Details

sample432.0ms

Algorithm

intervals

Results

203.0ms	117×	body	1280	valid
124.0ms	66×	body	640	valid
30.0ms	256×	pre	80	true
20.0ms	23×	body	320	valid
10.0ms	41×	body	80	valid
5.0ms	9×	body	160	valid

simplify6.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
296	4996
295	4982
294	4965
293	4949
292	4933
291	4913
290	4898
289	4882
288	4860
287	4846
286	4831
285	4813
284	4797
283	4783
282	4766
281	4750
280	4734
279	4714
278	4699
277	4683
276	4663
275	4649
274	4634
273	4616
272	4600
271	4586
270	4569
269	4553
268	4537
267	4517
266	4502
265	4486
264	4466
263	4452
262	4437
261	4419
260	4403
259	4389
258	4372
257	4356
256	4340
255	4320
254	4305
253	4289
252	4269
251	4255
250	4240
249	4222
248	4206
247	4192
246	4175
245	4159
244	4143
243	4125
242	4110
241	4094
240	4074
239	4060
238	4045
237	4027
236	4011
235	3997
234	3980
233	3964
232	3948
231	3930
230	3915
229	3899
228	3879
227	3865
226	3850
225	3832
224	3816
223	3802
222	3785
221	3769
220	3753
219	3735
218	3720
217	3704
216	3684
215	3670
214	3655
213	3637
212	3621
211	3607
210	3590
209	3574
208	3558
207	3540
206	3525
205	3509
204	3489
203	3475
202	3460
201	3442
200	3426
199	3412
198	3395
197	3379
196	3363
195	3345
194	3330
193	3314
192	3294
191	3280
190	3265
189	3247
188	3231
187	3217
186	3200
185	3184
184	3168
183	3148
182	3133
181	3117
180	3097
179	3083
178	3068
177	3050
176	3034
175	3020
174	3003
173	2987
172	2971
171	2951
170	2936
169	2920
168	2898
167	2884
166	2869
165	2851
164	2835
163	2821
162	2804
161	2788
160	2772
159	2754
158	2739
157	2723
156	2701
155	2687
154	2672
153	2654
152	2638
151	2624
150	2607
149	2591
148	2575
147	2557
146	2542
145	2526
144	2504
143	2490
142	2475
141	2457
140	2441
139	2427
138	2410
137	2394
136	2378
135	2358
134	2343
133	2327
132	2307
131	2293
130	2278
129	2260
128	2244
127	2230
126	2213
125	2197
124	2181
123	2163
122	2148
121	2132
120	2112
119	2098
118	2083
117	2065
116	2049
115	2035
114	2018
113	2002
112	1986
111	1968
110	1953
109	1937
108	1917
107	1903
106	1888
105	1870
104	1854
103	1840
102	1823
101	1807
100	1791
99	1771
98	1756
97	1740
96	1720
95	1706
94	1691
93	1673
92	1657
91	1643
90	1626
89	1610
88	1594
87	1574
86	1559
85	1543
84	1521
83	1507
82	1492
81	1474
80	1458
79	1444
78	1427
77	1411
76	1395
75	1377
74	1362
73	1346
72	1324
71	1310
70	1295
69	1277
68	1261
67	1247
66	1230
65	1214
64	1198
63	1178
62	1163
61	1147
60	1127
59	1113
58	1098
57	1080
56	1064
55	1050
54	1033
53	1017
52	1001
51	983
50	968
49	952
48	932
47	918
46	903
45	885
44	869
43	855
42	838
41	822
40	806
39	786
38	771
37	755
36	733
35	719
34	704
33	686
32	670
31	656
30	639
29	623
28	607
27	587
26	572
25	556
24	534
23	520
22	505
21	487
20	471
19	457
18	440
17	424
16	408
15	386
14	370
13	360
12	330
11	270
10	178
9	126
8	93
7	78
6	58
5	46
4	35
3	29
2	22
1	15
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.1b	(tan (+ y z))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
5×	`tan-quot`
4×	`tan-sum`
3×	`expm1-log1p-u` `pow1` `+-commutative` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
2×	`sum-log` `sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--`
1×	`associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 77

Calls

3 calls:

21.0ms	(+ x (- (tan (+ y z)) (tan a)))
24.0ms	(- (tan (+ y z)) (tan a))
14.0ms	(tan (+ y z))

series482.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(+ x (- (tan (+ y z)) (tan a)))
174.0ms	(- (tan (+ y z)) (tan a))
108.0ms	(tan (+ y z))

simplify2.1s

Counts

86 → 86

Iterations

Iter	Nodes
done	5014
3	2098
2	668
1	297
0	138

prune543.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

856×	`*-un-lft-identity`
586×	`associate-l`
520×	`add-sqr-sqrt`
382×	`distribute-lft-out--`
342×	`times-frac`
156×	`difference-of-squares`
138×	`unswap-sqr`
88×	`add-cube-cbrt`
77×	`distribute-lft-out`
66×	`associate-r`
22×	`*-commutative`
19×	`associate-/l*`
18×	`associate-/r*`
16×	`associate-*l/`
14×	`tan-quot`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/l/`
6×	`frac-sub` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `frac-add` `prod-exp` `cbrt-unprod` `flip-+`
2×	`frac-times` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-*r/` `associate-/r/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `div-sub` `div-inv`

