Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	201×	body	80	valid
11.0ms	34×	body	2560	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

simplify58.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	87	16
5	95	16
done	95	16

prune8.0ms

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: 32.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.8b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b	(- (* b b) (* (* 3.0 a) c))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

12.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
8.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
17.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
10.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3min

Counts

84 → 84

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	63	23
done	63	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	214	12
5	263	12
6	288	12
7	346	12
8	555	12
9	1480	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	628	12
4	3225	12
done	5000	12
0	13	30
1	39	24
2	128	22
3	370	20
4	531	20
5	558	20
6	660	20
7	1001	20
8	2339	20
done	5001	20
0	11	20
1	31	20
2	99	18
3	379	16
4	1027	16
5	1481	16
6	1979	16
7	3146	16
done	5001	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	42	10
3	96	10
4	254	10
5	834	10
6	4965	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	103	10
4	210	10
5	652	10
6	2953	10
done	5001	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	920	11
5	4638	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	621	11
4	3194	11
done	5001	11
0	12	29
1	38	23
2	127	21
3	376	19
4	530	19
5	557	19
6	663	19
7	1006	19
8	2362	19
done	5000	19
0	6	6
1	14	6
2	35	6
3	53	6
done	53	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1029	15
5	1449	15
6	1950	15
7	3164	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
done	53	6
0	12	14
1	20	13
2	39	13
3	67	13
4	74	13
5	80	13
6	84	13
7	100	13
8	104	13
9	109	13
10	116	13
11	134	13
12	155	13
13	172	13
14	175	13
done	175	13
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	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	67	27
done	67	27
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	12	38
1	21	38
2	53	14
3	121	14
4	231	14
5	605	14
6	2448	14
done	5000	14
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	13	16
1	33	16
2	72	16
3	140	16
4	304	16
5	745	16
6	2570	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	638	22
9	694	22
10	766	22
done	766	22
0	2	2
done	2	2
0	11	25
1	22	13
2	55	13
3	112	13
4	162	7
5	246	6
6	979	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	63	14
