Details

sample82.0ms

Algorithm

intervals

Results

19.0ms	35×	body	1280	valid
18.0ms	178×	body	80	valid
12.0ms	31×	body	640	valid
11.0ms	256×	pre	80	true
3.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.3s

Counts

1 → 1

Iterations

Iter	Nodes
95	824
94	824
93	820
92	818
91	812
90	807
89	805
88	798
87	795
86	789
85	786
84	780
83	777
82	771
81	768
80	762
79	759
78	753
77	750
76	744
75	741
74	735
73	732
72	726
71	723
70	717
69	714
68	708
67	705
66	699
65	696
64	690
63	687
62	681
61	678
60	672
59	669
58	663
57	660
56	654
55	651
54	645
53	642
52	636
51	633
50	627
49	624
48	618
47	615
46	609
45	606
44	600
43	597
42	591
41	588
40	582
39	579
38	573
37	570
36	564
35	561
34	555
33	552
32	546
31	543
30	537
29	534
28	528
27	525
26	519
25	516
24	510
23	507
22	501
21	498
20	492
19	489
18	483
17	480
16	474
15	471
14	466
13	455
12	442
11	411
10	350
9	254
8	189
7	164
6	140
5	112
4	69
3	50
2	33
1	20
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite178.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `insert-posit16` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 67

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
125.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series134.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify970.0ms

Counts

73 → 73

Iterations

Iter	Nodes
3	2968
2	956
1	328
0	126

prune688.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite600.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 115

Calls

4 calls:

414.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
29.0ms	(/ alpha (+ (+ alpha beta) 2.0))
22.0ms	(/ beta (+ (+ alpha beta) 2.0))
133.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series300.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
57.0ms	(/ alpha (+ (+ alpha beta) 2.0))
63.0ms	(/ beta (+ (+ alpha beta) 2.0))
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
3	4669
2	1259
1	454
0	197

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `times-frac` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

10.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
145.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series547.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ (+ alpha beta) 2.0))
168.0ms	(cbrt (+ (+ alpha beta) 2.0))
164.0ms	(cbrt (+ (+ alpha beta) 2.0))
84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify766.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2005
2	698
1	284
0	122

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

146×	`*-un-lft-identity`
119×	`add-sqr-sqrt` `times-frac`
81×	`sqrt-prod`
68×	`add-cube-cbrt`
42×	`distribute-lft-out`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`flip3-+` `cbrt-unprod` `flip-+` `insert-posit16` `div-inv`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 222

Calls

4 calls:

162.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
31.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
24.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
137.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series392.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
109.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
81.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
110.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify772.0ms

Counts

234 → 234

Iterations

Iter	Nodes
2	2030
1	785
0	292

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

regimes200.0ms

Accuracy

74.6% (3.3b remaining)

Error of 6.3b against oracle of 3.1b and baseline of 15.9b

bsearch82.0ms

Steps

Iters	Range		Point
8	2.0198517632767668e+31	2.8356818473805023e+35	2.0657930263664172e+31

simplify10.0ms

Iterations

Iter	Nodes
2	30
1	30
0	27

end0.0ms

sample2.5s

Algorithm

intervals

Results

836.0ms	852×	body	1280	valid
511.0ms	5818×	body	80	valid
413.0ms	8000×	pre	80	true
334.0ms	712×	body	640	valid
148.0ms	430×	body	320	valid
32.0ms	188×	body	160	valid

Iter	Nodes
95	824
94	824
93	820
92	818
91	812
90	807
89	805
88	798
87	795
86	789
85	786
84	780
83	777
82	771
81	768
80	762
79	759
78	753
77	750
76	744
75	741
74	735
73	732
72	726
71	723
70	717
69	714
68	708
67	705
66	699
65	696
64	690
63	687
62	681
61	678
60	672
59	669
58	663
57	660
56	654
55	651
54	645
53	642
52	636
51	633
50	627
49	624
48	618
47	615
46	609
45	606
44	600
43	597
42	591
41	588
40	582
39	579
38	573
37	570
36	564
35	561
34	555
33	552
32	546
31	543
30	537
29	534
28	528
27	525
26	519
25	516
24	510
23	507
22	501
21	498
20	492
19	489
18	483
17	480
16	474
15	471
14	466
13	455
12	442
11	411
10	350
9	254
8	189
7	164
6	140
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
95	824
94	824
93	820
92	818
91	812
90	807
89	805
88	798
87	795
86	789
85	786
84	780
83	777
82	771
81	768
80	762
79	759
78	753
77	750
76	744
75	741
74	735
73	732
72	726
71	723
70	717
69	714
68	708
67	705
66	699
65	696
64	690
63	687
62	681
61	678
60	672
59	669
58	663
57	660
56	654
55	651
54	645
53	642
52	636
51	633
50	627
49	624
48	618
47	615
46	609
45	606
44	600
43	597
42	591
41	588
40	582
39	579
38	573
37	570
36	564
35	561
34	555
33	552
32	546
31	543
30	537
29	534
28	528
27	525
26	519
25	516
24	510
23	507
22	501
21	498
20	492
19	489
18	483
17	480
16	474
15	471
14	466
13	455
12	442
11	411
10	350
9	254
8	189
7	164
6	140
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
95	824
94	824
93	820
92	818
91	812
90	807
89	805
88	798
87	795
86	789
85	786
84	780
83	777
82	771
81	768
80	762
79	759
78	753
77	750
76	744
75	741
74	735
73	732
72	726
71	723
70	717
69	714
68	708
67	705
66	699
65	696
64	690
63	687
62	681
61	678
60	672
59	669
58	663
57	660
56	654
55	651
54	645
53	642
52	636
51	633
50	627
49	624
48	618
47	615
46	609
45	606
44	600
43	597
42	591
41	588
40	582
39	579
38	573
37	570
36	564
35	561
34	555
33	552
32	546
31	543
30	537
29	534
28	528
27	525
26	519
25	516
24	510
23	507
22	501
21	498
20	492
19	489
18	483
17	480
16	474
15	471
14	466
13	455
12	442
11	411
10	350
9	254
8	189
7	164
6	140
5	112
4	69
3	50
2	33
1	20
0	10