Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	63×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
done	6	6

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: 23.3b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

21.8b

(sqrt (+ (* x x) y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

4.0ms

(sqrt (+ (* x x) y))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(sqrt (+ (* x x) y))

simplify18.2s

Counts

18 → 18

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	7	15
1	8	15
done	8	15
0	6	7
1	7	7
done	7	7
0	7	20
1	9	12
2	20	8
3	29	8
4	35	8
5	45	8
6	66	8
7	129	8
8	345	8
9	1263	8
done	5000	8
0	7	14
1	9	7
done	9	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	2	2
1	4	1
done	4	1
0	5	6
1	6	6
done	6	6
0	8	10
1	24	10
2	48	8
3	84	8
4	175	8
5	463	8
6	1477	8
done	5001	8
0	9	18
1	23	16
2	48	14
3	86	12
4	139	12
5	238	12
6	486	12
7	1217	12
8	4797	12
done	5000	12
0	7	12
1	16	12
2	27	10
3	51	8
4	99	8
5	189	8
6	350	8
7	832	8
8	3577	8
done	5001	8
0	5	6
1	7	6
2	8	6
done	8	6
0	3	3
1	6	1
done	6	1
0	6	7
1	7	7
done	7	7
0	6	7
1	7	7
done	7	7
0	15	19
1	40	19
2	108	19
3	190	17
4	316	17
5	647	17
6	1756	17
done	5000	17
0	6	7
1	10	7
2	13	7
3	17	7
4	18	7
done	18	7
0	7	8
1	14	8
2	28	7
3	42	7
4	53	7
5	56	7
done	56	7

prune29.0ms

Filtered

15 candidates to 18 candidates (-20.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Merged error: 0b

Counts

19 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/2 (/ y x)) x)
0.0b	(* 1/2 (/ y x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

6.0ms	(+ (* 1/2 (/ y x)) x)
11.0ms	(* 1/2 (/ y x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+ (* 1/2 (/ y x)) x)
4.0ms	(* 1/2 (/ y x))