Counts

4 → 474

Calls

4 calls:

18.0ms	(+ (tan z) (tan y))
34.0ms	(* (tan z) (tan y))
34.0ms	(* (tan z) (tan y))
1.6s	(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))

series1.3s

Counts

4 → 12

Calls

4 calls:

174.0ms	(+ (tan z) (tan y))
144.0ms	(* (tan z) (tan y))
140.0ms	(* (tan z) (tan y))
859.0ms	(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))

simplify3.4s

Counts

486 → 486

Iterations

Iter	Nodes
done	5000
2	4403
1	1285
0	435

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan z) (tan y))
0.2b	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
0.2b	(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)))
28.4b	(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))

rewrite6.6s

Algorithm

rewrite-expression-head

Rules

4026×	`add-sqr-sqrt`
2433×	`*-un-lft-identity`
2189×	`unswap-sqr`
2065×	`associate-l`
1016×	`difference-of-squares`
1007×	`times-frac`
992×	`distribute-lft-out--`
842×	`cbrt-prod`
232×	`tan-quot`
216×	`distribute-lft-out`
192×	`swap-sqr`
149×	`add-cube-cbrt`
147×	`frac-times`
126×	`associate-r`
116×	`*-commutative`
101×	`associate-*l/`
75×	`associate-*r/`
63×	`cbrt-div`
53×	`associate-/r*`
45×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
18×	`pow-prod-down`
10×	`prod-exp` `cbrt-unprod`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3-+` `pow-plus` `div-exp` `pow3` `frac-add` `associate-/r/` `rem-cbrt-cube` `flip-+`
1×	`pow2` `clear-num` `frac-2neg` `pow1/3` `div-sub` `div-inv`

Counts

4 → 1380

Calls

4 calls:

33.0ms	(* (tan z) (tan y))
127.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
5.7s	(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)))
433.0ms	(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))

series1.3s

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (tan z) (tan y))
178.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))
810.0ms	(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)))
171.0ms	(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))

simplify4.0s

Counts

1392 → 1392

Iterations

Iter	Nodes
done	5000
1	3573
0	1275

prune6.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (- 1 (* (tan z) (tan y))) (sin a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
0.5b	(* (* (+ (tan z) (tan y)) (cos a)) (* (+ (tan z) (tan y)) (cos a)))
1.7b	(/ (- (* (* (+ (tan z) (tan y)) (cos a)) (* (+ (tan z) (tan y)) (cos a))) (* (* (- 1 (* (tan z) (tan y))) (sin a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (* (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)) (+ (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))))
28.4b	(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))

rewrite29.4s

Algorithm

rewrite-expression-head

Rules

81442×	`*-un-lft-identity`
70140×	`associate-l`
67606×	`add-sqr-sqrt`
38174×	`unswap-sqr`
26683×	`swap-sqr`
25779×	`distribute-lft-out--`
18600×	`times-frac`
16132×	`difference-of-squares`
11668×	`distribute-lft-out`
9544×	`cbrt-prod`
4576×	`associate-r`
2882×	`*-commutative`
1366×	`add-cube-cbrt`
598×	`associate-*l/`
348×	`tan-quot`
290×	`frac-times`
248×	`associate-/l*`
130×	`associate-*r/`
122×	`associate-/l/`
120×	`frac-sub`
115×	`flip3--` `flip--`
96×	`frac-add`
82×	`pow1`
81×	`flip3-+` `flip-+`
75×	`associate-/r*`
63×	`cbrt-div`
37×	`add-cbrt-cube` `add-exp-log`
34×	`pow-prod-down`
26×	`associate-/r/`
19×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `pow-plus` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `pow3` `rem-cbrt-cube`
1×	`clear-num` `frac-2neg` `pow1/3` `div-sub` `div-inv`

Counts

4 → 19459

Calls

4 calls:

544.0ms	(* (* (- 1 (* (tan z) (tan y))) (sin a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
191.0ms	(* (* (+ (tan z) (tan y)) (cos a)) (* (+ (tan z) (tan y)) (cos a)))
23.1s	(/ (- (* (* (+ (tan z) (tan y)) (cos a)) (* (+ (tan z) (tan y)) (cos a))) (* (* (- 1 (* (tan z) (tan y))) (sin a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (* (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)) (+ (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))))
427.0ms	(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))

series1.8s

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (* (- 1 (* (tan z) (tan y))) (sin a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
164.0ms	(* (* (+ (tan z) (tan y)) (cos a)) (* (+ (tan z) (tan y)) (cos a)))
1.4s	(/ (- (* (* (+ (tan z) (tan y)) (cos a)) (* (+ (tan z) (tan y)) (cos a))) (* (* (- 1 (* (tan z) (tan y))) (sin a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (* (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)) (+ (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))))
96.0ms	(cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))

simplify18.7s

Counts

19471 → 19471

Iterations

Iter	Nodes
done	5034
0	5034

prune24.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes868.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample10.8s

Algorithm

intervals

Results

6.1s	3873×	body	1280	valid
2.0s	1983×	body	640	valid
974.0ms	8000×	pre	80	true
855.0ms	714×	body	320	valid
272.0ms	1146×	body	80	valid
127.0ms	284×	body	160	valid