Details

sample68.0ms

Algorithm

intervals

Results

18.0ms	34×	body	2560	valid
12.0ms	201×	body	80	valid
6.0ms	23×	body	1280	valid
6.0ms	103×	body	80	nan
2.0ms	11×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

14.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3min

Counts

161 → 161

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	23
1	17	23
2	34	23
3	59	23
4	61	23
done	61	23
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	32
1	18	20
2	44	12
3	107	12
4	213	12
5	264	12
6	289	12
7	349	12
8	550	12
9	1470	12
done	5000	12
0	11	22
1	18	11
2	35	11
3	60	11
4	62	11
done	62	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	2	2
1	4	1
done	4	1
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	12	14
1	36	14
2	132	12
3	630	12
4	3245	12
done	5001	12
0	13	30
1	39	24
2	129	22
3	380	20
4	534	20
5	561	20
6	669	20
7	1013	20
8	2351	20
done	5000	20
0	11	20
1	31	20
2	99	18
3	378	16
4	1004	16
5	1412	16
6	1854	16
7	3074	16
done	5000	16
0	9	10
1	14	10
2	20	10
done	20	10
0	3	3
1	6	1
done	6	1
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	20	10
2	39	10
3	96	10
4	255	10
5	831	10
6	4970	10
done	5000	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	18	10
2	45	10
3	105	10
4	215	10
5	657	10
6	2946	10
done	5000	10
0	10	21
1	16	21
2	33	21
3	58	21
4	60	21
done	60	21
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	10	29
1	17	29
2	48	11
3	174	11
4	916	11
5	4661	11
done	5000	11
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	11	13
1	35	13
2	131	11
3	622	11
4	3139	11
done	5000	11
0	12	29
1	38	23
2	128	21
3	371	19
4	514	19
5	541	19
6	646	19
7	990	19
8	2334	19
done	5001	19
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1013	15
5	1427	15
6	1886	15
7	3039	15
done	5000	15
0	8	9
1	13	9
2	19	9
done	19	9
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	12	14
1	20	13
2	39	13
3	67	13
4	72	13
5	78	13
6	82	13
7	98	13
8	102	13
9	107	13
10	114	13
11	133	13
12	154	13
13	166	13
14	169	13
done	169	13
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	11	13
1	22	13
2	42	13
3	70	13
4	80	13
5	84	13
6	100	13
7	104	13
8	109	13
9	116	13
10	134	13
11	155	13
12	173	13
13	176	13
done	176	13
0	12	27
1	20	27
2	38	27
3	63	27
4	65	27
done	65	27
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	12	38
1	21	38
2	53	14
3	121	14
4	231	14
5	605	14
6	2448	14
done	5001	14
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	13	16
1	33	16
2	72	16
3	140	16
4	303	16
5	736	16
6	2593	16
done	5001	16
0	13	38
1	26	24
2	61	24
3	117	22
4	167	22
5	250	22
6	423	22
7	536	22
8	642	22
9	698	22
10	770	22
done	770	22
0	2	2
done	2	2
0	11	25
1	22	13
2	55	13
3	112	13
4	160	7
5	244	6
6	974	6
done	5000	6
0	10	12
1	17	12
2	34	12
3	59	12
4	63	12
done	63	12
0	12	14
1	19	14
2	36	14
3	61	14
4	65	14
done	65	14
0	12	14
1	20	14
2	38	14
3	63	14
4	65	14
done	65	14
0	12	14
1	19	14
2	36	14
3	61	14
4	65	14
done	65	14
0	12	14
1	20	14
2	38	14
3	63	14
4	65	14
done	65	14
0	10	12
1	18	12
2	36	12
3	61	12
4	63	12
done	63	12
0	2	2
done	2	2
0	16	19
1	30	19
2	59	19
3	102	19
4	117	19
5	125	19
6	140	19
7	166	19
8	175	19
done	175	19
0	15	18
1	31	18
2	58	18
3	100	18
4	116	18
5	120	18
6	128	18
7	143	18
8	169	18
9	178	18
done	178	18
0	14	17
1	30	17
2	66	17
3	114	17
4	139	17
5	154	17
6	162	17
7	175	17
8	189	17
9	205	17
10	209	17
done	209	17
0	14	17
1	27	17
2	56	17
3	97	17
4	107	17
5	113	17
6	119	17
7	123	17
8	139	17
9	143	17
10	154	17
11	171	17
12	199	17
13	235	17
14	262	17
15	279	17
16	305	17
17	307	17
done	307	17
0	19	50
1	41	50
2	149	22
3	604	20
4	2453	18
done	5001	18
0	17	50
1	43	50
2	135	20
3	510	18
4	2132	18
done	5000	18
0	15	35
1	28	35
2	57	35
3	93	35
4	101	35
5	104	35
done	104	35
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	15	50
1	35	50
2	95	18
3	336	18
4	1583	18
done	5000	18
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	13	15
1	26	15
2	49	15
3	81	15
4	89	14
5	90	14
done	90	14
0	2	2
done	2	2
0	12	14
1	20	14
2	40	14
3	65	14
4	67	14
done	67	14
0	5	5
1	7	5
2	10	5
done	10	5
0	17	37
1	34	37
2	63	37
3	96	37
4	98	37
done	98	37
0	15	18
1	26	18
2	46	18
3	73	18
4	75	18
done	75	18
0	16	34
1	29	34
2	51	34
3	79	34
4	81	34
done	81	34
0	15	18
1	26	18
2	46	18
3	73	18
4	75	18
done	75	18
0	16	33
1	31	31
2	57	31
3	89	31
4	91	31
done	91	31
0	14	17
1	25	17
2	45	17
3	72	17
4	74	17
done	74	17
0	16	21
1	29	21
2	49	21
3	76	21
4	78	21
done	78	21
0	15	18
1	26	18
2	46	18
3	73	18
4	75	18
done	75	18
0	15	18
1	26	18
2	46	18
3	73	18
4	75	18
done	75	18
0	15	18
1	26	18
2	46	18
3	73	18
4	75	18
done	75	18
0	15	17
1	28	15
2	50	15
3	77	15
4	79	15
done	79	15
0	14	17
1	25	17
2	45	17
3	72	17
4	74	17
done	74	17
0	19	39
1	37	39
2	90	39
3	205	39
4	336	39
5	376	39
done	376	39
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	18	36
1	34	36
2	75	36
3	137	36
4	182	36
5	186	36
done	186	36
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	18	35
1	36	33
2	81	33
3	155	33
4	189	33
done	189	33
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	18	36
1	32	36
2	66	36
3	127	36
4	170	36
5	180	36
done	180	36
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	17	33
1	29	33
2	58	33
3	96	33
4	108	33
done	108	33
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	17	32
1	31	30
2	64	30
3	106	30
4	118	30
done	118	30
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	17	35
1	33	33
2	80	33
3	164	33
4	181	33
done	181	33
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	16	32
1	30	30
2	68	30
3	115	30
4	118	30
done	118	30
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	15	31
1	29	27
2	51	27
3	81	27
4	83	27
done	83	27
0	14	17
1	24	17
2	45	17
3	70	17
4	72	17
done	72	17
0	18	25
1	32	25
2	62	25
3	114	25
4	121	25
done	121	25
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	17	22
1	29	22
2	53	22
3	88	22
4	90	22
done	90	22
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	17	21
1	31	19
2	59	19
3	100	19
4	102	19
done	102	19
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	17	22
1	29	22
2	53	22
3	86	22
4	88	22
done	88	22
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	16	19
1	26	19
2	47	19
3	72	19
4	74	19
done	74	19
0	16	18
1	28	16
2	53	16
3	82	16
4	84	16
done	84	16
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	16	21
1	30	19
2	57	19
3	90	19
4	92	19
done	92	19
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	15	18
1	27	16
2	51	16
3	76	16
4	78	16
done	78	16
0	15	18
1	25	18
2	46	18
3	71	18
4	73	18
done	73	18
0	14	17
1	26	13
2	44	13
3	69	13
4	71	13
done	71	13
0	14	17
1	24	17
2	45	17
3	70	17
4	72	17
done	72	17
0	9	13
1	17	13
2	29	13
3	56	13
4	62	13