done	63	14
0	12	14
1	20	14
2	38	14
3	63	14
4	67	14
done	67	14
0	12	14
1	19	14
2	36	14
3	61	14
4	63	14
done	63	14
0	12	14
1	20	14
2	38	14
3	63	14
4	67	14
done	67	14
0	10	12
1	18	12
2	36	12
3	61	12
4	65	12
done	65	12
0	2	2
done	2	2
0	15	19
1	28	19
2	55	19
3	90	19
4	104	19
5	120	19
6	139	19
7	155	19
8	160	19
done	160	19
0	13	18
1	26	18
2	51	18
3	84	18
4	95	18
5	107	18
6	126	18
7	152	18
8	162	18
done	162	18
0	12	17
1	28	17
2	67	17
3	114	17
4	137	17
5	148	17
6	164	17
7	183	17
8	199	17
9	204	17
done	204	17
0	12	17
1	25	17
2	59	17
3	94	17
4	107	17
5	114	17
6	118	17
7	134	17
8	138	17
9	149	17
10	166	17
11	195	17
12	231	17
13	261	17
14	278	17
15	304	17
16	306	17
done	306	17
0	18	50
1	41	50
2	161	22
3	686	22
4	2721	20
done	5000	20
0	15	50
1	41	50
2	176	20
3	827	18
4	3200	18
done	5001	18
0	13	35
1	26	35
2	57	35
3	90	35
4	100	35
5	101	35
done	101	35
0	12	17
1	25	17
2	56	17
3	89	17
4	97	17
5	98	17
done	98	17
0	13	50
1	33	50
2	122	18
3	571	18
4	2580	18
done	5000	18
0	12	17
1	25	17
2	56	17
3	89	17
4	97	17
5	98	17
done	98	17
0	12	17
1	25	17
2	56	17
3	89	17
4	97	17
5	98	17
done	98	17
0	11	13
1	19	13
2	40	13
3	67	13
4	72	12
done	72	12
0	4	4
1	9	4
2	11	4
done	11	4
0	10	14
1	18	14
2	37	14
3	62	14
4	64	14
done	64	14
0	5	5
1	8	5
2	10	5
done	10	5
0	13	29
1	23	29
2	43	29
3	69	29
4	73	29
done	73	29
0	12	15
1	20	15
2	38	15
3	63	15
4	67	15
done	67	15
0	12	15
1	20	15
2	38	15
3	63	15
4	67	15
done	67	15
0	12	15
1	20	15
2	38	15
3	63	15
4	67	15
done	67	15
0	3	3
1	5	3
done	5	3
0	11	14
1	22	14
2	42	14
3	69	14
4	73	14
done	73	14
0	13	16
1	20	16
2	37	16
3	62	16
4	66	16
done	66	16
0	13	16
1	24	16
2	44	16
3	71	16
4	73	16
done	73	16
0	13	16
1	20	16
2	37	16
3	62	16
4	66	16
done	66	16
0	13	16
1	24	16
2	44	16
3	71	16
4	73	16
done	73	16
0	3	3
1	5	3
done	5	3
0	11	14
1	22	14
2	42	14
3	69	14
4	73	14
done	73	14
0	5	5
1	10	5
2	12	5
done	12	5
0	11	16
1	21	16
2	46	16
3	79	16
4	88	16
5	90	16
done	90	16
0	11	14
1	22	14
2	42	14
3	69	14
4	73	14
done	73	14
0	12	17
1	22	17
2	44	17
3	72	17
4	75	17
done	75	17
0	12	17
1	22	17
2	44	17
3	72	17
4	75	17
done	75	17
0	11	16
1	21	16
2	46	16
3	79	16
4	88	16
5	90	16
done	90	16
0	13	18
1	23	18
2	48	18
3	81	18
4	90	18
5	92	18
done	92	18
0	13	18
1	23	18
2	48	18
3	81	18
4	90	18
5	92	18
done	92	18
0	11	16
1	21	16
2	46	16
3	79	16
4	88	16
5	90	16
done	90	16
0	14	42
1	36	28
2	128	28
3	352	26
4	755	26
5	1171	26
6	1759	26
7	2632	26
8	3989	26
done	5000	26
0	11	16
1	27	16
2	71	16
3	106	16
4	108	16
done	108	16
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	10	11
1	18	11
2	33	11
3	50	11
4	62	11
5	65	11
done	65	11