simplify48.1s

Counts

49 → 49

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	8	8
1	13	8
2	20	8
3	29	8
4	35	8
5	45	8
6	52	8
7	64	8
8	87	8
9	101	8
10	107	8
done	107	8
0	7	7
1	11	7
2	17	7
3	26	7
4	36	7
5	45	7
6	50	7
7	59	7
8	76	7
9	95	7
10	103	7
done	103	7
0	6	6
1	12	6
2	21	6
3	35	6
4	55	6
5	69	6
6	81	6
7	99	6
8	115	6
9	122	6
10	139	6
11	141	6
done	141	6
0	6	6
1	11	6
2	20	6
3	36	5
4	70	5
5	145	5
6	339	5
7	1392	5
done	5000	5
0	11	17
1	28	13
2	96	9
3	348	7
4	1090	7
5	3073	7
done	5001	7
0	9	17
1	24	13
2	63	7
3	184	7
4	571	7
5	1584	7
6	3639	7
done	5000	7
0	7	13
1	10	13
2	13	13
3	17	13
4	18	13
done	18	13
0	6	6
1	9	6
2	12	6
3	16	6
4	17	6
done	17	6
0	7	17
1	21	15
2	73	7
3	271	7
4	828	7
5	2501	7
6	4539	7
done	5001	7
0	6	6
1	9	6
2	12	6
3	16	6
4	17	6
done	17	6
0	6	6
1	9	6
2	12	6
3	16	6
4	17	6
done	17	6
0	7	7
1	8	7
done	8	7
0	7	7
1	8	7
done	8	7
0	8	8
1	11	8
2	14	8
3	18	8
4	19	8
done	19	8
0	8	8
1	11	8
2	14	8
3	18	8
4	19	8
done	19	8
0	7	11
1	10	11
2	12	11
done	12	11
0	6	6
1	7	6
done	7	6
0	9	13
1	18	13
2	47	13
3	86	13
4	142	13
5	158	13
done	158	13
0	8	10
1	13	10
2	23	10
3	38	10
4	51	10
5	53	10
done	53	10
0	7	9
1	14	7
2	32	7
3	69	7
4	93	7
done	93	7
0	8	10
1	13	10
2	24	10
3	38	10
4	50	10
done	50	10
0	7	7
1	10	7
2	13	7
3	17	7
4	18	7
done	18	7
0	6	6
1	11	4
2	19	4
3	28	4
done	28	4
0	7	9
1	14	7
2	22	7
3	26	7
4	31	7
5	44	7
6	56	7
7	61	7
done	61	7
0	6	6
1	11	4
2	13	4
done	13	4
0	4	5
1	9	1
done	9	1
0	3	3
1	6	1
done	6	1
0	3	3
1	4	3
done	4	3
0	6	6
1	9	6
2	12	6
3	16	6
4	17	6
done	17	6
0	6	6
1	9	6
2	12	6
3	16	6
4	17	6
done	17	6
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	3	3
1	4	3
done	4	3
0	8	9
1	16	8
2	26	8
3	46	8
4	92	8
5	205	8
6	509	8
7	1950	8
done	5000	8
0	7	8
1	11	8
2	14	8
3	18	8
4	19	8
done	19	8
0	7	8
1	14	8
2	22	8
3	35	8
4	59	8
5	114	8
6	261	8
7	676	8
8	2548	8
done	5000	8
0	8	17
1	12	17
2	15	17
3	19	17
4	20	17
done	20	17
0	7	8
1	11	8
2	14	8
3	18	8
4	19	8
done	19	8
0	8	23
1	25	23
2	84	9
3	315	9
4	1118	9
5	3605	9
done	5000	9
0	7	8
1	11	8
2	14	8
3	18	8
4	19	8
done	19	8
0	7	8
1	11	8
2	14	8
3	18	8
4	19	8
done	19	8
0	9	11
1	30	11
2	80	11
3	275	11
4	991	11
5	4187	11
done	5000	11
0	10	23
1	31	19
2	91	19
3	222	17
4	520	17
5	1197	15
6	4357	15
done	5001	15
0	8	15
1	24	13
2	59	13
3	127	13
4	314	13
5	633	13
6	867	13
7	1239	13
8	4226	13
done	5001	13
0	6	7
1	11	7
2	15	7
3	19	7
4	20	7
done	20	7
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	6	7
1	10	7
2	13	7
3	17	7
4	18	7
done	18	7
0	6	7
1	10	7
2	13	7
3	17	7
4	18	7
done	18	7
0	6	7
1	10	7
2	13	7
3	17	7
4	18	7
done	18	7

prune57.0ms

Filtered

37 candidates to 49 candidates (-32.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	49	3	52

Merged error: 0b

Counts

52 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* (/ y x) -1/2) x)
0.0b	(* (/ y x) -1/2)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

2 → 44

Calls

2 calls:

6.0ms	(- (* (/ y x) -1/2) x)
7.0ms	(* (/ y x) -1/2)

series10.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (* (/ y x) -1/2) x)
4.0ms	(* (/ y x) -1/2)