done	62	13
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	8	10
1	14	10
2	20	10
3	28	10
done	28	10
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	6	9
1	12	7
2	22	7
3	32	7
done	32	7
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	8	10
1	14	10
2	20	10
3	26	10
done	26	10
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	7	7
1	11	7
2	14	7
done	14	7
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	5	6
1	9	4
2	16	4
done	16	4
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	6	9
1	12	7
2	16	7
3	26	7
4	28	7
done	28	7
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	5	6
1	9	4
2	11	4
3	15	4
done	15	4
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	3	5
1	7	1
done	7	1
0	13	16
1	26	16
2	55	16
3	91	16
4	99	16
5	102	16
done	102	16
0	19	26
1	32	26
2	61	26
3	113	26
4	121	26
done	121	26
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	18	23
1	29	23
2	52	23
3	85	23
4	87	23
done	87	23
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	18	22
1	31	20
2	58	20
3	99	20
4	103	20
done	103	20
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	18	23
1	29	23
2	52	23
3	85	23
4	87	23
done	87	23
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	17	20
1	26	20
2	46	20
3	71	20
4	73	20
done	73	20
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	17	19
1	28	17
2	52	17
3	81	17
4	83	17
done	83	17
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	17	22
1	30	20
2	56	20
3	89	20
4	91	20
done	91	20
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	16	19
1	27	17
2	50	17
3	75	17
4	77	17
done	77	17
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	15	18
1	26	14
2	43	14
3	68	14
4	70	14
done	70	14
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	19	26
1	32	26
2	61	26
3	113	26
4	121	26
done	121	26
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	18	23
1	29	23
2	52	23
3	85	23
4	87	23
done	87	23
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	18	22
1	31	20
2	58	20
3	99	20
4	103	20
done	103	20
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	18	23
1	29	23
2	52	23
3	85	23
4	87	23
done	87	23
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	17	20
1	26	20
2	46	20
3	71	20
4	73	20
done	73	20
0	17	20
1	30	20
2	59	20
3	97	20
4	105	20
5	108	20
done	108	20
0	17	19
1	28	17
2	52	17
3	81	17
4	83	17
done	83	17
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	17	22
1	30	20
2	56	20
3	89	20
4	91	20
done	91	20
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	16	19
1	27	17
2	50	17
3	75	17
4	77	17
done	77	17
0	16	19
1	29	19
2	58	19
3	96	19
4	106	19
5	109	19
done	109	19
0	15	18
1	26	14
2	43	14
3	68	14
4	70	14
done	70	14
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	9	13
1	17	13
2	29	13
3	56	13
4	62	13
done	62	13
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	8	10
1	14	10
2	20	10
3	28	10
done	28	10
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	6	9
1	12	7
2	22	7
3	32	7
done	32	7
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	8	10
1	14	10
2	20	10
3	26	10
done	26	10
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	7	7
1	11	7
2	14	7
done	14	7
0	15	18
1	28	18
2	57	18
3	93	18
4	101	18
5	104	18
done	104	18
0	5	6
1	9	4
2	16	4
done	16	4
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	6	9
1	12	7
2	16	7
3	26	7
4	28	7
done	28	7
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	5	6
1	9	4
2	11	4
3	15	4
done	15	4
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	3	5
1	7	1
done	7	1
0	13	16
1	26	16
2	55	16
3	91	16
4	99	16
5	102	16
done	102	16
0	5	7
1	9	7
done	9	7
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	4	4
1	6	4
done	6	4
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	2	3
1	4	1
done	4	1
0	13	16
1	26	16
2	55	16
3	91	16
4	99	16
5	102	16
done	102	16
0	13	18
1	26	18
2	51	18
3	81	18
4	88	18
done	88	18
0	6	6
1	10	6
2	13	6
done	13	6
0	12	15
1	23	15
2	43	15
3	70	15
4	74	15
done	74	15
0	6	6
1	10	6
2	13	6
done	13	6
0	12	14
1	25	12
2	47	12
3	72	12
4	76	12
done	76	12
0	5	5
1	9	5
2	12	5
done	12	5
0	3	3
1	5	3
done	5	3
0	13	16
1	26	16
2	49	16
3	77	16
4	83	16
5	88	16
6	91	16
7	93	16
done	93	16
0	15	20
1	30	20
2	65	20
3	117	20
4	140	20
5	151	20
6	152	20
done	152	20
0	14	17
1	27	17
2	56	17
3	94	17
4	102	17
5	105	17
done	105	17
0	14	16
1	29	14
2	59	14
3	91	14
4	96	14
done	96	14
0	14	17
1	25	17
2	45	17
3	72	17
4	74	17
done	74	17
0	14	17
1	25	17
2	45	17
3	72	17
4	74	17
done	74	17
0	15	18
1	25	18
2	46	18
3	72	18
4	76	18
5	78	18
6	79	18
done	79	18
0	15	18
1	25	18
2	46	18
3	72	18
4	76	18
5	78	18
6	79	18
done	79	18
0	14	17
1	24	17
2	45	17
3	71	17
4	75	17
5	77	17
6	78	17
done	78	17
0	15	18
1	25	18
2	46	18
3	72	18
4	76	18
5	78	18
6	79	18
done	79	18
0	15	18
1	25	18
2	46	18
3	72	18
4	76	18
5	78	18
6	79	18
done	79	18
0	14	17
1	24	17
2	45	17
3	71	17
4	75	17
5	77	17
6	78	17
done	78	17
0	14	17
1	27	17
2	50	17
3	78	17
4	82	17
5	87	17
6	90	17
7	92	17
done	92	17
0	14	17
1	27	17
2	50	17
3	78	17
4	82	17
5	87	17
6	90	17
7	92	17
done	92	17
0	13	16
1	26	16
2	49	16
3	77	16
4	83	16
5	88	16
6	91	16
7	93	16
done	93	16
0	16	19
1	29	19
2	52	19
3	82	19
4	86	19
5	91	19
6	94	19
7	96	19
done	96	19
0	16	19
1	29	19
2	52	19
3	82	19
4	86	19
5	91	19
6	94	19
7	96	19
done	96	19
0	15	18
1	28	18
2	51	18
3	79	18
4	83	18
5	88	18
6	91	18
7	93	18
done	93	18
0	16	19
1	29	19
2	52	19
3	82	19
4	86	19
5	91	19
6	94	19
7	96	19
done	96	19
0	16	19
1	29	19
2	52	19
3	82	19
4	86	19
5	91	19
6	94	19
7	96	19
done	96	19
0	15	18
1	28	18
2	51	18
3	79	18
4	83	18
5	88	18
6	91	18
7	93	18
done	93	18
0	14	17
1	27	17
2	50	17
3	78	17
4	82	17
5	87	17
6	90	17
7	92	17
done	92	17
0	14	17
1	27	17
2	50	17
3	78	17
4	82	17
5	87	17
6	90	17
7	92	17
done	92	17
0	13	16
1	26	16
2	49	16
3	77	16
4	83	16
5	88	16
6	91	16
7	93	16
done	93	16
0	13	16
1	26	16
2	49	16
3	77	16
4	83	16
5	88	16
6	91	16
7	93	16
done	93	16
0	5	5
1	9	5
2	12	3
3	18	3
4	25	3
5	30	3
done	30	3
0	3	3
1	4	3
done	4	3
0	12	13
1	27	13
2	70	13
3	137	11
4	216	11
5	231	11
6	253	11
7	315	11
8	533	11
9	1472	11
done	5000	11
0	8	9
1	16	9
2	39	9
3	94	9
4	200	9
5	276	9
6	286	9
done	286	9
0	8	9
1	16	9
2	31	9
3	52	9
4	81	9
5	92	9
done	92	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	13	15
1	31	15
2	71	15
3	124	13
4	220	13
5	294	13
6	409	13
7	706	13
8	1079	13
9	2184	13
done	5000	13
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	10	11
1	19	11
2	41	11
3	62	11
4	91	11
5	102	11
done	102	11
0	14	17
1	40	15
2	120	15
3	351	15
4	1057	13
5	2942	13
done	5000	13
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	9	11
1	19	9
2	36	9
3	54	9
4	66	9
5	69	9
done	69	9

