Details

sample28.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	47	15
3	86	15
4	166	15
5	291	15
6	520	15
7	870	15
8	2670	15
done	5000	15

prune9.0ms

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: 22.8b

Counts

2 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

22.5b

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `flip3-+` `flip-+`
3×	`add-sqr-sqrt` `add-cube-cbrt` `flip3--` `-un-lft-identity` `times-frac` `associate-/r` `flip--`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`pow1` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

13.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.5min

Counts

34 → 34

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	18
1	21	18
2	29	18
3	35	18
4	41	18
5	50	18
6	63	18
7	81	18
8	97	18
9	104	18
10	121	18
11	123	18
done	123	18
0	11	17
1	27	17
2	51	17
3	81	17
4	127	17
5	199	17
6	302	17
7	494	17
8	1534	17
9	4802	17
done	5000	17
0	10	16
1	26	16
2	59	16
3	114	16
4	210	16
5	345	16
6	586	16
7	958	16
8	2782	16
done	5000	16
0	10	16
1	23	16
2	48	16
3	92	16
4	192	16
5	361	16
6	738	16
7	1678	16
done	5001	16
0	15	47
1	58	47
2	271	21
3	1205	21
done	5000	21
0	13	47
1	54	47
2	279	19
3	1463	17
done	5000	17
0	11	33
1	24	33
2	49	33
3	88	33
4	168	33
5	293	33
6	522	33
7	869	33
8	2680	33
done	5000	33
0	10	16
1	23	16
2	48	16
3	87	16
4	168	16
5	293	16
6	522	16
7	872	16
8	2667	16
done	5001	16
0	11	47
1	31	47
2	105	17
3	515	17
4	3575	17
done	5000	17
0	10	16
1	23	16
2	48	16
3	87	16
4	168	16
5	293	16
6	522	16
7	872	16
8	2667	16
done	5001	16
0	10	16
1	23	16
2	48	16
3	87	16
4	168	16
5	293	16
6	522	16
7	872	16
8	2667	16
done	5001	16
0	6	8
1	20	8
2	57	8
3	127	8
4	233	7
5	408	7
6	680	7
7	1221	7
8	3342	7
done	5000	7
0	6	8
1	10	8
2	18	8
3	19	8
done	19	8
0	9	21
1	17	21
2	25	21
3	30	21
4	33	21
done	33	21
0	8	12
1	10	12
done	10	12
0	8	12
1	14	12
2	17	12
3	19	12
done	19	12
0	8	12
1	10	12
done	10	12
0	5	5
1	12	3
2	17	3
done	17	3
0	7	11
1	9	11
done	9	11
0	7	9
1	10	9
done	10	9
0	9	15
1	22	15
2	42	15
3	63	15
4	107	15
5	173	15
6	267	15
7	446	15
8	1469	15
9	4779	15
done	5000	15
0	11	25
1	29	25
2	67	25
3	131	25
4	268	25
5	472	25
6	858	25
7	1429	25
8	4138	25
done	5000	25
0	10	16
1	23	16
2	48	16
3	87	16
4	168	16
5	293	16
6	522	16
7	872	16
8	2667	16
done	5000	16
0	7	9
1	21	7
2	51	7
3	100	7
4	190	7
5	278	7
6	465	7
7	716	7
8	1770	7
9	4870	7
done	5000	7
0	7	11
1	9	11
done	9	11
0	12	19
1	42	19
2	104	15
3	198	15
4	424	15
5	974	15
6	2830	15
done	5000	15
0	11	23
1	36	23
2	90	19
3	252	15
4	938	9
5	2951	9
done	5000	9
0	12	31
1	35	27
2	152	27
3	744	27
4	3674	27
done	5000	27
0	11	23
1	24	21
2	84	21
3	392	21
4	1451	21
done	5001	21
0	11	23
1	30	21
2	121	21
3	446	21
4	1714	21
done	5001	21
0	9	15
1	17	15
2	60	15
3	224	15
4	591	15
5	1726	15
done	5001	15
0	9	19
1	24	17
2	78	17
3	227	17
4	597	17
5	1282	17
6	2555	17
done	5002	17
0	7	11
1	11	11
2	26	11
3	63	11
4	133	11
5	202	11
6	283	11
7	418	11
8	767	11
9	1576	11
10	3167	11
done	5000	11
0	9	19
1	23	17
2	74	17
3	212	17
4	485	17
5	915	17
6	1390	17
7	1723	17
8	2116	17
9	3504	17
done	5001	17
0	7	11
1	16	11
2	41	11
3	78	11
4	125	11
5	147	11
6	167	11
7	208	11
8	316	11
9	722	11
10	2542	11
done	5000	11
0	1	1
done	1	1
0	1	1
1	3	1
done	3	1
0	1	1
1	3	1
done	3	1

