Details

sample113.0ms

Algorithm

intervals

Results

34.0ms	25×	body	2560	valid
26.0ms	194×	body	80	valid
12.0ms	19×	body	1280	valid
12.0ms	256×	pre	80	true
4.0ms	10×	body	640	valid
3.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid

simplify6.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
59	2004
58	1998
57	1980
56	1947
55	1929
54	1896
53	1878
52	1845
51	1827
50	1794
49	1776
48	1743
47	1725
46	1692
45	1674
44	1641
43	1623
42	1590
41	1572
40	1539
39	1521
38	1488
37	1470
36	1437
35	1419
34	1386
33	1368
32	1335
31	1317
30	1284
29	1266
28	1233
27	1215
26	1182
25	1164
24	1131
23	1113
22	1080
21	1062
20	1029
19	1011
18	978
17	960
16	927
15	909
14	876
13	858
12	825
11	786
10	745
9	598
8	441
7	301
6	200
5	145
4	104
3	76
2	51
1	29
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
0.0b	(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
0.2b	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
17.0b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
87×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
45×	`sqrt-prod`
22×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
5×	`associate-/r/` `div-inv`
4×	`sqrt-div` `insert-posit16`
3×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `distribute-lft1-in` `sqrt-pow1` `distribute-rgt-out` `pow1/2` `distribute-lft-out`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg`

Counts

4 → 157

Calls

4 calls:

34.0ms	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
14.0ms	(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
32.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
85.0ms	(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
79.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
47.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	2001
3	2001
2	1781
1	641
0	261

prune540.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 13.0b

localize31.0ms

Local error

Found 4 expressions with local error:

17.0b	(sqrt (+ (* x x) (* p (* 4 p))))
17.0b	(sqrt (+ (* x x) (* p (* 4 p))))
17.0b	(sqrt (+ (* x x) (* p (* 4 p))))
19.6b	(cbrt (* (* (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
5×	`frac-times` `associate-*l/`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 66

Calls

4 calls:

6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
7.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
66.0ms	(cbrt (* (* (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
45.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
44.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
88.0ms	(cbrt (* (* (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))))

simplify852.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2016
4	2016
3	1419
2	397
1	157
0	80

prune327.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 13.0b

regimes46.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

950.0ms	6023×	body	80	valid
467.0ms	760×	body	2560	valid
357.0ms	622×	body	1280	valid
257.0ms	8000×	pre	80	true
109.0ms	312×	body	640	valid
82.0ms	64×	body	5120	valid
39.0ms	150×	body	320	valid
12.0ms	69×	body	160	valid