prune353.0ms

Filtered

116 candidates to 161 candidates (-38.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	151	10	161
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	11	162

Merged error: 6.0b

Counts

162 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-r`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-l`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 117

Calls

4 calls:

25.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
9.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
18.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1min

Counts

129 → 129

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	23
1	17	23
2	34	23
3	59	23
4	61	23
done	61	23
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	32
1	18	20
2	44	12
3	107	12
4	213	12
5	264	12
6	289	12
7	349	12
8	550	12
9	1470	12
done	5000	12
0	11	22
1	18	11
2	35	11
3	60	11
4	62	11
done	62	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	2	2
1	4	1
done	4	1
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	12	14
1	36	14
2	132	12
3	630	12
4	3245	12
done	5001	12
0	13	30
1	39	24
2	129	22
3	380	20
4	534	20
5	561	20
6	669	20
7	1013	20
8	2351	20
done	5000	20
0	11	20
1	31	20
2	99	18
3	378	16
4	1004	16
5	1412	16
6	1854	16
7	3074	16
done	5000	16
0	9	10
1	14	10
2	20	10
done	20	10
0	3	3
1	6	1
done	6	1
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	20	10
2	39	10
3	96	10
4	255	10
5	831	10
6	4970	10
done	5000	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	18	10
2	45	10
3	105	10
4	215	10
5	657	10
6	2946	10
done	5000	10
0	10	21
1	16	21
2	33	21
3	58	21
4	60	21
done	60	21
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	10	29
1	17	29
2	48	11
3	174	11
4	916	11
5	4661	11
done	5000	11
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	11	13
1	35	13
2	131	11
3	622	11
4	3139	11
done	5000	11
0	12	29
1	38	23
2	128	21
3	371	19
4	514	19
5	541	19
6	646	19
7	990	19
8	2334	19
done	5001	19
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1013	15
5	1427	15
6	1886	15
7	3039	15
done	5000	15
0	8	9
1	13	9
2	19	9
done	19	9
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	12	14
1	20	13
2	39	13
3	67	13
4	72	13
5	78	13
6	82	13
7	98	13
8	102	13
9	107	13
10	114	13
11	133	13
12	154	13
13	166	13
14	169	13
done	169	13
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	11	13
1	22	13
2	42	13
3	70	13
4	80	13
5	84	13
6	100	13
7	104	13
8	109	13
9	116	13
10	134	13
11	155	13
12	173	13
13	176	13
done	176	13
0	12	27
1	20	27
2	38	27
3	63	27
4	65	27
done	65	27
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	12	38
1	21	38
2	53	14
3	121	14
4	231	14
5	605	14
6	2448	14
done	5001	14
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	11	13
1	19	13
2	37	13
3	62	13
4	64	13
done	64	13
0	13	16
1	33	16
2	72	16
3	140	16
4	303	16
5	736	16
6	2593	16
done	5001	16
0	13	38
1	26	24
2	61	24
3	117	22
4	167	22
5	250	22
6	423	22
7	536	22
8	642	22
9	698	22
10	770	22
done	770	22
0	2	2
done	2	2
0	11	25
1	22	13
2	55	13
3	112	13
4	160	7
5	244	6
6	974	6
done	5000	6
0	10	12
1	17	12
2	34	12
3	59	12
4	63	12
done	63	12
0	12	14
1	19	14
2	36	14
3	61	14
4	65	14
done	65	14
0	12	14
1	20	14
2	38	14
3	63	14
4	65	14
done	65	14
0	12	14
1	19	14
2	36	14
3	61	14
4	65	14
done	65	14
0	12	14
1	20	14
2	38	14
3	63	14
4	65	14
done	65	14
0	10	12
1	18	12
2	36	12
3	61	12
4	63	12
done	63	12
0	2	2
done	2	2
0	15	18
1	30	18
2	65	18
3	151	16
4	310	16
5	431	16
6	543	16
7	593	16
8	629	16
9	633	16
done	633	16
0	17	20
1	30	20
2	58	19
3	99	19
4	118	19
5	141	19
6	157	19
7	174	19
8	176	19
done	176	19
0	18	21
1	35	20
2	77	19
3	158	19
4	262	19
5	365	19
6	400	19
7	447	19
done	447	19
0	19	22
1	38	21
2	79	20
3	167	19
4	268	19
5	375	19
6	411	19
7	454	19
done	454	19
0	18	21
1	37	20
2	71	19
3	139	19
4	221	19
5	309	19
6	376	19
7	423	19
done	423	19
0	17	20
1	33	20
2	67	19
3	120	18
4	185	18
5	267	18
6	365	18
7	416	18
8	419	18
done	419	18
0	16	19
1	34	19
2	79	19
3	189	17
4	406	17
5	613	17
6	877	17
7	1002	17
8	1041	17
9	1045	17
done	1045	17
0	16	19
1	33	19
2	79	19
3	184	17
4	427	17
5	766	17
6	1772	17
done	5000	17
0	23	56
1	52	52
2	170	24
3	731	22
4	4603	22
done	5000	22
0	21	56
1	52	56
2	187	24
3	913	22
4	4935	20
done	5000	20
0	19	56
1	44	56
2	143	22
3	587	22
4	3307	18
done	5000	18
0	17	39
1	32	39
2	67	39
3	153	35
4	323	35
5	443	35
6	551	35
7	601	35
8	647	35
9	651	35
done	651	35
0	16	19
1	31	19
2	66	19
3	154	17
4	313	17
5	435	17
6	543	17
7	591	17
8	630	17
9	634	17
done	634	17
0	17	56
1	42	56
2	156	20
3	837	18
4	4774	18
done	5000	18
0	16	19
1	31	19
2	66	19
3	154	17
4	313	17
5	435	17
6	543	17
7	591	17
8	630	17
9	634	17
done	634	17
0	16	19
1	31	19
2	66	19
3	154	17
4	313	17
5	435	17
6	543	17
7	591	17
8	630	17
9	634	17
done	634	17
0	17	20
1	42	20
2	90	18
3	241	18
4	716	18
5	2697	18
done	5001	18
0	14	40
1	28	26
2	77	26
3	176	24
4	312	24
5	508	24
6	798	24
7	1114	24
8	1496	24
9	2007	24
10	2200	24
11	2234	24
done	2234	24
0	15	29
1	31	17
2	79	15
3	243	15
4	633	9
5	1466	8
6	3584	8
done	5001	8
0	11	14
1	19	14
2	44	14
3	69	14
4	71	14
done	71	14
0	17	20
1	30	20
2	51	20
3	76	20
4	80	20
done	80	20
0	17	20
1	30	20
2	51	20
3	76	20
4	80	20
done	80	20
0	18	21
1	31	21
2	52	21
3	83	21
4	86	21
done	86	21
0	18	21
1	31	21
2	52	21
3	83	21
4	86	21
done	86	21
0	19	22
1	34	21
2	63	21
3	109	19
4	169	19
5	174	19
done	174	19
0	19	22
1	34	21
