Details

sample79.0ms

Algorithm

intervals

Results

27.0ms	53×	body	1280	valid
20.0ms	50×	body	640	valid
13.0ms	128×	body	80	valid
5.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.6b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

17.0ms	(/ x (+ x 1))
18.0ms	(/ (+ x 1) (- x 1))
94.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ x (+ x 1))
31.0ms	(/ (+ x 1) (- x 1))
113.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.0s

Counts

762 → 762

Iterations

Iter	Nodes
done	2001
2	2001
1	1369
0	584

prune2.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.6b	(/ 3 (* x (* x x)))
0.8b	(/ 1 (* x x))
7.3b	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
26×	`pow1`
23×	`*-un-lft-identity` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`times-frac` `prod-exp` `add-log-exp`
8×	`distribute-lft-out`
7×	`div-exp` `cbrt-unprod`
6×	`fma-def` `pow-prod-up` `div-inv` `pow-flip` `associate-/l*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-l`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `pow-plus` `distribute-rgt-out` `1-exp` `pow-sqr` `flip-+`
1×	`+-commutative` `associate-+l+` `cube-unmult` `associate-r` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

28.0ms	(* x (* x x))
27.0ms	(/ 3 (* x (* x x)))
19.0ms	(/ 1 (* x x))
152.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* x (* x x))
48.0ms	(/ 3 (* x (* x x)))
30.0ms	(/ 1 (* x x))
42.0ms	(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))

simplify887.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	2001
2	2001
1	483
0	172

prune369.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ -1 (- x 1))
2.6b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
34.1b	(fma (/ -1 (- x 1)) (+ x 1) (/ (+ x 1) (- x 1)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

1292×	`*-un-lft-identity`
993×	`times-frac`
861×	`add-sqr-sqrt`
612×	`prod-diff`
525×	`add-cube-cbrt`
247×	`distribute-lft-out`
166×	`difference-of-squares`
110×	`associate-/r/`
94×	`distribute-lft-out--`
81×	`difference-of-sqr-1`
55×	`div-inv`
36×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`fma-neg`
14×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef`

Counts

4 → 776

Calls

4 calls:

38.0ms	(/ (+ x 1) (- x 1))
15.0ms	(/ -1 (- x 1))
77.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0ms	(fma (/ -1 (- x 1)) (+ x 1) (/ (+ x 1) (- x 1)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ x 1) (- x 1))
24.0ms	(/ -1 (- x 1))
99.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
164.0ms	(fma (/ -1 (- x 1)) (+ x 1) (/ (+ x 1) (- x 1)))

simplify1.8s

Counts

788 → 788

Iterations

Iter	Nodes
done	2001
2	2001
1	1462
0	635

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ -1 (- x 1))
0.0b	(/ (- x 1) (+ x 1))
2.6b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
34.8b	(fma (/ -1 (- x 1)) (+ x 1) (/ 1 (/ (- x 1) (+ x 1))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

1292×	`*-un-lft-identity`
993×	`times-frac`
861×	`add-sqr-sqrt`
612×	`prod-diff`
525×	`add-cube-cbrt`
247×	`distribute-lft-out`
166×	`difference-of-squares`
110×	`associate-/r/`
94×	`distribute-lft-out--`
81×	`difference-of-sqr-1`
55×	`div-inv`
36×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
10×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub` `fma-udef`

Counts

4 → 777

Calls

4 calls:

8.0ms	(/ -1 (- x 1))
16.0ms	(/ (- x 1) (+ x 1))
65.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0ms	(fma (/ -1 (- x 1)) (+ x 1) (/ 1 (/ (- x 1) (+ x 1))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ -1 (- x 1))
32.0ms	(/ (- x 1) (+ x 1))
88.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
144.0ms	(fma (/ -1 (- x 1)) (+ x 1) (/ 1 (/ (- x 1) (+ x 1))))

simplify1.4s

Counts

789 → 789

Iterations

Iter	Nodes
done	2000
2	2000
1	1519
0	663

prune2.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.1b

bsearch182.0ms

Steps

Iters	Range		Point
11	5.037382729650074e-10	1937402784720.5117	7862.0498067640765
8	-44481.00103279522	-87.25999490770408	-6263.833804380613

