Details

sample32.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify45.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	35	21
2	64	21
3	145	21
4	350	21
5	736	21
6	1037	21
7	1273	21
8	1504	21
9	1876	21
10	2604	21
11	3382	21
12	4156	21
13	4163	21
14	4168	21
15	4173	21
16	4178	21
17	4183	21
18	4188	21
19	4193	21
20	4198	21
21	4203	21
22	4208	21
23	4213	21
24	4218	21
25	4223	21
26	4228	21
27	4233	21
28	4238	21
29	4243	21
30	4248	21
31	4253	21
32	4258	21
33	4263	21
34	4268	21
35	4273	21
36	4278	21
37	4283	21
38	4288	21
39	4293	21
40	4298	21
41	4303	21
42	4308	21
43	4313	21
44	4318	21
45	4323	21
46	4328	21
47	4333	21
48	4338	21
49	4343	21
50	4348	21
51	4353	21
52	4358	21
53	4363	21
54	4368	21
55	4373	21
56	4378	21
57	4383	21
58	4388	21
59	4393	21
60	4398	21
61	4403	21
62	4408	21
63	4413	21
64	4418	21
65	4423	21
66	4428	21
67	4433	21
68	4438	21
69	4443	21
70	4448	21
71	4453	21
72	4458	21
73	4463	21
74	4468	21
75	4473	21
76	4478	21
77	4483	21
78	4488	21
79	4493	21
80	4498	21
81	4503	21
82	4508	21
83	4513	21
84	4518	21
85	4523	21
86	4528	21
87	4533	21
88	4538	21
89	4543	21
90	4548	21
91	4553	21
92	4558	21
93	4563	21
94	4568	21
95	4573	21
96	4578	21
97	4583	21
98	4588	21
99	4593	21
100	4598	21
101	4603	21
102	4608	21
103	4613	21
104	4618	21
105	4623	21
106	4628	21
107	4633	21
108	4638	21
109	4643	21
110	4648	21
111	4653	21
112	4658	21
113	4663	21
114	4668	21
115	4673	21
116	4678	21
117	4683	21
118	4688	21
119	4693	21
120	4698	21
121	4703	21
122	4708	21
123	4713	21
124	4718	21
125	4723	21
126	4728	21
127	4733	21
128	4738	21
129	4743	21
130	4748	21
131	4753	21
132	4758	21
133	4763	21
134	4768	21
135	4773	21
136	4778	21
137	4783	21
138	4788	21
139	4793	21
140	4798	21
141	4803	21
142	4808	21
143	4813	21
144	4818	21
145	4823	21
146	4828	21
147	4833	21
148	4838	21
149	4843	21
150	4848	21
151	4853	21
152	4858	21
153	4863	21
154	4868	21
155	4873	21
156	4878	21
157	4883	21
158	4888	21
159	4893	21
160	4898	21
161	4903	21
162	4908	21
163	4913	21
164	4918	21
165	4923	21
166	4928	21
167	4933	21
168	4938	21
169	4943	21
170	4948	21
171	4953	21
172	4958	21
173	4963	21
174	4968	21
175	4973	21
176	4978	21
177	4983	21
178	4988	21
179	4993	21
180	4998	21
done	5000	21

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.7b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.2b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

14.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
44.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
74.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
62.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series343.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
69.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
68.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
171.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.5s

Counts

90 → 90

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	173	1478
1	501	1446
2	2555	1268
done	5001	1258

prune381.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.2b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-*r/` `clear-num` `sum-log`

Counts

4 → 96

Calls

4 calls:

9.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
28.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
98.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
73.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series393.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
101.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
175.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
70.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.2s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	192	2166
1	523	2136
2	2341	1914
done	5000	1910

prune520.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
0.3b	(* (* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
36×	`associate-r`
32×	`sqrt-prod`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-/r/`
6×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
5×	`sqrt-div`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
3×	`unswap-sqr`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 134

Calls

4 calls:

118.0ms	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
214.0ms	(* (* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
86.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
92.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series923.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
456.0ms	(* (* y (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (sqrt (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
85.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
99.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.1s

Counts

146 → 146

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	229	4560
1	600	4038
2	2967	3648
done	5002	3620

prune871.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.2b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.2b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.3b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite430.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

234.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
34.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
33.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
115.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
87.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
74.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
196.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.3s

Counts

162 → 162

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	258	4914
1	742	4689
2	3859	4195
done	5000	4141

prune736.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes176.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.5b

bsearch208.0ms

Steps

Iters	Range		Point
9	7337.051904760935	9334432389.324938	646280.956370811
8	-1.0383637353396325e+34	-1.2103392472203764e+30	-2.2225531905367537e+30

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	36	69
1	53	51
done	53	51

end0.0ms

sample1.2s

Algorithm

intervals

Results

853.0ms

8000×

body

valid