Details

sample165.0ms

Algorithm

intervals

Results

67.0ms	85×	body	1280	valid
38.0ms	20×	body	2560	valid
31.0ms	63×	body	640	valid
11.0ms	29×	body	320	valid
5.0ms	47×	body	80	valid
3.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize45.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
4.3b	(sin (+ x eps))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

35.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
4	3108
3	1127
2	429
1	201
0	92

prune513.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize41.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

22.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series100.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
34.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.9s

Counts

38 → 38

Iterations

Iter	Nodes
5	3026
4	1701
3	796
2	336
1	148
0	70

prune421.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (fma 1/2 eps x)) (sin (* eps 1/2)))
4.1b	(cos (fma 1/2 eps x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

37.0ms	(* (cos (fma 1/2 eps x)) (sin (* eps 1/2)))
10.0ms	(cos (fma 1/2 eps x))

series113.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* (cos (fma 1/2 eps x)) (sin (* eps 1/2)))
33.0ms	(cos (fma 1/2 eps x))

simplify2.1s

Counts

38 → 38

Iterations

Iter	Nodes
5	2761
4	1426
3	729
2	325
1	135
0	68

prune495.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* 1/2 eps)) (cos x))
0.2b	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
0.2b	(* (sin (* 1/2 eps)) (sin x))
0.2b	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 88

Calls

4 calls:

24.0ms	(* (cos (* 1/2 eps)) (cos x))
45.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
27.0ms	(* (sin (* 1/2 eps)) (sin x))
157.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos (* 1/2 eps)) (cos x))
116.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
77.0ms	(* (sin (* 1/2 eps)) (sin x))
169.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (* eps 1/2)))

simplify4.2s

Counts

100 → 100

Iterations

Iter	Nodes
3	3395
2	1040
1	365
0	161

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes272.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.5m

Iterations

Iter	Nodes
329	2001
328	1995
327	1989
326	1983
325	1977
324	1971
323	1965
322	1959
321	1953
320	1947
319	1941
318	1935
317	1929
316	1923
315	1917
314	1911
313	1905
312	1899
311	1893
310	1887
309	1881
308	1875
307	1869
306	1863
305	1857
304	1851
303	1845
302	1839
301	1833
300	1827
299	1821
298	1815
297	1809
296	1803
295	1797
294	1791
293	1785
292	1779
291	1773
290	1767
289	1761
288	1755
287	1749
286	1743
285	1737
284	1731
283	1725
282	1719
281	1713
280	1707
279	1701
278	1695
277	1689
276	1683
275	1677
274	1671
273	1665
272	1659
271	1653
270	1647
269	1641
268	1635
267	1629
266	1623
265	1617
264	1611
263	1605
262	1599
261	1593
260	1587
259	1581
258	1575
257	1569
256	1563
255	1557
254	1551
253	1545
252	1539
251	1533
250	1527
249	1521
248	1515
247	1509
246	1503
245	1497
244	1491
243	1485
242	1479
241	1473
240	1467
239	1461
238	1455
237	1449
236	1443
235	1437
234	1431
233	1425
232	1419
231	1413
230	1407
229	1401
228	1395
227	1389
226	1383
225	1377
224	1371
223	1365
222	1359
221	1353
220	1347
219	1341
218	1335
217	1329
216	1323
215	1317
214	1311
213	1305
212	1299
211	1293
210	1287
209	1281
208	1275
207	1269
206	1263
205	1257
204	1251
203	1245
202	1239
201	1233
200	1227
199	1221
198	1215
197	1209
196	1203
195	1197
194	1191
193	1185
192	1179
191	1173
190	1167
189	1161
188	1155
187	1149
186	1143
185	1137
184	1131
183	1125
182	1119
181	1113
180	1107
179	1101
178	1095
177	1089
176	1083
175	1077
174	1071
173	1065
172	1059
171	1053
170	1047
169	1041
168	1035
167	1029
166	1023
165	1017
164	1011
163	1005
162	999
161	993
160	987
159	981
158	975
157	969
156	963
155	957
154	951
153	945
152	939
151	933
150	927
149	921
148	915
147	909
146	903
145	897
144	891
143	885
142	879
141	873
140	867
139	861
138	855
137	849
136	843
135	837
134	831
133	825
132	819
131	813
130	807
129	801
128	795
127	789
126	783
125	777
124	771
123	765
122	759
121	753
120	747
119	741
118	735
117	729
116	723
115	717
114	711
113	705
112	699
111	693
110	687
109	681
108	675
107	669
106	663
105	657
104	651
103	645
102	639
101	633
100	627
99	621
98	615
97	609
96	603
95	597
94	591
93	585
92	579
91	573
90	567
89	561
88	555
87	549
86	543
85	537
84	531
83	525
82	519
81	513
80	507
79	501
78	495
77	489
76	483
75	477
74	471
73	465
72	459
71	453
70	447
69	441
68	435
67	429
66	423
65	417
64	411
63	405
62	399
61	393
60	387
59	381
58	375
57	369
56	363
55	357
54	351
53	345
52	339
51	333
50	327
49	321
48	315
47	309
46	303
45	297
44	291
43	285
42	279
41	273
40	267
39	261
38	255
37	249
36	243
35	237
34	231
33	225
32	219
31	213
30	207
29	201
28	195
27	189
26	183
25	177
24	171
23	165
22	159
21	153
20	147
19	141
18	135
17	129
16	123
15	117
14	111
13	105
12	99
11	93
10	87
9	81
8	75
7	69
6	63
5	57
4	49
3	40
2	32
1	23
0	16

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.5s	3311×	body	1280	valid
1.2s	633×	body	2560	valid
1.1s	1788×	body	640	valid
299.0ms	822×	body	320	valid
130.0ms	1123×	body	80	valid
68.0ms	323×	body	160	valid