2	63	21
3	109	19
4	169	19
5	174	19
done	174	19
0	18	21
1	33	21
2	62	21
3	108	19
4	171	19
5	178	19
done	178	19
0	18	21
1	33	21
2	62	21
3	108	19
4	171	19
5	178	19
done	178	19
0	17	26
1	32	26
2	61	26
3	103	26
4	119	26
5	127	26
done	127	26
0	16	19
1	29	19
2	56	19
3	88	19
4	94	19
done	94	19
0	19	28
1	38	28
2	91	28
3	223	28
4	416	28
5	639	28
6	797	28
7	836	28
8	837	28
done	837	28
0	18	25
1	33	25
2	67	25
3	145	25
4	225	25
5	292	25
6	341	25
7	346	25
done	346	25
0	17	24
1	32	22
2	73	22
3	170	22
4	266	22
5	375	22
6	438	22
7	472	22
done	472	22
0	18	23
1	33	23
2	68	23
3	144	23
4	207	23
5	272	23
6	307	23
7	314	23
done	314	23
0	17	20
1	30	20
2	57	20
3	106	20
4	131	20
5	147	20
6	158	20
done	158	20
0	16	19
1	29	17
2	60	17
3	104	17
4	130	17
5	164	17
6	189	17
7	195	17
done	195	17
0	21	30
1	44	28
2	125	26
3	400	24
4	1180	24
5	2175	24
6	3137	24
7	3713	24
8	3970	24
done	3970	24
0	20	27
1	41	25
2	102	23
3	273	21
4	654	21
5	1023	21
6	1364	21
7	1544	21
8	1650	21
done	1650	21
0	19	26
1	40	22
2	113	20
3	274	18
4	517	18
5	761	18
6	953	18
7	1087	18
8	1094	18
done	1094	18
0	20	27
1	39	25
2	97	23
3	257	21
4	713	21
5	1161	21
6	1511	21
7	1706	21
8	1816	21
done	1816	21
0	19	24
1	36	22
2	81	20
3	193	18
4	403	18
5	573	18
6	692	18
7	742	18
8	788	18
9	792	18
done	792	18
0	18	23
1	35	19
2	88	17
3	180	15
4	304	15
5	445	15
6	537	15
7	587	15
8	591	15
done	591	15
0	18	26
1	37	22
2	104	20
3	227	18
4	407	18
5	651	18
6	837	18
7	974	18
8	1002	18
done	1002	18
0	17	23
1	34	19
2	84	17
3	156	15
4	247	15
5	386	15
6	471	15
7	516	15
8	535	15
done	535	15
0	16	22
1	33	14
2	60	12
3	103	12
4	118	12
5	126	12
done	126	12
0	20	27
1	39	26
2	93	26
3	264	24
4	822	24
5	1937	24
6	2838	24
7	3535	24
8	3844	24
done	3844	24
0	19	24
1	36	23
2	76	23
3	191	21
4	500	21
5	874	21
6	1170	21
7	1356	21
8	1455	21
done	1455	21
0	18	23
1	35	20
2	84	20
3	197	18
4	396	18
5	620	18
6	782	18
7	932	18
8	970	18
done	970	18
0	19	24
1	36	23
2	82	23
3	204	21
4	525	21
5	987	21
6	1304	21
7	1549	21
8	1678	21
done	1678	21
0	18	21
1	33	20
2	68	20
3	154	18
4	324	18
5	433	18
6	540	18
7	590	18
8	625	18
9	629	18
done	629	18
0	17	20
1	32	17
2	74	17
3	143	15
4	248	15
5	369	15
6	446	15
7	500	15
8	512	15
done	512	15
0	17	23
1	34	20
2	73	18
3	183	18
4	358	18
5	588	18
6	763	18
7	934	18
8	959	18
done	959	18
0	16	20
1	31	17
2	61	15
3	132	15
4	221	15
5	354	15
6	435	15
7	493	15
8	508	15
done	508	15
0	15	19
1	30	14
2	57	12
3	100	12
4	115	12
5	123	12
done	123	12
0	19	26
1	38	26
2	92	26
3	263	24
4	809	24
5	1956	24
6	2840	24
7	3572	24
8	3954	24
done	3954	24
0	18	23
1	35	23
2	75	23
3	192	21
4	497	21
5	871	21
6	1162	21
7	1335	21
8	1436	21
done	1436	21
0	17	22
1	34	20
2	83	20
3	196	18
4	392	18
5	606	18
6	771	18
7	923	18
8	955	18
done	955	18
0	18	23
1	35	23
2	81	23
3	203	21
4	524	21
5	978	21
6	1302	21
7	1555	21
8	1694	21
done	1694	21
0	17	20
1	32	20
2	67	20
3	153	18
4	314	18
5	423	18
6	528	18
7	578	18
8	622	18
9	626	18
done	626	18
0	16	19
1	31	17
2	73	17
3	142	15
4	245	15
5	366	15
6	441	15
7	501	15
8	513	15
done	513	15
0	16	22
1	33	20
2	72	18
3	182	18
4	358	18
5	587	18
6	766	18
7	920	18
8	961	18
done	961	18
0	15	19
1	30	17
2	60	15
3	131	15
4	220	15
5	353	15
6	433	15
7	506	15
8	524	15
done	524	15
0	14	18
1	29	14
2	56	12
3	101	12
4	116	12
5	124	12
done	124	12
0	15	20
1	30	20
2	64	18
3	153	18
4	259	18
5	336	18
6	404	18
7	430	18
8	453	18
9	455	18
done	455	18
0	14	17
1	27	17
2	54	15
3	114	15
4	158	15
5	186	15
6	205	15
7	207	15
8	208	15
done	208	15
0	13	16
1	26	14
2	55	12
3	98	12
4	113	12
5	121	12
done	121	12
0	15	20
1	30	20
2	64	18
3	153	18
4	259	18
5	336	18
6	404	18
7	430	18
8	453	18
9	455	18
done	455	18
0	14	17
1	27	17
2	54	15
3	114	15
4	158	15
5	186	15
6	205	15
7	207	15
8	208	15
done	208	15
0	13	16
1	26	14
2	55	12
3	98	12
4	113	12
5	121	12
done	121	12
0	12	14
1	23	12
2	50	12
3	86	12
4	99	12
5	103	12
done	103	12
0	14	16
1	27	16
2	54	14
3	114	14
4	158	14
5	185	14
6	202	14
7	204	14
8	205	14
done	205	14
0	16	19
1	31	19
2	60	19
3	108	17
4	171	17
5	186	17
done	186	17
0	16	19
1	31	19
2	60	19
3	108	17
4	171	17
5	186	17
done	186	17
0	15	18
1	30	18
2	65	18
3	151	16
4	310	16
5	431	16
6	543	16
7	593	16
8	629	16
9	633	16
done	633	16
0	17	20
1	32	20
2	67	20
3	153	18
4	323	18
5	443	18
6	563	18
7	600	18
8	621	18
done	621	18
0	17	20
1	32	20
2	67	20
3	153	18
4	323	18
5	443	18
6	563	18
7	600	18
8	621	18
done	621	18
0	15	18
1	30	18
2	65	18
3	151	16
4	310	16
5	431	16
6	543	16
7	593	16
8	629	16
9	633	16
done	633	16
0	14	16
1	27	16
2	54	14
3	114	14
4	158	14
5	185	14
6	202	14
7	204	14
8	205	14
done	205	14
0	18	22
1	45	22
2	101	22
3	280	20
4	1154	20
done	5001	20
0	16	31
1	34	19
2	90	19
3	289	17
4	1132	11
5	2927	10
done	5000	10
0	12	13
1	27	13
2	70	13
3	137	11
4	216	11
5	231	11
6	253	11
7	315	11
8	533	11
9	1472	11
done	5000	11
0	8	9
1	16	9
2	39	9
3	94	9
4	200	9
5	276	9
6	286	9
done	286	9
0	8	9
1	16	9
2	31	9
3	52	9
4	81	9
5	92	9
done	92	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	13	15
1	31	15
2	71	15
3	124	13
4	220	13
5	294	13
6	409	13
7	706	13
8	1079	13
9	2184	13
done	5000	13
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	10	11
1	19	11
2	41	11
3	62	11
4	91	11
5	102	11
done	102	11
0	14	17
1	40	15
2	120	15
3	351	15
4	1057	13
5	2942	13
done	5000	13
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	9	11
1	19	9
2	36	9
3	54	9
4	66	9
5	69	9
done	69	9

