Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	27×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify9.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	121	13
6	153	13
7	198	13
8	246	13
9	311	13
10	412	13
11	468	13
12	501	13
13	550	13
14	584	13
15	628	13
16	660	13
17	705	13
18	735	13
19	780	13
20	807	13
21	850	13
22	879	13
23	922	13
24	951	13
25	994	13
26	1023	13
27	1068	13
28	1099	13
29	1142	13
30	1170	13
31	1215	13
32	1245	13
33	1288	13
34	1316	13
35	1361	13
36	1392	13
37	1435	13
38	1463	13
39	1506	13
40	1535	13
41	1580	13
42	1610	13
43	1655	13
44	1686	13
45	1731	13
46	1762	13
47	1807	13
48	1833	13
49	1876	13
50	1901	13
51	1944	13
52	1973	13
53	2016	13
54	2046	13
55	2091	13
56	2122	13
57	2169	13
58	2202	13
59	2249	13
60	2277	13
61	2320	13
62	2347	13
63	2390	13
64	2419	13
65	2464	13
66	2496	13
67	2543	13
68	2576	13
69	2625	13
70	2653	13
71	2698	13
72	2730	13
73	2777	13
74	2812	13
75	2861	13
76	2894	13
77	2941	13
78	2974	13
79	3021	13
80	3054	13
81	3099	13
82	3127	13
83	3170	13
84	3196	13
85	3239	13
86	3267	13
87	3310	13
88	3339	13
89	3382	13
90	3409	13
91	3452	13
92	3482	13
93	3527	13
94	3558	13
95	3605	13
96	3640	13
97	3687	13
98	3718	13
99	3763	13
100	3795	13
101	3842	13
102	3877	13
103	3928	13
104	3963	13
105	4010	13
106	4042	13
107	4089	13
108	4117	13
109	4160	13
110	4187	13
111	4230	13
112	4260	13
113	4303	13
114	4330	13
115	4373	13
116	4404	13
117	4449	13
118	4481	13
119	4528	13
120	4561	13
121	4606	13
122	4637	13
123	4680	13
124	4710	13
125	4755	13
126	4786	13
127	4831	13
128	4859	13
129	4904	13
130	4933	13
131	4978	13
done	5000	13

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
19.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series28.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
20.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify707.0ms

Counts

71 → 71

Iterations

Useful iterations: done (705.0ms)

Iter	Nodes	Cost
0	124	1134
1	321	1074
2	867	1014
3	2641	1006
done	5001	1005

prune136.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 16.2b

Counts

72 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

29.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
9.0ms	(/ alpha (+ (+ alpha beta) 2.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series44.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

123 → 123

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	193	1936
1	460	1819
2	1278	1736
3	4162	1700
done	5001	1698

prune201.0ms

Filtered

87 candidates to 123 candidates (-41.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Merged error: 3.2b

Counts

135 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

13.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series75.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify502.0ms

Counts

73 → 73

Iterations

Useful iterations: done (500.0ms)

Iter	Nodes	Cost
0	123	1336
1	268	1308
2	658	1183
3	1748	1142
done	5000	1116

prune216.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Merged error: 3.2b

Counts

80 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
8×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `times-frac` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify649.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	59	1172
1	131	1160
2	301	1040
3	746	1008
4	2263	1008
done	5000	1008

prune254.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	72	7	79

Merged error: 3.2b

Counts

79 → 7

regimes129.0ms

Accuracy

78.1% (2.8b remaining)

Error of 5.9b against oracle of 3.1b and baseline of 15.8b

bsearch14.0ms

Steps

Iters	Range		Point
6	7170427078.972401	99835565477.3547	18187930964.32793

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	44
1	37	44
done	37	44

end0.0ms

sample919.0ms

Algorithm

intervals

Results

221.0ms	5836×	body	80	valid
153.0ms	854×	body	1280	valid
132.0ms	8000×	pre	80	true
99.0ms	702×	body	640	valid
39.0ms	376×	body	320	valid
20.0ms	232×	body	160	valid

Details

sample33.0ms

simplify9.2s

prune3.0ms

localize8.0ms

rewrite33.0ms

series28.0ms

simplify707.0ms

prune136.0ms

localize10.0ms

rewrite65.0ms

series44.0ms

simplify1.0s

prune201.0ms

localize14.0ms

rewrite64.0ms

series75.0ms

simplify502.0ms

prune216.0ms

localize18.0ms

rewrite66.0ms

series50.0ms

simplify649.0ms

prune254.0ms

regimes129.0ms

bsearch14.0ms

simplify3.0ms

end0.0ms

sample919.0ms

Profiling