prune52.0ms

Filtered

32 candidates to 34 candidates (-6.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Merged error: 1.1b

Counts

35 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts: 0 → 0

prune5.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Merged error: 1.1b

Counts

4 → 4

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
21.8b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
18×	`associate-r`
9×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`associate-l`
4×	`pow1` `associate-/r/` `associate-/l*`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 78

Calls

2 calls:

16.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
8.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series21.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
9.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify2.0min

Counts

84 → 84

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	14	13
done	14	13
0	8	12
1	13	12
2	15	12
3	16	12
done	16	12
0	8	12
1	10	12
done	10	12
0	11	35
1	46	35
2	156	15
3	432	13
4	1209	13
5	3286	13
done	5000	13
0	9	25
1	11	25
done	11	25
0	8	12
1	10	12
done	10	12
0	9	35
1	18	35
2	50	13
3	122	13
4	315	13
5	709	13
6	1632	13
7	4368	13
done	5000	13
0	8	12
1	10	12
done	10	12
0	8	12
1	10	12
done	10	12
0	4	4
1	8	4
2	10	4
3	11	4
done	11	4
0	6	8
1	10	8
2	18	8
3	19	8
done	19	8
0	11	27
1	19	27
2	28	27
3	34	27
done	34	27
0	9	13
1	11	13
done	11	13
0	10	18
1	14	18
2	16	18
3	17	18
done	17	18
0	9	13
1	11	13
done	11	13
0	7	11
1	12	9
2	18	9
3	23	9
done	23	9
0	8	12
1	10	12
done	10	12
0	10	22
1	14	22
done	14	22
0	9	13
1	11	13
done	11	13
0	9	13
1	11	13
done	11	13
0	9	13
1	11	13
done	11	13
0	6	6
1	9	4
2	11	4
done	11	4
0	8	12
1	10	12
done	10	12
0	9	19
1	14	19
done	14	19
0	8	12
1	10	12
done	10	12
0	8	10
1	11	10
done	11	10
0	8	12
1	10	12
done	10	12
0	2	3
1	4	1
done	4	1
0	7	11
1	9	11
done	9	11
0	9	19
1	14	19
done	14	19
0	8	12
1	10	12
done	10	12
0	8	10
1	11	10
done	11	10
0	8	12
1	10	12
done	10	12
0	2	3
1	4	1
done	4	1
0	7	11
1	9	11
done	9	11
0	7	9
1	10	9
done	10	9
0	7	11
1	9	11
done	9	11
0	9	21
1	13	21
done	13	21
0	8	12
1	10	12
done	10	12
0	5	5
1	8	3
2	10	3
done	10	3
0	8	12
1	10	12
done	10	12
0	8	12
1	10	12
done	10	12
0	7	11
1	9	11
done	9	11
0	7	11
1	9	11
done	9	11
0	10	15
1	29	15
2	66	11
3	121	11
4	263	11
5	695	11
6	2337	11
done	5000	11
0	9	19
1	23	19
2	43	15
3	92	11
4	225	11
5	596	11
6	1501	11
done	5000	11
0	9	19
1	24	17
2	78	17
3	227	17
4	597	17
5	1282	17
6	2555	17
done	5002	17
0	7	11
1	11	11
2	26	11
3	63	11
4	133	11
5	202	11
6	283	11
7	418	11
8	767	11
9	1576	11
10	3167	11
done	5000	11
0	9	15
1	16	15
2	34	15
3	72	15
4	125	15
5	203	15
6	345	15
7	609	15
8	1427	15
9	4670	15
done	5000	15
0	12	18
1	21	18
2	29	18
3	38	18
4	44	18
5	54	18
6	61	18
7	73	18
8	96	18
9	110	18
10	116	18
done	116	18
0	11	17
1	19	17
2	26	17
3	35	17
4	45	17
5	54	17
6	59	17
7	68	17
8	85	17
9	104	17
10	112	17
done	112	17
0	10	16
1	20	16
2	44	16
3	92	16
4	164	16
5	256	16
6	410	16
7	692	16
8	1520	16
9	4770	16
done	5000	16
0	10	16
1	19	16
2	48	16
3	102	16
4	213	16
5	427	16
6	923	16
7	2780	16
done	5001	16
0	15	47
1	58	47
2	233	21
3	965	19
4	4972	19
done	5000	19
0	13	47
1	30	47
2	108	19
3	415	19
4	2048	17
done	5001	17