prune251.0ms

Filtered

101 candidates to 129 candidates (-27.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	131	9	140

Merged error: 6.0b

Counts

140 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
14.7b	(/ (* 4.0 (* a c)) (* a 2.0))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`*-un-lft-identity`
6×	`cbrt-undiv` `add-sqr-sqrt` `div-exp`
5×	`pow1` `add-cube-cbrt`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `diff-log` `clear-num` `associate-/r` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 64

Calls

4 calls:

7.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(/ (* 4.0 (* a c)) (* a 2.0))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(/ (* 4.0 (* a c)) (* a 2.0))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3min

Counts

76 → 76

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	23
1	17	23
2	34	23
3	59	23
4	61	23
done	61	23
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	32
1	18	20
2	44	12
3	107	12
4	213	12
5	264	12
6	289	12
7	349	12
8	550	12
9	1470	12
done	5000	12
0	11	22
1	18	11
2	35	11
3	60	11
4	62	11
done	62	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	2	2
1	4	1
done	4	1
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	12	14
1	36	14
2	132	12
3	630	12
4	3245	12
done	5001	12
0	13	30
1	39	24
2	129	22
3	380	20
4	534	20
5	561	20
6	669	20
7	1013	20
8	2351	20
done	5000	20
0	11	20
1	31	20
2	99	18
3	378	16
4	1004	16
5	1412	16
6	1854	16
7	3074	16
done	5000	16
0	9	10
1	14	10
2	20	10
done	20	10
0	3	3
1	6	1
done	6	1
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	12	14
1	23	14
2	60	14
3	171	14
4	364	10
5	655	8
6	3320	8
done	5000	8
0	12	13
1	23	13
2	51	13
3	128	13
4	291	10
5	552	8
6	3011	8
done	5000	8
0	12	13
1	23	13
2	52	13
3	138	13
4	330	10
5	612	8
6	3071	8
done	5000	8
0	11	12
1	23	12
2	45	12
3	108	12
4	260	10
5	505	8
6	2947	8
done	5001	8
0	11	12
1	23	12
2	50	12
3	121	12
4	331	9
5	578	7
6	2521	7
done	5001	7
0	10	11
1	23	11
2	46	11
3	98	11
4	259	11
5	497	9
6	840	7
7	3724	7
done	5001	7
0	9	10
1	24	10
2	93	10
3	298	8
4	708	6
5	2896	6
done	5000	6
0	9	10
1	21	10
2	72	10
3	218	8
4	442	6
5	1472	6
done	5000	6
0	16	29
1	42	29
2	317	19
3	3723	13
done	5001	13
0	16	29
1	46	29
2	336	17
3	4353	17
done	5000	17
0	16	29
1	46	29
2	303	17
3	3604	17
done	5001	17
0	14	29
1	48	29
2	322	15
3	4169	15
done	5000	15
0	14	29
1	42	29
2	298	15
3	4178	15
done	5000	15
0	12	29
1	44	29
2	321	13
3	4836	11
done	5000	11
0	10	21
1	22	21
2	71	21
3	201	17
4	377	13
5	1205	13
done	5000	13
0	9	10
1	21	10
2	70	10
3	200	8
4	373	6
5	1197	6
done	5001	6
0	10	29
1	29	29
2	166	11
3	1607	9
done	5000	9
0	9	10
1	21	10
2	70	10
3	200	8
4	373	6
5	1197	6
done	5001	6
0	9	10
1	21	10
2	70	10
3	200	8
4	373	6
5	1197	6
done	5001	6
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	4	4
1	9	4
2	11	4
done	11	4
0	3	3
done	3	3
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	5	5
1	10	5
2	12	5
done	12	5
0	8	9
1	20	9
2	63	9
3	173	9
4	303	7
5	356	5
6	1235	5
done	5000	5
0	6	7
1	12	7
2	27	7
3	52	5
4	75	3
5	204	3
6	1089	3
7	4974	3
done	5000	3
0	6	7
1	15	7
2	36	5
3	66	3
4	156	3
5	601	3
6	2440	3
done	5001	3
0	10	11
1	20	10
2	39	10
3	96	10
4	255	10
5	831	10
6	4970	10
done	5000	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	18	10
2	45	10
3	105	10
4	215	10
5	657	10
6	2946	10
done	5000	10
0	10	21
1	16	21
2	33	21
3	58	21
4	60	21
done	60	21
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	10	29
1	17	29
2	48	11
3	174	11
4	916	11
5	4661	11
done	5000	11
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	11	13
1	35	13
2	131	11
3	622	11
4	3139	11
done	5000	11
0	12	29
1	38	23
2	128	21
3	371	19
4	514	19
5	541	19
6	646	19
7	990	19
8	2334	19
done	5001	19
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1013	15
5	1427	15
6	1886	15
7	3039	15
done	5000	15
0	8	9
1	13	9
2	19	9
done	19	9
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	12	14
1	21	13
2	39	13
3	64	13
4	66	13
done	66	13
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	11	13
1	21	13
2	39	13
3	64	13
4	66	13
done	66	13
0	12	27
1	19	27
2	36	27
3	61	27
4	65	27
done	65	27
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	12	38
1	32	38
2	80	14
3	170	14
4	379	14
5	1444	14
done	5000	14
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	13	16
1	32	16
2	58	16
3	109	16
4	225	16
5	427	16
6	875	16
7	2730	16
done	5000	16
0	13	38
1	27	24
2	69	24
3	143	22
4	239	22
5	397	22
6	665	22
7	741	22
8	768	22
done	768	22
0	11	25
1	22	13
2	55	13
3	112	13
4	160	7
5	244	6
6	974	6
done	5000	6
0	10	12
1	18	12
2	36	12
3	61	12
4	63	12
done	63	12
0	10	12
1	17	12
2	34	12
3	59	12
4	63	12
done	63	12
0	12	13
1	27	13
2	70	13
3	137	11
4	216	11
5	231	11
6	253	11
7	315	11
8	533	11
9	1472	11
done	5000	11
0	8	9
1	16	9
2	39	9
3	94	9
4	200	9
5	276	9
6	286	9
done	286	9
0	8	9
1	16	9
2	31	9
3	52	9
4	81	9
5	92	9
done	92	9
0	3	3
1	4	3
done	4	3
0	3	3
1	4	3
done	4	3
0	3	3
1	4	3
done	4	3
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	13	15
1	31	15
2	80	15
3	151	13
4	233	13
5	282	13
6	378	13
7	547	13
8	818	13
9	1833	13
done	5000	13
0	10	11
1	19	11
2	42	11
3	97	11
4	203	11
5	279	11
6	289	11
done	289	11
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7

prune155.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	3	3	6
Picked	1	0	1
Done	0	2	2
Total	78	7	85

Merged error: 5.9b

Counts

85 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (neg (* 2.0 c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.2b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
22.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
8×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

