Details

sample64.0ms

Algorithm

intervals

Results

21.0ms	364×	body	80	nan
13.0ms	314×	body	80	valid

simplify6.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	21	10
3	36	10
4	61	10
5	102	10
6	164	10
7	332	10
8	1616	10
done	5000	10

prune4.0ms

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: 27.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (sqrt (- (* y y) (* z z))))
2.6b	(- (* y y) (* z z))
26.6b	(sqrt (- (* y y) (* z z)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-l` `flip--` `difference-of-squares`
2×	`associate-*r/` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 54

Calls

3 calls:

8.0ms	(* x (sqrt (- (* y y) (* z z))))
5.0ms	(- (* y y) (* z z))
4.0ms	(sqrt (- (* y y) (* z z)))

series40.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* x (sqrt (- (* y y) (* z z))))
12.0ms	(- (* y y) (* z z))
8.0ms	(sqrt (- (* y y) (* z z)))

simplify4.7min

Counts

63 → 63

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	8	19
1	13	19
2	20	19
3	35	19
4	60	19
5	101	19
6	159	19
7	327	19
8	1602	19
done	5000	19
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	8	26
1	14	16
2	34	10
3	85	10
4	178	10
5	274	10
6	458	10
7	898	10
8	3735	10
done	5000	10
0	8	18
1	14	9
2	21	9
3	36	9
4	61	9
5	102	9
6	158	9
7	326	9
8	1613	9
done	5000	9
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	2	2
1	4	1
done	4	1
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	4	4
1	5	4
done	5	4
0	4	4
1	6	4
2	7	4
done	7	4
0	9	12
1	28	12
2	90	8
3	219	8
4	552	8
5	1963	8
done	5000	8
0	10	24
1	31	20
2	63	18
3	84	16
4	113	16
5	161	16
6	323	16
7	832	16
8	3018	16
done	5000	16
0	8	16
1	21	16
2	44	12
3	90	8
4	215	8
5	576	8
6	1483	8
done	5001	8
0	6	8
1	7	8
done	7	8
0	3	3
1	6	1
done	6	1
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	7	9
1	12	9
2	19	9
3	34	9
4	59	9
5	100	9
6	156	9
7	324	9
8	1653	9
done	5000	9
0	7	9
1	13	8
2	25	8
3	52	8
4	141	8
5	464	8
6	2518	8
done	5001	8
0	6	8
1	11	8
2	21	8
3	37	8
4	62	8
5	103	8
6	161	8
7	329	8
8	1610	8
done	5000	8
0	6	8
1	14	8
2	29	8
3	64	8
4	142	8
5	361	8
6	1304	8
done	5000	8
0	7	17
1	12	17
2	19	17
3	34	17
4	59	17
5	100	17
6	156	17
7	324	17
8	1653	17
done	5000	17
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	7	23
1	13	23
2	45	9
3	236	9
4	1272	9
done	5000	9
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	8	11
1	27	11
2	89	7
3	214	7
4	541	7
5	1943	7
done	5000	7
0	9	23
1	30	19
2	62	17
3	85	15
4	114	15
5	162	15
6	328	15
7	830	15
8	3018	15
done	5000	15
0	3	4
1	6	4
done	6	4
0	7	15
1	20	15
2	41	11
3	87	7
4	212	7
5	581	7
6	1497	7
done	5000	7
0	5	7