0	11	33
1	18	33
2	36	33
3	74	33
4	127	33
5	203	33
6	343	33
7	610	33
8	1424	33
9	4684	33
done	5001	33
0	10	16
1	17	16
2	35	16
3	73	16
4	126	16
5	209	16
6	349	16
7	616	16
8	1431	16
9	4698	16
done	5000	16
0	11	47
1	28	47
2	113	17
3	576	17
4	2717	17
done	5000	17
0	10	16
1	17	16
2	35	16
3	73	16
4	126	16
5	209	16
6	349	16
7	616	16
8	1431	16
9	4698	16
done	5000	16
0	10	16
1	17	16
2	35	16
3	73	16
4	126	16
5	209	16
6	349	16
7	616	16
8	1431	16
9	4698	16
done	5000	16
0	8	11
1	31	11
2	72	11
3	238	11
4	697	11
5	2328	11
done	5001	11
0	9	19
1	23	17
2	78	17
3	240	17
4	547	17
5	1034	17
6	1434	17
7	1653	17
8	2039	17
9	3436	17
done	5000	17
0	7	11
1	19	11
2	54	11
3	145	11
4	330	11
5	921	11
6	4155	11
done	5000	11
0	7	11
1	16	11
2	49	11
3	88	11
4	127	11
5	147	11
6	167	11
7	206	11
8	323	11
9	726	11
10	2561	11
done	5000	11
0	11	17
1	16	17
2	17	17
done	17	17
0	11	17
1	16	17
2	17	17
done	17	17
0	12	18
1	19	18
2	23	18
3	27	18
4	28	18
done	28	18
0	12	18
1	19	18
2	23	18
3	27	18
4	28	18
done	28	18
0	11	29
1	18	29
2	27	29
3	44	29
4	56	29
5	64	29
done	64	29
0	10	16
1	15	16
2	22	16
3	27	16
4	31	16
done	31	16
0	13	31
1	26	31
2	62	31
3	166	31
4	353	31
5	575	31
6	741	31
7	783	31
8	785	31
done	785	31
0	12	22
1	21	22
2	38	22
3	91	22
4	167	22
5	234	22
6	283	22
7	288	22
done	288	22
0	9	15
1	19	13
2	43	13
3	116	13
4	208	13
5	321	13
6	386	13
7	420	13
done	420	13
0	12	26
1	21	26
2	39	26
3	88	26
4	147	26
5	212	26
6	247	26
7	254	26
done	254	26
0	11	17
1	18	17
2	28	17
3	52	17
4	75	17
5	91	17
6	102	17
done	102	17
0	8	10
1	16	8
2	30	8
3	49	8
4	73	8
5	107	8
6	132	8
7	138	8
done	138	8
0	11	23
1	21	23
2	38	21
3	103	21
4	207	21
5	280	21
6	353	21
7	383	21
8	401	21
9	403	21
done	403	21
0	10	14
1	18	14
2	28	12
3	63	12
4	105	12
5	132	12
6	151	12
7	153	12
8	154	12
done	154	12
0	6	7
1	13	5
2	25	3
3	43	3
4	54	3
5	58	3
done	58	3
0	11	23
1	21	23
2	38	21
3	103	21
4	207	21
5	280	21
6	353	21
7	383	21
8	401	21
9	403	21
done	403	21
0	10	14
1	18	14
2	28	12
3	63	12
4	105	12
5	132	12
6	151	12
7	153	12
8	154	12
done	154	12
0	6	7
1	13	5
2	25	3
3	43	3
4	54	3
5	58	3
done	58	3
0	5	5
1	10	3
2	20	3
3	31	3
4	40	3
5	44	3
done	44	3
0	5	7
1	15	7
2	34	7
3	56	7
4	101	7
5	167	7
6	261	7
7	440	7
8	1436	7
9	4384	7
done	5000	7
0	12	19
1	36	19
2	91	15
3	184	15
4	379	15
5	889	15
6	2622	15
done	5001	15
0	11	23
1	30	23
2	74	19
3	218	15
4	763	9
5	2269	9
done	5000	9
0	10	16
1	17	16
2	29	16
3	33	16
4	42	16
5	44	16
6	50	16
7	54	16
8	60	16
9	62	16
done	62	16
0	10	16
1	17	16
2	29	16
3	33	16
4	42	16
5	44	16
6	50	16
7	54	16
8	60	16
9	62	16
done	62	16
0	9	15
1	16	15
2	34	15
3	72	15
4	125	15
5	203	15
6	345	15
7	609	15
8	1427	15
9	4670	15
done	5000	15
0	11	17
1	18	17
2	36	17
3	76	17
4	135	17
5	210	17
6	329	17
7	547	17
8	879	17
9	1365	17
10	1706	17
11	1833	17
12	1834	17
done	1834	17
0	9	15
1	16	15
2	34	15
3	72	15
4	125	15
5	203	15
6	345	15
7	609	15
8	1427	15
9	4670	15
done	5000	15
0	5	7
1	15	7
2	34	7
3	56	7
4	101	7
5	167	7
6	261	7
7	440	7
8	1436	7
9	4384	7
done	5000	7
0	12	19
1	30	19
2	69	19
3	197	19
4	688	19
5	2789	19
done	5000	19
0	9	19
1	18	19
2	45	19
3	144	19
4	379	19
5	780	19
6	2362	19
done	5000	19
0	1	1
done	1	1
0	1	1
done	1	1
0	1	1
done	1	1
0	1	1
done	1	1
0	1	1
1	3	1
done	3	1
0	1	1
1	3	1
done	3	1