16.0ms	(/ (neg (* 2.0 c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (neg (* 2.0 c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3min

Counts

101 → 101

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	23
1	17	23
2	34	23
3	59	23
4	61	23
done	61	23
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	11	32
1	18	20
2	44	12
3	107	12
4	213	12
5	264	12
6	289	12
7	349	12
8	550	12
9	1470	12
done	5000	12
0	11	22
1	18	11
2	35	11
3	60	11
4	62	11
done	62	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	2	2
1	4	1
done	4	1
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	12	14
1	36	14
2	132	12
3	630	12
4	3245	12
done	5001	12
0	13	30
1	39	24
2	129	22
3	380	20
4	534	20
5	561	20
6	669	20
7	1013	20
8	2351	20
done	5000	20
0	11	20
1	31	20
2	99	18
3	378	16
4	1004	16
5	1412	16
6	1854	16
7	3074	16
done	5000	16
0	9	10
1	14	10
2	20	10
done	20	10
0	3	3
1	6	1
done	6	1
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	16	11
2	33	11
3	58	11
4	60	11
done	60	11
0	10	11
1	20	10
2	39	10
3	96	10
4	255	10
5	831	10
6	4970	10
done	5000	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	18	10
2	45	10
3	105	10
4	215	10
5	657	10
6	2946	10
done	5000	10
0	10	21
1	16	21
2	33	21
3	58	21
4	60	21
done	60	21
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	10	29
1	17	29
2	48	11
3	174	11
4	916	11
5	4661	11
done	5000	11
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	9	10
1	15	10
2	32	10
3	57	10
4	59	10
done	59	10
0	11	13
1	35	13
2	131	11
3	622	11
4	3139	11
done	5000	11
0	12	29
1	38	23
2	128	21
3	371	19
4	514	19
5	541	19
6	646	19
7	990	19
8	2334	19
done	5001	19
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1013	15
5	1427	15
6	1886	15
7	3039	15
done	5000	15
0	8	9
1	13	9
2	19	9
done	19	9
0	6	6
1	14	6
2	35	6
3	53	6
4	54	6
done	54	6
0	12	14
1	21	13
2	39	13
3	64	13
4	66	13
done	66	13
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	11	13
1	21	13
2	39	13
3	64	13
4	66	13
done	66	13
0	12	27
1	19	27
2	36	27
3	61	27
4	65	27
done	65	27
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	12	38
1	32	38
2	80	14
3	170	14
4	379	14
5	1444	14
done	5000	14
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	11	13
1	18	13
2	35	13
3	60	13
4	64	13
done	64	13
0	13	16
1	32	16
2	58	16
3	109	16
4	225	16
5	427	16
6	875	16
7	2730	16
done	5000	16
0	13	38
1	27	24
2	69	24
3	143	22
4	239	22
5	397	22
6	665	22
7	741	22
8	768	22
done	768	22
0	11	25
1	22	13
2	55	13
3	112	13
4	160	7
5	244	6
6	974	6
done	5000	6
0	10	12
1	18	12
2	36	12
3	61	12
4	63	12
done	63	12
0	10	12
1	17	12
2	34	12
3	59	12
4	63	12
done	63	12
0	16	19
1	30	19
2	55	19
3	94	19
4	110	19
5	116	19
6	128	19
7	146	19
8	172	19
9	208	19
10	238	19
11	251	19
12	282	19
13	285	19
done	285	19
0	15	18
1	32	18
2	65	18
3	117	18
4	161	18
5	186	18
6	202	18
7	226	18
8	262	18
9	292	18
10	305	18
11	336	18
12	339	18
done	339	18
0	15	18
1	29	18
2	57	18
3	94	18
4	113	18
5	139	18
6	183	18
7	294	18
8	581	18
9	1341	18
10	3878	18
done	5001	18
0	18	53
1	58	51
2	228	21
3	1484	19
done	5001	19
0	16	37
1	30	37
2	55	37
3	92	37
4	104	37
5	107	37
done	107	37
0	15	18
1	29	18
2	54	18
3	89	18
4	101	18
5	104	18
done	104	18
0	16	53
1	37	53
2	109	19
3	439	19
4	2444	19
done	5001	19
0	15	18
1	29	18
2	54	18
3	89	18
4	101	18
5	104	18
done	104	18
0	15	18
1	29	18
2	54	18
3	89	18
4	101	18
5	104	18
done	104	18
0	5	5
1	10	3
2	17	3
3	26	3
done	26	3
0	11	13
1	21	13
2	40	13
3	66	13
4	68	13
done	68	13
0	12	14
1	19	1
2	36	1
3	61	1
4	65	1
done	65	1
0	13	16
1	23	16
2	44	16
3	72	16
4	77	16
done	77	16
0	18	39
1	36	39
2	63	39
3	94	39
4	98	39
done	98	39
0	16	19
1	28	19
2	46	19
3	71	19
4	73	19
done	73	19
0	17	25
1	31	25
2	51	25
3	77	25
4	79	25
done	79	25