1	6	7
done	6	7
0	3	3
1	4	3
done	4	3
0	3	3
1	5	3
2	6	3
done	6	3
0	3	4
1	6	4
done	6	4
0	8	10
1	14	10
2	21	10
3	36	10
4	61	10
5	102	10
6	164	10
7	332	10
8	1616	10
done	5000	10
0	10	12
1	16	12
2	23	12
3	38	12
4	63	12
5	104	12
6	162	12
7	330	12
8	1618	12
done	5000	12
0	9	11
1	18	11
2	26	11
3	41	11
4	66	11
5	107	11
6	167	11
7	335	11
8	1621	11
done	5000	11
0	9	11
1	17	11
2	30	11
3	53	11
4	101	11
5	198	11
6	406	11
7	1045	11
8	4343	11
done	5000	11
0	12	32
1	24	22
2	75	14
3	300	14
4	1084	12
5	2730	12
done	5000	12
0	10	23
1	16	23
2	23	23
3	38	23
4	63	23
5	104	23
6	160	23
7	328	23
8	1625	23
done	5000	23
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	165	11
7	333	11
8	1613	11
done	5000	11
0	10	32
1	26	32
2	62	12
3	171	12
4	664	12
5	1835	12
6	3757	12
done	5000	12
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	165	11
7	333	11
8	1613	11
done	5000	11
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	165	11
7	333	11
8	1613	11
done	5000	11
0	10	12
1	16	12
2	23	12
3	38	12
4	63	12
5	104	12
6	162	12
7	330	12
8	1618	12
done	5000	12
0	10	12
1	16	12
2	23	12
3	38	12
4	63	12
5	104	12
6	162	12
7	330	12
8	1618	12
done	5000	12
0	10	12
1	16	12
2	23	12
3	38	12
4	63	12
5	104	12
6	162	12
7	330	12
8	1618	12
done	5000	12
0	10	12
1	16	12
2	23	12
3	38	12
4	63	12
5	104	12
6	162	12
7	330	12
8	1618	12
done	5000	12
0	10	21
1	18	21
2	27	21
3	42	21
4	67	21
5	108	21
6	168	21
7	336	21
8	1613	21
done	5000	21
0	10	20
1	17	11
2	24	11
3	39	11
4	64	11
5	105	11
6	161	11
7	329	11
8	1615	11
done	5000	11
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	165	11
7	333	11
8	1613	11
done	5000	11
0	4	4
1	7	3
done	7	3
0	6	6
1	8	6
done	8	6
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	165	11
7	333	11
8	1613	11
done	5000	11
0	3	3
1	6	1
done	6	1
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	167	11
7	335	11
8	1622	11
done	5000	11
0	9	11
1	15	11
2	22	11
3	37	11
4	62	11
5	103	11
6	167	11
7	335	11
8	1622	11
done	5000	11
0	8	10
1	14	10
2	21	10
3	36	10
4	61	10
5	102	10
6	164	10
7	332	10
8	1616	10
done	5000	10
0	11	14
1	31	14
2	93	10
3	222	10
4	541	10
5	1952	10
done	5000	10
0	10	18
1	24	18
2	43	14
3	89	10
4	214	10
5	581	10
6	1496	10
done	5000	10
0	5	5
1	9	4
done	9	4
0	1	1
done	1	1
0	3	3
1	5	2
done	5	2
0	6	7
1	16	7
2	46	7
3	57	7
4	81	7
5	123	7
6	204	7
7	380	7
8	963	7
9	4078	7
done	5000	7
0	6	7
1	16	7
2	46	7
3	57	7
4	81	7
5	123	7
6	204	7
7	380	7
8	963	7
9	4078	7
done	5000	7
0	6	7
1	16	7
2	46	7
3	57	7
4	81	7
5	123	7
6	204	7
7	380	7
8	963	7
9	4078	7
done	5000	7
0	1	1
done	1	1
0	3	3
1	4	3
done	4	3
0	5	5
1	10	4
2	22	4
done	22	4