prune75.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	84	4	88

Merged error: 1.1b

Counts

88 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts: 0 → 0

prune0.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Merged error: 1.1b

Counts

4 → 4

regimes144.0ms

Accuracy

77.6% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 21.6b

bsearch47.0ms

Steps

Iters	Range	Point
8	4.069757028539003e-168	3.930823303569919e-164	3.841202637489845e-164
9	-5.818553297753976e-161	-2.4680099843550082e-166	-2.0187795395447341e-162
7	-7.372936928343149e+154	-4.675996499956814e+152	-1.2614853870113369e+153

Iters

Range

Point

4.069757028539003e-168

3.930823303569919e-164

3.841202637489845e-164

-5.818553297753976e-161

-2.4680099843550082e-166

-2.0187795395447341e-162

-7.372936928343149e+154

-4.675996499956814e+152

-1.2614853870113369e+153

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	20	44
1	28	30
done	28	30

end0.0ms

sample787.0ms

Algorithm

intervals

Results

366.0ms	8000×	body	80	valid
168.0ms	8000×	pre	80	true

Details

sample28.0ms

simplify3.9s

prune9.0ms

localize10.0ms

rewrite14.0ms

series12.0ms

simplify1.5min

prune52.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune5.0ms

localize13.0ms

rewrite28.0ms

series21.0ms

simplify2.0min

prune75.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune0.0ms

regimes144.0ms

bsearch47.0ms

simplify2.0ms

end0.0ms

sample787.0ms

Profiling