0	16	19
1	28	19
2	46	19
3	71	19
4	73	19
done	73	19
0	8	13
1	17	11
2	25	11
3	30	11
done	30	11
0	15	18
1	27	18
2	45	18
3	70	18
4	72	18
done	72	18
0	8	13
1	17	11
2	25	11
3	30	11
done	30	11
0	15	18
1	27	18
2	45	18
3	70	18
4	72	18
done	72	18
0	17	33
1	31	33
2	49	33
3	74	33
4	76	33
done	76	33
0	16	19
1	28	19
2	46	19
3	71	19
4	73	19
done	73	19
0	16	19
1	28	19
2	46	19
3	71	19
4	73	19
done	73	19
0	16	19
1	28	19
2	46	19
3	71	19
4	73	19
done	73	19
0	7	7
1	14	5
2	18	5
done	18	5
0	15	18
1	27	18
2	45	18
3	70	18
4	72	18
done	72	18
0	7	7
1	14	5
2	18	5
done	18	5
0	15	18
1	27	18
2	45	18
3	70	18
4	72	18
done	72	18
0	14	29
1	25	29
2	42	29
3	67	29
4	71	29
done	71	29
0	15	18
1	29	18
2	54	18
3	89	18
4	101	18
5	104	18
done	104	18
0	13	15
1	22	15
2	39	15
3	64	15
4	66	15
done	66	15
0	15	18
1	29	18
2	54	18
3	89	18
4	101	18
5	104	18
done	104	18
0	2	3
1	4	1
done	4	1
0	14	17
1	28	17
2	53	17
3	90	17
4	102	17
5	105	17
done	105	17
0	2	3
1	4	1
done	4	1
0	14	17
1	28	17
2	53	17
3	90	17
4	102	17
5	105	17
done	105	17
0	14	29
1	23	29
2	40	29
3	65	29
4	67	29
done	67	29
0	14	17
1	24	17
2	45	17
3	75	17
4	78	17
done	78	17
0	13	15
1	20	15
2	37	15
3	62	15
4	66	15
done	66	15
0	14	17
1	24	17
2	45	17
3	75	17
4	78	17
done	78	17
0	3	3
1	5	1
done	5	1
0	13	16
1	23	16
2	44	16
3	72	16
4	77	16
done	77	16
0	3	3
1	5	1
done	5	1
0	13	16
1	23	16
2	44	16
3	72	16
4	77	16
done	77	16
0	15	30
1	26	30
2	46	30
3	73	30
4	75	30
done	75	30
0	12	15
1	19	15
2	36	15
3	61	15
4	65	15
done	65	15
0	14	16
1	23	16
2	40	16
3	65	16
4	67	16
done	67	16
0	12	15
1	19	15
2	36	15
3	61	15
4	65	15
done	65	15
0	4	4
1	8	2
2	12	2
done	12	2
0	11	14
1	18	14
2	35	14
3	60	14
4	64	14
done	64	14
0	4	4
1	8	2
2	12	2
done	12	2
0	11	14
1	18	14
2	35	14
3	60	14
4	64	14
done	64	14
0	14	29
1	23	29
2	40	29
3	65	29
4	67	29
done	67	29
0	13	16
1	22	16
2	38	16
3	63	16
4	65	16
done	65	16
0	13	15
1	20	15
2	37	15
3	62	15
4	66	15
done	66	15
0	13	16
1	22	16
2	38	16
3	63	16
4	65	16
done	65	16
0	3	3
1	5	1
done	5	1
0	12	15
1	21	15
2	37	15
3	62	15
4	64	15
done	64	15
0	3	3
1	5	1
done	5	1
0	12	15
1	21	15
2	37	15
3	62	15
4	64	15
done	64	15
0	12	14
1	21	14
2	38	14
3	63	14
4	65	14
done	65	14
0	14	17
1	26	17
2	48	17
3	77	17
4	79	17
done	79	17
0	13	16
1	23	16
2	44	16
3	72	16
4	77	16
done	77	16
0	16	32
1	32	32
2	72	32
3	140	32
4	175	32
5	182	32
done	182	32
0	15	18
1	29	18
2	54	18
3	89	18
4	101	18
5	104	18
done	104	18
0	6	6
1	15	4
2	28	4
3	45	4
4	72	4
5	77	4
done	77	4
0	6	6
1	15	4
2	28	4
3	45	4
4	72	4
5	77	4
done	77	4
0	15	18
1	27	18
2	45	18
3	70	18
4	72	18
done	72	18
0	15	18
1	27	18
2	45	18
3	70	18
4	72	18
done	72	18
0	14	17
1	26	17
2	48	17
3	77	17
4	79	17
done	79	17
0	13	16
1	23	16
2	42	16
3	67	16
4	71	16
done	71	16
0	11	14
1	18	14
2	35	14
3	60	14
4	64	14
done	64	14
0	12	15
1	19	15
2	35	15
3	60	15
4	64	15
done	64	15
0	17	21
1	43	21
2	77	21
3	140	21
4	264	21
5	509	21
6	971	21
7	2999	21
done	5000	21
0	15	30
1	33	18
2	88	18
3	232	18
4	425	12
5	743	11
6	2177	8
done	5001	8
0	12	13
1	27	13
2	70	13
3	137	11
4	216	11
5	231	11
6	253	11
7	315	11
8	533	11
9	1472	11
done	5000	11
0	8	9
1	16	9
2	39	9
3	94	9
4	200	9
5	276	9
6	286	9
done	286	9
0	8	9
1	16	9
2	31	9
3	52	9
4	81	9
5	92	9
done	92	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	9	9
1	20	9
2	45	9
3	75	9
4	83	9
5	93	9
6	115	9
7	176	9
8	390	9
9	1312	9
done	5001	9
0	13	15
1	31	15
2	80	15
3	151	13
4	233	13
5	282	13
6	378	13
7	547	13
8	818	13
9	1833	13
done	5000	13
0	10	11
1	19	11
2	42	11
3	97	11
4	203	11
5	279	11
6	289	11
done	289	11
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	1	1
done	1	1
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	15	20
1	38	18
2	108	16
3	257	16
4	695	16
5	2571	16
done	5000	16

