Details

sample51.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify43.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	408
1	35	408
2	64	408
3	145	408
4	349	408
5	714	408
6	1028	408
7	1265	408
8	1482	408
9	1862	408
10	2709	408
11	4021	408
12	4049	408
13	4056	408
14	4061	408
15	4066	408
16	4071	408
17	4076	408
18	4081	408
19	4086	408
20	4091	408
21	4096	408
22	4101	408
23	4106	408
24	4111	408
25	4116	408
26	4121	408
27	4126	408
28	4131	408
29	4136	408
30	4141	408
31	4146	408
32	4151	408
33	4156	408
34	4161	408
35	4166	408
36	4171	408
37	4176	408
38	4181	408
39	4186	408
40	4191	408
41	4196	408
42	4201	408
43	4206	408
44	4211	408
45	4216	408
46	4221	408
47	4226	408
48	4231	408
49	4236	408
50	4241	408
51	4246	408
52	4251	408
53	4256	408
54	4261	408
55	4266	408
56	4271	408
57	4276	408
58	4281	408
59	4286	408
60	4291	408
61	4296	408
62	4301	408
63	4306	408
64	4311	408
65	4316	408
66	4321	408
67	4326	408
68	4331	408
69	4336	408
70	4341	408
71	4346	408
72	4351	408
73	4356	408
74	4361	408
75	4366	408
76	4371	408
77	4376	408
78	4381	408
79	4386	408
80	4391	408
81	4396	408
82	4401	408
83	4406	408
84	4411	408
85	4416	408
86	4421	408
87	4426	408
88	4431	408
89	4436	408
90	4441	408
91	4446	408
92	4451	408
93	4456	408
94	4461	408
95	4466	408
96	4471	408
97	4476	408
98	4481	408
99	4486	408
100	4491	408
101	4496	408
102	4501	408
103	4506	408
104	4511	408
105	4516	408
106	4521	408
107	4526	408
108	4531	408
109	4536	408
110	4541	408
111	4546	408
112	4551	408
113	4556	408
114	4561	408
115	4566	408
116	4571	408
117	4576	408
118	4581	408
119	4586	408
120	4591	408
121	4596	408
122	4601	408
123	4606	408
124	4611	408
125	4616	408
126	4621	408
127	4626	408
128	4631	408
129	4636	408
130	4641	408
131	4646	408
132	4651	408
133	4656	408
134	4661	408
135	4666	408
136	4671	408
137	4676	408
138	4681	408
139	4686	408
140	4691	408
141	4696	408
142	4701	408
143	4706	408
144	4711	408
145	4716	408
146	4721	408
147	4726	408
148	4731	408
149	4736	408
150	4741	408
151	4746	408
152	4751	408
153	4756	408
154	4761	408
155	4766	408
156	4771	408
157	4776	408
158	4781	408
159	4786	408
160	4791	408
161	4796	408
162	4801	408
163	4806	408
164	4811	408
165	4816	408
166	4821	408
167	4826	408
168	4831	408
169	4836	408
170	4841	408
171	4846	408
172	4851	408
173	4856	408
174	4861	408
175	4866	408
176	4871	408
177	4876	408
178	4881	408
179	4886	408
180	4891	408
181	4896	408
182	4901	408
183	4906	408
184	4911	408
185	4916	408
186	4921	408
187	4926	408
188	4931	408
189	4936	408
190	4941	408
191	4946	408
192	4951	408
193	4956	408
194	4961	408
195	4966	408
196	4971	408
197	4976	408
198	4981	408
199	4986	408
200	4991	408
201	4996	408
done	5000	408

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.1b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 88

Calls

4 calls:

27.0ms	(* (+ z 6.012459259764103) z)
33.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
67.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
57.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series396.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (+ z 6.012459259764103) z)
71.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
64.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
190.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.5s

Counts

100 → 100

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	192	29980
1	557	26219
2	2949	25659
done	5000	25499

prune587.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

7.9b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 150

Calls

4 calls:

180.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
26.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
54.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
75.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
63.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
154.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify3.4s

Counts

162 → 162

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	258	84739
1	742	79661
2	3895	77730
done	5001	77050

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize104.0ms

Local error

Found 4 expressions with local error:

14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

12.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
396.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
67.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
54.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
135.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	155	42743
1	365	39052
2	1442	38564
done	5000	38204

prune858.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize97.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`times-frac` `sqrt-prod`
15×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`
1×	`associate-*r/`

Counts

4 → 105

Calls

4 calls:

73.0ms	(/ (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
22.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
24.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
78.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
55.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
50.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
148.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.8s

Counts

117 → 117

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	219	56980
1	556	52245
2	2538	50639
done	5001	50319

prune905.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes293.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.6b

bsearch222.0ms

Steps

Iters	Range		Point
7	261980.93535209994	64260609.3427585	696494.0227427928
6	-3.0211995487281625e+33	-3.273789768584435e+32	-3.353776223874111e+32

simplify23.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	36	1072
1	54	1072
done	54	1072

end0.0ms

sample1.1s

Algorithm

intervals

Results

868.0ms

8000×

body

valid