prune201.0ms

Filtered

66 candidates to 84 candidates (-27.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	10	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 6.0b

Counts

85 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
0.8b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b	(- (* b b) (* (* 3.0 a) c))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

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) (* (* 3.0 a) c))) b) 3.0) a)
9.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
18.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
10.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 3.0 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	63	23
done	63	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	214	12
5	263	12
6	288	12
7	346	12
8	555	12
9	1480	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	628	12
4	3225	12
done	5000	12
0	13	30
1	39	24
2	128	22
3	370	20
4	531	20
5	558	20
6	660	20
7	1001	20
8	2339	20
done	5001	20
0	11	20
1	31	20
2	99	18
3	379	16
4	1027	16
5	1481	16
6	1979	16
7	3146	16
done	5001	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	42	10
3	96	10
4	254	10
5	834	10
6	4965	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	103	10
4	210	10
5	652	10
6	2953	10
done	5001	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	920	11
5	4638	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	621	11
4	3194	11
done	5001	11
0	12	29
1	38	23
2	127	21
3	376	19
4	530	19
5	557	19
6	663	19
7	1006	19
8	2362	19
done	5000	19
0	6	6
1	14	6
2	35	6
3	53	6
done	53	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1029	15
5	1449	15
6	1950	15
7	3164	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
done	53	6
0	12	14
1	20	13
2	39	13
3	67	13
4	74	13
5	80	13
6	84	13
7	100	13
8	104	13
9	109	13
10	116	13
11	134	13
12	155	13
13	172	13
14	175	13
done	175	13
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	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	67	27
done	67	27
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	12	38
1	21	38
2	53	14
3	121	14
4	231	14
5	605	14
6	2448	14
done	5000	14
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	13	16
1	33	16
2	72	16
3	140	16
4	304	16
5	745	16
6	2570	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	638	22
9	694	22
10	766	22
done	766	22
0	2	2
done	2	2
0	11	25
1	22	13
2	55	13
3	112	13
4	162	7
5	246	6
6	979	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	63	14
done	63	14
0	12	14
1	20	14
2	38	14
3	63	14
4	67	14
done	67	14
0	12	14
1	19	14
2	36	14
3	61	14
4	63	14
done	63	14
0	12	14
1	20	14
2	38	14
3	63	14
4	67	14
done	67	14
0	10	12
1	18	12
2	36	12
3	61	12
4	65	12
done	65	12
0	2	2
done	2	2
0	15	19
1	29	19
2	58	19
3	101	19
4	112	19
5	120	19
6	135	19
7	161	19
8	170	19
done	170	19
0	14	18
1	30	18
2	57	18
3	101	18
4	117	18
5	121	18
6	129	18
7	144	18
8	170	18
9	179	18
done	179	18
0	13	17
1	28	17
2	63	17
3	113	17
4	140	17
5	155	17
6	163	17
7	176	17
8	190	17
9	206	17
10	210	17
done	210	17
0	13	17
1	25	17
2	53	17
3	92	17
4	104	17
5	110	17
6	116	17
7	120	17
8	136	17
9	140	17
10	151	17
11	168	17
12	196	17
13	232	17
14	258	17
15	275	17
16	301	17
17	303	17
done	303	17
0	18	50
1	40	50
2	148	22
3	604	20
4	2449	18
done	5000	18
0	16	50
1	42	50
2	133	20
3	505	18
4	2120	18
done	5001	18
0	14	35
1	26	35
2	54	35
3	90	35
4	98	35
5	101	35
done	101	35
0	13	17
1	25	17
2	53	17
3	89	17
4	99	17
5	102	17
done	102	17
0	14	50
1	33	50
2	92	18
3	335	18
4	1600	18
done	5000	18
0	13	17
1	25	17
2	53	17
3	89	17
4	99	17
5	102	17
done	102	17
0	13	17
1	25	17
2	53	17
3	89	17
4	99	17
5	102	17
done	102	17
0	12	15
1	25	15
2	48	15
3	80	15
4	88	14
5	89	14
done	89	14
0	2	2
done	2	2
0	11	14
1	18	14
2	37	14
3	62	14
4	64	14
done	64	14
0	5	5
1	7	5
2	10	5
done	10	5
0	16	37
1	33	37
2	62	37
3	95	37
4	97	37
done	97	37
0	14	18
1	25	18
2	45	18
3	72	18
4	74	18
done	74	18
0	15	34
1	28	34
2	50	34
3	78	34
4	80	34
done	80	34
0	14	18
1	25	18
2	45	18
3	72	18
4	74	18
done	74	18
0	15	33
1	30	31
2	56	31
3	88	31
4	90	31
done	90	31
0	13	17
1	24	17
2	44	17
3	71	17
4	73	17
done	73	17
0	15	21
1	28	21
2	48	21
3	75	21
4	77	21
done	77	21
0	14	18
1	25	18
2	45	18
3	72	18
4	74	18
done	74	18
0	14	18
1	25	18
2	45	18
3	72	18
4	74	18
done	74	18
0	14	18
1	25	18
2	45	18
3	72	18
4	74	18
done	74	18
0	14	17
1	27	15
2	49	15
3	76	15
4	78	15
done	78	15
0	13	17
1	24	17
2	44	17
3	71	17
4	73	17
done	73	17
0	18	39
1	36	39
2	89	39
3	202	39
4	336	39
5	375	39
done	375	39
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	17	36
1	33	36
2	74	36
3	136	36
4	179	36
5	185	36
done	185	36
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	17	35
1	35	33
2	80	33
3	156	33
4	188	33
done	188	33
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	17	36
1	31	36
2	65	36
