640×	body	2560	valid
506.0ms	759×	body	320	valid
194.0ms	1093×	body	80	valid
152.0ms	374×	body	160	valid