simplify5.3m

Iterations

Iter	Nodes
done	2000
420	2000
419	1998
418	1993
417	1989
416	1984
415	1980
414	1975
413	1971
412	1966
411	1962
410	1957
409	1953
408	1948
407	1944
406	1939
405	1935
404	1930
403	1926
402	1921
401	1917
400	1912
399	1908
398	1903
397	1899
396	1894
395	1890
394	1885
393	1881
392	1876
391	1872
390	1867
389	1863
388	1858
387	1854
386	1849
385	1845
384	1840
383	1836
382	1831
381	1827
380	1822
379	1818
378	1813
377	1809
376	1804
375	1800
374	1795
373	1791
372	1786
371	1782
370	1777
369	1773
368	1768
367	1764
366	1759
365	1755
364	1750
363	1746
362	1741
361	1737
360	1732
359	1728
358	1723
357	1719
356	1714
355	1710
354	1705
353	1701
352	1696
351	1692
350	1687
349	1683
348	1678
347	1674
346	1669
345	1665
344	1660
343	1656
342	1651
341	1647
340	1642
339	1638
338	1633
337	1629
336	1624
335	1620
334	1615
333	1611
332	1606
331	1602
330	1597
329	1593
328	1588
327	1584
326	1579
325	1575
324	1570
323	1566
322	1561
321	1557
320	1552
319	1548
318	1543
317	1539
316	1534
315	1530
314	1525
313	1521
312	1516
311	1512
310	1507
309	1503
308	1498
307	1494
306	1489
305	1485
304	1480
303	1476
302	1471
301	1467
300	1462
299	1458
298	1453
297	1449
296	1444
295	1440
294	1435
293	1431
292	1426
291	1422
290	1417
289	1413
288	1408
287	1404
286	1399
285	1395
284	1390
283	1386
282	1381
281	1377
280	1372
279	1368
278	1363
277	1359
276	1354
275	1350
274	1345
273	1341
272	1336
271	1332
270	1327
269	1323
268	1318
267	1314
266	1309
265	1305
264	1300
263	1296
262	1291
261	1287
260	1282
259	1278
258	1273
257	1269
256	1264
255	1260
254	1255
253	1251
252	1246
251	1242
250	1237
249	1233
248	1228
247	1224
246	1219
245	1215
244	1210
243	1206
242	1201
241	1197
240	1192
239	1188
238	1183
237	1179
236	1174
235	1170
234	1165
233	1161
232	1156
231	1152
230	1147
229	1143
228	1138
227	1134
226	1129
225	1125
224	1120
223	1116
222	1111
221	1107
220	1102
219	1098
218	1093
217	1089
216	1084
215	1080
214	1075
213	1071
212	1066
211	1062
210	1057
209	1053
208	1048
207	1044
206	1039
205	1035
204	1030
203	1026
202	1021
201	1017
200	1012
199	1008
198	1003
197	999
196	994
195	990
194	985
193	981
192	976
191	972
190	967
189	963
188	958
187	954
186	949
185	945
184	940
183	936
182	931
181	927
180	922
179	918
178	913
177	909
176	904
175	900
174	895
173	891
172	886
171	882
170	877
169	873
168	868
167	864
166	859
165	855
164	850
163	846
162	841
161	837
160	832
159	828
158	823
157	819
156	814
155	810
154	805
153	801
152	796
151	792
150	787
149	783
148	778
147	774
146	769
145	765
144	760
143	756
142	751
141	747
140	742
139	738
138	733
137	729
136	724
135	720
134	715
133	711
132	706
131	702
130	697
129	693
128	688
127	684
126	679
125	675
124	670
123	666
122	661
121	657
120	652
119	648
118	643
117	639
116	634
115	630
114	625
113	621
112	616
111	612
110	607
109	603
108	598
107	594
106	589
105	585
104	580
103	576
102	571
101	567
100	562
99	558
98	553
97	549
96	544
95	540
94	535
93	531
92	526
91	522
90	517
89	513
88	508
87	504
86	499
85	495
84	490
83	486
82	481
81	477
80	472
79	468
78	463
77	459
76	454
75	450
74	445
73	441
72	436
71	432
70	427
69	423
68	418
67	414
66	409
65	405
64	400
63	396
62	391
61	387
60	382
59	378
58	373
57	369
56	364
55	360
54	355
53	351
52	346
51	342
50	337
49	333
48	328
47	324
46	319
45	315
44	310
43	306
42	301
41	297
40	292
39	288
38	283
37	279
36	274
35	270
34	265
33	261
32	256
31	252
30	247
29	243
28	238
27	234
26	229
25	225
24	220
23	216
22	211
21	207
20	202
19	198
18	193
17	189
16	184
15	180
14	175
13	171
12	166
11	162
10	157
9	145
8	138
7	129
6	121
5	112
4	102
3	93
2	82
1	59
0	35

end0.0ms

sample1.3s

Algorithm

intervals

Results

539.0ms	1741×	body	1280	valid
287.0ms	1232×	body	640	valid
226.0ms	4052×	body	80	valid
113.0ms	652×	body	320	valid
32.0ms	323×	body	160	valid