Details

sample32.0ms

Algorithm

intervals

Results

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

simplify3.9s

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	163	13
7	213	13
8	256	13
9	337	13
10	397	13
11	465	13
12	508	13
13	551	13
14	611	13
15	644	13
16	678	13
17	738	13
18	771	13
19	805	13
20	865	13
21	898	13
22	932	13
23	992	13
24	1025	13
25	1059	13
26	1119	13
27	1152	13
28	1186	13
29	1246	13
30	1279	13
31	1313	13
32	1373	13
33	1406	13
34	1440	13
35	1500	13
36	1533	13
37	1567	13
38	1627	13
39	1660	13
40	1694	13
41	1754	13
42	1787	13
43	1821	13
44	1881	13
45	1914	13
46	1948	13
47	2008	13
48	2041	13
49	2075	13
50	2135	13
51	2168	13
52	2202	13
53	2262	13
54	2295	13
55	2329	13
56	2389	13
57	2422	13
58	2456	13
59	2516	13
60	2549	13
61	2583	13
62	2643	13
63	2676	13
64	2710	13
65	2770	13
66	2803	13
67	2837	13
68	2897	13
69	2930	13
70	2964	13
71	3024	13
72	3057	13
73	3091	13
74	3151	13
75	3184	13
76	3218	13
77	3278	13
78	3311	13
79	3345	13
80	3405	13
81	3438	13
82	3472	13
83	3532	13
84	3565	13
85	3599	13
86	3659	13
87	3692	13
88	3726	13
89	3786	13
90	3819	13
91	3853	13
92	3913	13
93	3946	13
94	3980	13
95	4040	13
96	4073	13
97	4107	13
98	4167	13
99	4200	13
100	4234	13
101	4294	13
102	4327	13
103	4361	13
104	4421	13
105	4454	13
106	4488	13
107	4548	13
108	4581	13
109	4615	13
110	4675	13
111	4708	13
112	4742	13
113	4802	13
114	4835	13
115	4869	13
116	4929	13
117	4962	13
118	4996	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)

rewrite32.0ms

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)

series24.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify724.0ms

Counts

71 → 71

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	124	1134
1	321	1074
2	867	1014
3	2928	1006
done	5000	1005

prune127.0ms

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)

rewrite64.0ms

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:

28.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
11.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series39.0ms

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

simplify971.0ms

Counts

123 → 123

Iterations

Useful iterations: 3 (412.0ms)

Iter	Nodes	Cost
0	193	1936
1	460	1814
2	1405	1730
3	4747	1698
done	5000	1698

prune190.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	129	6	135

Merged error: 3.2b

Counts

135 → 6

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)

rewrite61.0ms

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)
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series72.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify514.0ms

Counts

73 → 73

Iterations

Useful iterations: done (512.0ms)

Iter	Nodes	Cost
0	123	1336
1	268	1308
2	656	1180
3	1731	1139
done	5000	1106

prune202.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 3.2b

Counts

79 → 6

localize20.0ms

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)

rewrite61.0ms

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:

14.0ms	(- (/ 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)
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series53.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify626.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	59	1172
1	131	1160
2	299	1040
3	759	1008
4	2252	1008
done	5000	1008

prune244.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 3.2b

Counts

78 → 6

regimes117.0ms

Accuracy

78.1% (2.8b remaining)

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

bsearch13.0ms

Steps

Iters	Range		Point
6	7170427078.972401	99835565477.3547	18187930964.32793

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	44
1	33	44
done	33	44

end0.0ms

sample888.0ms

Algorithm

intervals

Results

210.0ms	5836×	body	80	valid
140.0ms	8000×	pre	80	true
140.0ms	854×	body	1280	valid
95.0ms	702×	body	640	valid
37.0ms	376×	body	320	valid
15.0ms	232×	body	160	valid

Details

sample32.0ms

simplify3.9s

prune3.0ms

localize8.0ms

rewrite32.0ms

series24.0ms

simplify724.0ms

prune127.0ms

localize10.0ms

rewrite64.0ms

series39.0ms

simplify971.0ms

prune190.0ms

localize14.0ms

rewrite61.0ms

series72.0ms

simplify514.0ms

prune202.0ms

localize20.0ms

rewrite61.0ms

series53.0ms

simplify626.0ms

prune244.0ms

regimes117.0ms

bsearch13.0ms

simplify3.0ms

end0.0ms

sample888.0ms

Profiling