prune84.0ms

Filtered

48 candidates to 63 candidates (-31.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Merged error: 0.2b

Counts

64 → 4

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts: 0 → 0

prune6.0ms

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: 0.2b

Counts

4 → 4

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts: 0 → 0

prune7.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0.2b

Counts

4 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- y z))
0.0b	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
0.3b	(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
22×	`add-sqr-sqrt`
18×	`sqrt-prod`
15×	`*-un-lft-identity`
13×	`pow1`
12×	`associate-*r/`
10×	`add-exp-log` `associate-l` `add-cbrt-cube`
9×	`add-cube-cbrt` `associate-r`
8×	`frac-times`
7×	`flip3--` `flip--`
6×	`flip3-+` `pow-prod-down` `flip-+`
4×	`associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`sqrt-pow1` `pow1/2` `add-log-exp`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-unprod` `distribute-lft-out`

Counts

3 → 84

Calls

3 calls:

4.0ms	(sqrt (- y z))
14.0ms	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
12.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

series53.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(sqrt (- y z))
25.0ms	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
14.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

simplify2.2min

Counts

93 → 93

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	9	7
2	24	7
3	52	7
4	93	7
5	146	7
6	211	7
7	323	7
8	942	7
9	3249	7
done	5000	7
0	7	9
1	11	9
2	12	9
done	12	9
0	5	7
1	9	7
2	24	7
3	52	7
4	93	7
5	146	7
6	211	7
7	323	7
8	942	7
9	3249	7
done	5000	7
0	9	11
1	13	11
2	14	11
done	14	11
0	8	10
1	15	10
2	17	10
done	17	10
0	8	10
1	14	10
2	21	10
3	29	10
4	52	10
5	108	10
6	254	10
7	716	10
8	2716	10
done	5000	10
0	11	29
1	21	17
2	69	13
3	234	13
4	614	11
5	1298	11
6	2771	11
done	5000	11
0	9	21
1	13	21
2	14	21
done	14	21
0	8	10
1	12	10
2	13	10
done	13	10
0	9	29
1	23	29
2	53	11
3	145	11
4	408	11
5	795	11
6	1507	11
7	3112	11
done	5001	11
0	5	7
1	9	7
2	24	7
3	52	7
4	93	7
5	146	7
6	211	7
7	323	7
8	942	7
9	3249	7
done	5000	7
0	8	10
1	12	10
2	13	10
done	13	10
0	8	10
1	12	10
2	13	10
done	13	10
0	10	17
1	27	17
2	49	17
3	83	17
4	173	17
5	505	17
6	2273	17
done	5000	17
0	12	25
1	26	21
2	48	21
3	64	21
4	85	21
5	106	21
6	129	21
7	155	21
8	207	21
9	288	21
10	318	21
11	333	21
12	334	21
done	334	21
0	12	17
1	30	17
2	46	17
3	78	17
4	144	17
5	302	17
6	792	17
7	2807	17
done	5000	17
0	11	17
1	21	15
2	36	15
3	49	15
4	69	15
5	90	15
6	107	15
7	130	15
8	173	15
9	235	15
10	236	15
done	236	15
0	12	17
1	31	17
2	58	17
3	103	17
4	217	17
5	592	17
6	2426	17
done	5000	17
0	11	17
1	21	15
2	30	15
3	31	15
4	32	15
done	32	15
0	7	17
1	12	7
2	20	7
3	35	7
4	60	7
5	101	7
6	157	7
7	325	7
8	1595	7
done	5000	7
0	7	9
1	11	9
2	12	9
done	12	9
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	11
1	13	11
2	14	11
done	14	11
0	9	16
1	15	16
2	18	16
done	18	16
0	9	15
1	14	10
2	15	10
done	15	10
0	8	10
1	12	10
2	13	10
done	13	10
0	7	7
1	11	6
done	11	6
0	9	11
1	12	11
done	12	11
0	7	7
1	11	6
done	11	6
0	8	10
1	12	10
2	13	10
done	13	10
0	6	6
1	10	4
2	13	4
done	13	4
0	8	10
1	12	10
2	13	10
done	13	10
0	8	10
1	12	10
2	13	10
done	13	10
0	8	10
1	12	10
2	13	10
done	13	10
0	7	9
1	11	9
2	12	9
done	12	9
0	7	9
1	11	9
2	12	9
done	12	9
0	8	10
1	12	10
2	13	10
done	13	10
