Details

sample434.0ms

Algorithm

intervals

Results

227.0ms	132×	body	1280	valid
63.0ms	23×	body	320	valid
57.0ms	53×	body	640	valid
21.0ms	256×	pre	80	true
9.0ms	39×	body	80	valid
4.0ms	9×	body	160	valid

simplify10.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
295	4987
294	4970
293	4954
292	4938
291	4920
290	4905
289	4889
288	4867
287	4853
286	4838
285	4820
284	4804
283	4790
282	4773
281	4757
280	4741
279	4721
278	4706
277	4690
276	4670
275	4656
274	4641
273	4623
272	4607
271	4593
270	4576
269	4560
268	4544
267	4524
266	4509
265	4493
264	4473
263	4459
262	4444
261	4426
260	4410
259	4396
258	4379
257	4363
256	4347
255	4327
254	4312
253	4296
252	4274
251	4260
250	4245
249	4227
248	4211
247	4197
246	4180
245	4164
244	4148
243	4130
242	4115
241	4099
240	4077
239	4063
238	4048
237	4030
236	4014
235	4000
234	3983
233	3967
232	3951
231	3933
230	3918
229	3902
228	3880
227	3866
226	3851
225	3833
224	3817
223	3803
222	3786
221	3770
220	3754
219	3736
218	3721
217	3705
216	3685
215	3671
214	3656
213	3638
212	3622
211	3608
210	3591
209	3575
208	3559
207	3539
206	3524
205	3508
204	3488
203	3474
202	3459
201	3441
200	3425
199	3411
198	3394
197	3378
196	3362
195	3344
194	3329
193	3313
192	3293
191	3279
190	3264
189	3246
188	3230
187	3216
186	3199
185	3183
184	3167
183	3147
182	3132
181	3116
180	3094
179	3080
178	3065
177	3047
176	3031
175	3017
174	3000
173	2984
172	2968
171	2950
170	2935
169	2919
168	2897
167	2883
166	2868
165	2850
164	2834
163	2820
162	2803
161	2787
160	2771
159	2753
158	2738
157	2722
156	2700
155	2686
154	2671
153	2653
152	2637
151	2623
150	2606
149	2590
148	2574
147	2554
146	2539
145	2523
144	2503
143	2489
142	2474
141	2456
140	2440
139	2426
138	2409
137	2393
136	2377
135	2359
134	2344
133	2328
132	2308
131	2294
130	2279
129	2261
128	2245
127	2231
126	2214
125	2198
124	2182
123	2164
122	2149
121	2133
120	2113
119	2099
118	2084
117	2066
116	2050
115	2036
114	2019
113	2003
112	1987
111	1967
110	1952
109	1936
108	1916
107	1902
106	1887
105	1869
104	1853
103	1839
102	1822
101	1806
100	1790
99	1772
98	1757
97	1741
96	1721
95	1707
94	1692
93	1674
92	1658
91	1644
90	1627
89	1611
88	1595
87	1575
86	1560
85	1544
84	1524
83	1510
82	1495
81	1477
80	1461
79	1447
78	1430
77	1414
76	1398
75	1378
74	1363
73	1347
72	1327
71	1313
70	1298
69	1280
68	1264
67	1250
66	1233
65	1217
64	1201
63	1181
62	1166
61	1150
60	1128
59	1114
58	1099
57	1081
56	1065
55	1051
54	1034
53	1018
52	1002
51	982
50	967
49	951
48	931
47	917
46	902
45	884
44	868
43	854
42	837
41	821
40	805
39	785
38	770
37	754
36	732
35	718
34	703
33	685
32	669
31	655
30	638
29	622
28	606
27	588
26	573
25	557
24	535
23	521
22	506
21	488
20	472
19	458
18	441
17	425
16	409
15	387
14	371
13	358
12	328
11	265
10	176
9	126
8	93
7	78
6	58
5	46
4	35
3	29
2	22
1	15
0	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.6b	(tan (+ y z))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 42

Calls

3 calls:

30.0ms	(+ x (- (tan (+ y z)) (tan a)))
35.0ms	(- (tan (+ y z)) (tan a))
20.0ms	(tan (+ y z))

series618.0ms

Counts

3 → 9

Calls

3 calls:

266.0ms	(+ x (- (tan (+ y z)) (tan a)))
246.0ms	(- (tan (+ y z)) (tan a))
105.0ms	(tan (+ y z))

simplify2.8s

Counts

51 → 51

Iterations

Iter	Nodes
done	5030
3	1485
2	469
1	196
0	91

prune543.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

18.0ms	(+ (tan y) (tan z))
298.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
178.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
34.0ms	(* (tan y) (tan z))

series1.9s

Counts

4 → 12

Calls

4 calls:

183.0ms	(+ (tan y) (tan z))
758.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
803.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
201.0ms	(* (tan y) (tan z))

simplify4.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	3363
2	1016
1	375
0	154

prune893.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
0.2b	(/ (* (sin y) (tan z)) (cos y))
0.2b	(* (sin y) (tan z))

rewrite853.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`times-frac`
3×	`tan-quot` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `diff-log` `associate-*r/` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-+r-` `flip3--` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

483.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
315.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
29.0ms	(/ (* (sin y) (tan z)) (cos y))
22.0ms	(* (sin y) (tan z))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
878.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
200.0ms	(/ (* (sin y) (tan z)) (cos y))
167.0ms	(* (sin y) (tan z))

simplify5.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	4881
2	1159
1	398
0	165

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan a) (tan a))
0.3b	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
0.9b	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite538.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
80×	`times-frac`
72×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
27×	`swap-sqr`
24×	`associate-r` `associate-l`
23×	`distribute-lft-out`
22×	`add-exp-log` `add-cbrt-cube`
21×	`tan-quot`
20×	`pow1`
11×	`associate-/r/` `associate-/l/`
9×	`frac-times` `associate-r/` `associate-l/` `frac-sub`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv` `difference-of-squares`
4×	`associate-/r` `associate-/l` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`frac-2neg` `flip3-+` `div-sub` `frac-add` `clear-num` `flip-+`

Counts

4 → 188

Calls

4 calls:

27.0ms	(* (tan y) (tan z))
33.0ms	(* (tan a) (tan a))
141.0ms	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
321.0ms	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

series3.3s

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (tan y) (tan z))
69.0ms	(* (tan a) (tan a))
451.0ms	(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
2.6s	(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

simplify5.2s

Counts

200 → 200

Iterations

Iter	Nodes
done	5009
2	4065
1	1104
0	344

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes829.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample15.6s

Algorithm

intervals

Results

9.1s	3935×	body	1280	valid
3.3s	1929×	body	640	valid
927.0ms	8000×	pre	80	true
817.0ms	1124×	body	80	valid
591.0ms	715×	body	320	valid
143.0ms	297×	body	160	valid