simplify42.7s

Counts

50 → 50

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	5
1	8	5
2	11	5
3	13	5
4	15	5
5	16	5
done	16	5
0	8	8
1	13	8
2	23	8
3	32	8
4	41	8
5	46	8
6	55	8
7	72	8
8	91	8
9	99	8
done	99	8
0	7	7
1	11	7
2	17	7
3	26	7
4	36	7
5	45	7
6	50	7
7	59	7
8	76	7
9	95	7
10	103	7
done	103	7
0	6	6
1	12	6
2	21	6
3	33	6
4	51	6
5	64	6
6	76	6
7	88	6
8	111	6
9	123	6
10	139	6
11	141	6
done	141	6
0	6	6
1	11	6
2	21	6
3	32	6
4	51	6
5	103	6
6	226	6
7	605	6
8	2487	6
done	5001	6
0	11	17
1	28	13
2	96	9
3	361	7
4	1197	7
5	3185	7
done	5000	7
0	9	17
1	24	13
2	64	7
3	191	7
4	632	7
5	1689	7
6	3629	7
done	5000	7
0	7	13
1	10	13
2	13	13
3	15	13
4	17	13
5	18	13
done	18	13
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	7	17
1	21	15
2	73	7
3	291	7
4	835	7
5	2297	7
6	4413	7
done	5000	7
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	7	7
1	8	7
done	8	7
0	7	7
1	8	7
done	8	7
0	8	8
1	11	8
2	14	8
3	16	8
4	18	8
5	19	8
done	19	8
0	8	8
1	11	8
2	14	8
3	16	8
4	18	8
5	19	8
done	19	8
0	7	9
1	12	9
2	20	9
3	28	9
4	37	9
5	43	9
6	48	9
done	48	9
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	5	5
1	10	3
2	20	3
done	20	3
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	7	7
1	10	7
2	13	7
3	15	7
4	17	7
5	18	7
done	18	7
0	7	7
1	10	7
2	13	7
3	15	7
4	17	7
5	18	7
done	18	7
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	7	7
1	10	7
2	13	7
3	15	7
4	17	7
5	18	7
done	18	7
0	7	7
1	10	7
2	13	7
3	15	7
4	17	7
5	18	7
done	18	7
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	6	6
1	9	6
2	12	6
3	14	6
4	16	6
5	17	6
done	17	6
0	5	5
1	8	5
2	11	5
3	13	5
4	15	5
5	16	5
done	16	5
0	5	5
1	8	5
2	11	5
3	13	5
4	15	5
5	16	5
done	16	5
0	5	5
1	10	3
2	12	3
done	12	3
0	3	3
1	4	3
done	4	3
0	8	9
1	15	8
2	27	8
3	43	8
4	77	8
5	181	8
6	528	8
7	2099	8
done	5000	8
0	7	8
1	12	8
2	16	8
3	18	8
4	20	8
5	21	8
done	21	8
0	7	8
1	15	8
2	25	8
3	38	8
4	71	8
5	153	8
6	443	8
7	1224	8
8	4070	8
done	5000	8
0	8	17
1	13	17
2	17	17
3	19	17
4	21	17
5	22	17
done	22	17
0	7	8
1	12	8
2	16	8
3	18	8
4	20	8
5	21	8
done	21	8
0	8	23
1	14	23
2	32	9
3	109	9
4	419	9
5	1574	9
done	5000	9
0	7	8
1	12	8
2	16	8
3	18	8
4	20	8
5	21	8
done	21	8
0	7	8
1	12	8
2	16	8
3	18	8
4	20	8
5	21	8
done	21	8
0	9	11
1	31	11
2	94	11
3	311	11
4	1051	11
5	4270	11
done	5000	11
0	10	23
1	30	19
2	78	19
3	161	17
4	299	17
5	480	17
6	1275	15
done	5000	15
0	2	2
done	2	2
0	8	15
1	24	13
2	59	13
3	129	13
4	297	13
5	595	13
6	869	13
7	1242	13
8	4203	13
done	5001	13
0	6	7
1	10	7
2	13	7
3	15	7
4	17	7
5	18	7
done	18	7
0	2	2
done	2	2
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	7	8
1	14	8
2	28	7
3	42	7
4	53	7
5	56	7
done	56	7
0	7	8
1	14	8
2	28	7
3	42	7
4	53	7
5	56	7
done	56	7
0	7	8
1	14	8
2	28	7
3	42	7
4	53	7
5	56	7
done	56	7

prune55.0ms

Filtered

39 candidates to 50 candidates (-28.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	50	3	53

Merged error: 0b

Counts

53 → 3

regimes233.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.2b

bsearch27.0ms

Steps

Iters	Range		Point
9	1.425720447435824e+82	1.5930955846765611e+87	7.009825188869956e+86
7	-3.3260857371803445e+155	-4.8701329249536646e+153	-1.3422856710707495e+154

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	22	28
done	22	28

end0.0ms

sample629.0ms

Algorithm

intervals

Results

238.0ms	8000×	body	80	valid
78.0ms	2710×	body	80	nan

Details

sample22.0ms

simplify2.0ms

prune3.0ms

localize5.0ms

rewrite5.0ms

series6.0ms

simplify18.2s

prune29.0ms

localize5.0ms

rewrite18.0ms

series9.0ms

simplify48.1s

prune57.0ms

localize5.0ms

rewrite14.0ms

series10.0ms

simplify42.7s

prune55.0ms

regimes233.0ms

bsearch27.0ms

simplify3.0ms

end0.0ms

sample629.0ms

Profiling