0	7	9
1	11	9
2	12	9
done	12	9
0	10	13
1	27	13
2	49	13
3	83	13
4	167	13
5	501	13
6	2253	13
done	5000	13
0	9	13
1	15	13
2	21	13
3	36	13
4	61	13
5	102	13
6	160	13
7	328	13
8	1596	13
done	5000	13
0	10	13
1	27	13
2	37	13
3	54	13
4	95	13
5	213	13
6	630	13
7	2464	13
done	5000	13
0	9	13
1	16	13
2	28	13
3	53	13
4	81	13
5	134	13
6	283	13
7	1483	13
done	5001	13
0	9	11
1	16	11
2	23	11
3	25	11
done	25	11
0	9	11
1	16	11
2	23	11
3	25	11
done	25	11
0	12	14
1	19	14
2	26	14
done	26	14
0	11	13
1	19	13
2	25	13
3	29	13
done	29	13
0	10	12
1	20	12
2	34	12
3	46	12
4	48	12
done	48	12
0	10	12
1	19	12
2	34	12
3	59	12
4	116	12
5	253	12
6	620	12
7	1798	12
done	5000	12
0	15	35
1	31	23
2	120	17
3	602	17
4	2592	15
done	5000	15
0	13	35
1	33	35
2	102	15
3	445	15
4	2013	13
done	5002	13
0	11	25
1	18	25
2	25	25
3	27	25
done	27	25
0	10	12
1	17	12
2	24	12
done	24	12
0	11	35
1	28	35
2	100	13
3	417	13
4	1363	13
5	3987	13
done	5000	13
0	10	12
1	17	12
2	24	12
done	24	12
0	10	12
1	17	12
2	24	12
done	24	12
0	6	6
1	8	6
done	8	6
0	10	12
1	17	12
2	24	12
3	26	12
done	26	12
0	10	12
1	17	12
2	24	12
3	26	12
done	26	12
0	9	11
1	16	11
2	23	11
3	25	11
done	25	11
0	12	19
1	32	19
2	60	19
3	94	19
4	182	19
5	519	19
6	2325	19
done	5000	19
0	14	19
1	35	19
2	57	19
3	89	19
4	153	19
5	311	19
6	795	19
7	2807	19
done	5000	19
0	14	19
1	36	19
2	69	19
3	114	19
4	227	19
5	603	19
6	2426	19
done	5000	19
0	9	19
1	17	9
2	37	9
3	83	9
4	168	9
5	254	9
6	420	9
7	789	9
8	3457	9
done	5000	9
0	12	15
1	32	15
2	60	15
3	94	15
4	182	15
5	519	15
6	2315	15
done	5000	15
0	11	15
1	20	15
2	32	15
3	47	15
4	72	15
5	113	15
6	173	15
7	341	15
8	1587	15
done	5000	15
0	12	15
1	32	15
2	48	15
3	65	15
4	104	15
5	216	15
6	630	15
7	2466	15
done	5000	15
0	11	15
1	21	15
2	39	15
3	64	15
4	92	15
5	144	15
6	291	15
7	1431	15
done	5001	15
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	6	11
1	8	11
2	9	11
done	9	11
0	5	5
1	7	5
2	8	5
done	8	5
0	6	14
1	9	8
2	19	6
3	29	6
4	39	6
5	49	6
6	70	6
7	128	6
8	341	6
9	1259	6
done	5000	6
0	6	10
1	9	5
2	10	5
done	10	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	2	2
1	4	1
done	4	1
0	4	4
1	6	4
2	7	4
done	7	4
0	6	6
1	7	6
done	7	6
0	6	6
1	8	6
2	9	6
done	9	6
0	2	2
1	4	1
done	4	1
0	4	4
1	6	4
2	7	4
done	7	4
0	7	8
1	22	8
2	44	8
3	78	8
4	165	8
5	497	8
6	2266	8
done	5000	8
0	8	12
1	15	10
2	23	10
3	26	10
4	27	10
done	27	10
0	6	8
1	11	8
2	18	8
3	33	8
4	58	8
5	99	8
6	157	8
7	325	8
8	1570	8
done	5000	8
0	4	4
1	5	4
done	5	4
0	3	3
1	6	1
done	6	1
0	5	5
1	7	5
2	8	5
done	8	5
0	5	5
1	7	5
2	8	5
done	8	5
0	4	4
1	5	4
done	5	4
0	1	1
done	1	1
0	14	25
1	38	25
2	142	25
3	299	25
4	925	17
5	3521	17
done	5000	17
0	1	1
done	1	1
0	3	3
1	4	3
done	4	3
0	12	17
1	27	17
2	78	17
3	221	17
4	804	13
5	3185	13
done	5000	13
0	16	19
1	42	19
2	123	19
3	282	17
4	606	17
5	1356	15
6	4165	15
done	5001	15
0	14	19
1	39	19
2	115	19
3	325	19
4	1204	15
5	3877	15
done	5000	15
0	14	19
1	39	19
2	115	19
3	325	19
4	1204	15
5	3877	15
done	5000	15

prune98.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	93	4	97

Merged error: 0.2b

Counts

97 → 4

Details

sample64.0ms

simplify6.8s

prune4.0ms

localize8.0ms

rewrite18.0ms

series40.0ms

simplify4.7min

prune84.0ms

localize4.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune6.0ms

localize2.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune7.0ms

localize9.0ms

rewrite33.0ms

series53.0ms

simplify2.2min

prune98.0ms

regimes567.0ms

bsearch18.0ms

Profiling