prune171.0ms

Filtered

81 candidates to 101 candidates (-24.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	99	9	108

Merged error: 5.9b

Counts

108 → 9

regimes343.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.9b

bsearch104.0ms

Steps

Iters	Range	Point
6	8.452635886898758e+130	9.412684251322846e+131	1.1115227370785376e+131
9	-4.034898188869506e-219	-6.5582180480617695e-226	-1.909915866640199e-222
8	-3.3260857371803445e+155	-4.675996499956814e+152	-3.629137574162212e+153

Iters

Range

Point

8.452635886898758e+130

9.412684251322846e+131

1.1115227370785376e+131

-4.034898188869506e-219

-6.5582180480617695e-226

-1.909915866640199e-222

-3.3260857371803445e+155

-4.675996499956814e+152

-3.629137574162212e+153

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	59
1	45	59
2	47	59
done	47	59

end0.0ms

sample1.9s

Algorithm

intervals

Results

363.0ms	1002×	body	2560	valid
359.0ms	5928×	body	80	valid
261.0ms	947×	body	1280	valid
192.0ms	2954×	body	80	nan
103.0ms	421×	body	640	valid
46.0ms	101×	body	5120	valid
39.0ms	236×	body	320	valid
11.0ms	99×	body	160	valid

Details

sample68.0ms

simplify56.0ms

prune9.0ms

localize12.0ms

rewrite39.0ms

series79.0ms

simplify1.3min

prune353.0ms

localize13.0ms

rewrite49.0ms

series81.0ms

simplify3.1min

prune251.0ms

localize14.0ms

rewrite28.0ms

series49.0ms

simplify2.3min

prune155.0ms

localize13.0ms

rewrite35.0ms

series108.0ms

simplify1.3min

prune171.0ms

regimes343.0ms

bsearch104.0ms

simplify6.0ms

end0.0ms

sample1.9s

Profiling