Details

sample178.0ms

Algorithm

intervals

Results

116.0ms	172×	body	1280	valid
19.0ms	246×	body	80	valid
18.0ms	43×	body	640	valid
7.0ms	27×	body	320	valid
2.0ms	10×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
265	2000
264	1991
263	1986
262	1977
261	1972
260	1963
259	1958
258	1949
257	1944
256	1935
255	1930
254	1921
253	1916
252	1907
251	1902
250	1893
249	1888
248	1879
247	1874
246	1865
245	1860
244	1851
243	1846
242	1837
241	1832
240	1823
239	1818
238	1809
237	1804
236	1795
235	1790
234	1781
233	1776
232	1767
231	1762
230	1753
229	1748
228	1739
227	1734
226	1725
225	1720
224	1711
223	1706
222	1697
221	1692
220	1683
219	1678
218	1669
217	1664
216	1655
215	1650
214	1641
213	1636
212	1627
211	1622
210	1613
209	1608
208	1599
207	1594
206	1585
205	1580
204	1571
203	1566
202	1557
201	1552
200	1543
199	1538
198	1529
197	1524
196	1515
195	1510
194	1501
193	1496
192	1487
191	1482
190	1473
189	1468
188	1459
187	1454
186	1445
185	1440
184	1431
183	1426
182	1417
181	1412
180	1403
179	1398
178	1389
177	1384
176	1375
175	1370
174	1361
173	1356
172	1347
171	1342
170	1333
169	1328
168	1319
167	1314
166	1305
165	1300
164	1291
163	1286
162	1277
161	1272
160	1263
159	1258
158	1249
157	1244
156	1235
155	1230
154	1221
153	1216
152	1207
151	1202
150	1193
149	1188
148	1179
147	1174
146	1165
145	1160
144	1151
143	1146
142	1137
141	1132
140	1123
139	1118
138	1109
137	1104
136	1095
135	1090
134	1081
133	1076
132	1067
131	1062
130	1053
129	1048
128	1039
127	1034
126	1025
125	1020
124	1011
123	1006
122	997
121	992
120	983
119	978
118	969
117	964
116	955
115	950
114	941
113	936
112	927
111	922
110	913
109	908
108	899
107	894
106	885
105	880
104	871
103	866
102	857
101	852
100	843
99	838
98	829
97	824
96	815
95	810
94	801
93	796
92	787
91	782
90	773
89	768
88	759
87	754
86	745
85	740
84	731
83	726
82	717
81	712
80	703
79	698
78	689
77	684
76	675
75	670
74	661
73	656
72	647
71	642
70	633
69	628
68	619
67	614
66	605
65	600
64	591
63	586
62	577
61	572
60	563
59	558
58	549
57	544
56	535
55	530
54	521
53	516
52	507
51	502
50	493
49	488
48	479
47	474
46	465
45	460
44	451
43	446
42	437
41	432
40	423
39	418
38	409
37	404
36	395
35	390
34	381
33	376
32	367
31	362
30	353
29	348
28	339
27	334
26	325
25	320
24	311
23	306
22	295
21	290
20	283
19	278
18	263
17	257
16	241
15	235
14	228
13	223
12	206
11	198
10	177
9	150
8	99
7	71
6	62
5	58
4	55
3	41
2	25
1	15
0	7

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2)
4.8b	(+ (- (exp x) 2) (exp (- x)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Counts

2 → 67

Calls

2 calls:

20.0ms	(- (exp x) 2)
81.0ms	(+ (- (exp x) 2) (exp (- x)))

series109.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (exp x) 2)
84.0ms	(+ (- (exp x) 2) (exp (- x)))

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
3	2665
2	818
1	283
0	124

prune540.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (* x x) (* x x)) 1/12 (* x x))
0.1b	(* (* x x) (* (* x x) (* x x)))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

848×	`pow1`
370×	`pow-prod-up`
175×	`pow-prod-down`
153×	`pow-sqr`
140×	`pow-plus`
99×	`pow2`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`cube-unmult` `fma-udef`

Counts

4 → 337

Calls

4 calls:

0.0ms	(fma (* (* x x) (* x x)) 1/12 (* x x))
106.0ms	(* (* x x) (* (* x x) (* x x)))
23.0ms	(* (* x x) (* x x))
27.0ms	(* (* x x) (* x x))

series323.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(fma (* (* x x) (* x x)) 1/12 (* x x))
70.0ms	(* (* x x) (* (* x x) (* x x)))
44.0ms	(* (* x x) (* x x))
51.0ms	(* (* x x) (* x x))

simplify4.5s

Counts

349 → 349

Iterations

Iter	Nodes
3	4861
2	819
1	308
0	135

prune3.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) (exp x) -4)
0.0b	(/ (fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2)) (* (+ (exp x) 2) (exp x)))
0.0b	(* (+ (exp x) 2) (exp x))
5.7b	(fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma (exp x) (exp x) -4)
22.0ms	(/ (fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2)) (* (+ (exp x) 2) (exp x)))
55.0ms	(* (+ (exp x) 2) (exp x))
1.0ms	(fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma (exp x) (exp x) -4)
244.0ms	(/ (fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2)) (* (+ (exp x) 2) (exp x)))
32.0ms	(* (+ (exp x) 2) (exp x))
92.0ms	(fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2))

simplify2.6s

Counts

84 → 84

Iterations

Iter	Nodes
3	4228
2	1011
1	309
0	128

prune851.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2) (exp x))
0.0b	(* (+ (exp x) 2) (exp x))
1.0b	(* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x))))
5.7b	(fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow1`
28×	`sqrt-pow1`
22×	`pow-prod-down`
18×	`add-sqr-sqrt` `associate-*l/`
16×	`*-un-lft-identity`
12×	`sqrt-div` `associate-l` `add-cube-cbrt`
10×	`add-cbrt-cube` `pow1/2` `associate-r` `pow-prod-up`
8×	`flip3-+` `add-exp-log` `flip-+`
6×	`pow-sqr`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*r/` `distribute-lft-out`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `fma-udef`

Counts

4 → 119

Calls

4 calls:

57.0ms	(* (+ (exp x) 2) (exp x))
55.0ms	(* (+ (exp x) 2) (exp x))
124.0ms	(* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x))))
1.0ms	(fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2))

series230.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ (exp x) 2) (exp x))
38.0ms	(* (+ (exp x) 2) (exp x))
31.0ms	(* (sqrt (* (+ (exp x) 2) (exp x))) (sqrt (* (+ (exp x) 2) (exp x))))
120.0ms	(fma (exp x) (fma (exp x) (exp x) -4) (+ (exp x) 2))

simplify1.7s

Counts

131 → 131

Iterations

Iter	Nodes
3	2990
2	879
1	311
0	133

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.5s	5649×	body	1280	valid
934.0ms	7974×	body	80	valid
574.0ms	1271×	body	640	valid
174.0ms	613×	body	320	valid
39.0ms	297×	body	160	valid