3	126	36
4	172	36
5	182	36
done	182	36
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	16	33
1	28	33
2	57	33
3	95	33
4	107	33
done	107	33
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	16	32
1	30	30
2	63	30
3	105	30
4	117	30
done	117	30
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	17	35
1	33	33
2	80	33
3	164	33
4	181	33
done	181	33
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	16	32
1	30	30
2	68	30
3	115	30
4	120	30
done	120	30
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	15	31
1	29	27
2	51	27
3	81	27
4	83	27
done	83	27
0	13	17
1	22	17
2	42	17
3	67	17
4	71	17
done	71	17
0	17	25
1	31	25
2	61	25
3	113	25
4	120	25
done	120	25
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	16	22
1	28	22
2	52	22
3	85	22
4	89	22
done	89	22
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	16	21
1	30	19
2	58	19
3	99	19
4	101	19
done	101	19
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	16	22
1	28	22
2	52	22
3	85	22
4	89	22
done	89	22
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	15	19
1	25	19
2	46	19
3	71	19
4	73	19
done	73	19
0	15	18
1	27	16
2	52	16
3	81	16
4	83	16
done	83	16
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	16	21
1	30	19
2	57	19
3	90	19
4	92	19
done	92	19
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	15	18
1	27	16
2	51	16
3	76	16
4	78	16
done	78	16
0	14	18
1	24	18
2	45	18
3	70	18
4	72	18
done	72	18
0	14	17
1	26	13
2	44	13
3	69	13
4	71	13
done	71	13
0	13	17
1	22	17
2	42	17
3	67	17
4	71	17
done	71	17
0	9	13
1	17	13
2	29	13
3	56	13
4	62	13
done	62	13
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	8	10
1	14	10
2	20	10
3	28	10
done	28	10
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	6	9
1	12	7
2	22	7
3	32	7
done	32	7
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	8	10
1	14	10
2	20	10
3	26	10
done	26	10
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	7	7
1	11	7
2	14	7
done	14	7
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	5	6
1	9	4
2	16	4
done	16	4
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	6	9
1	12	7
2	16	7
3	26	7
4	28	7
done	28	7
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	5	6
1	9	4
2	11	4
3	15	4
done	15	4
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	3	5
1	7	1
done	7	1
0	12	16
1	24	16
2	52	16
3	88	16
4	98	16
5	101	16
done	101	16
0	18	26
1	31	26
2	60	26
3	112	26
4	119	26
done	119	26
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	17	23
1	28	23
2	51	23
3	86	23
4	90	23
done	90	23
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	17	22
1	30	20
2	57	20
3	98	20
4	100	20
done	100	20
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	17	23
1	28	23
2	51	23
3	82	23
4	84	23
done	84	23
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	16	20
1	25	20
2	45	20
3	70	20
4	72	20
done	72	20
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	16	19
1	27	17
2	51	17
3	78	17
4	80	17
done	80	17
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	17	22
1	30	20
2	56	20
3	89	20
4	91	20
done	91	20
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	16	19
1	27	17
2	50	17
3	75	17
4	77	17
done	77	17
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	15	18
1	26	14
2	43	14
3	68	14
4	70	14
done	70	14
0	14	18
1	26	18
2	54	18
3	90	18
4	98	18
5	101	18
done	101	18
0	18	26
1	31	26
2	60	26
3	112	26
4	119	26
done	119	26
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	17	23
1	28	23
2	51	23
3	86	23
4	90	23
done	90	23
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	17	22
1	30	20
2	57	20
3	98	20
4	100	20
done	100	20
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	17	23
1	28	23
2	51	23
3	82	23
4	84	23
done	84	23
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	16	20
1	25	20
2	45	20
3	70	20
4	72	20
done	72	20
0	16	20
1	29	20
2	58	20
3	96	20
4	104	20
5	107	20
done	107	20
0	16	19
1	27	17
2	51	17
3	78	17
4	80	17
done	80	17
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	17	22
1	30	20
2	56	20
3	89	20
4	91	20
done	91	20
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	16	19
1	27	17
2	50	17
3	75	17
4	77	17
done	77	17
0	15	19
1	28	19
2	57	19
3	93	19
4	101	19
5	104	19
done	104	19
0	15	18
1	26	14
2	43	14
3	68	14
4	70	14
done	70	14
0	14	18
1	26	18
2	54	18
3	90	18
4	98	18
5	101	18
done	101	18
0	9	13
1	17	13
2	29	13
3	56	13
4	62	13
done	62	13
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	8	10
1	14	10
2	20	10
3	28	10
done	28	10
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	6	9
1	12	7
2	22	7
3	32	7
done	32	7
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	8	10
1	14	10
2	20	10
3	26	10
done	26	10
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	7	7
1	11	7
2	14	7
done	14	7
0	14	18
1	27	18
2	56	18
3	94	18
4	102	18
5	105	18
done	105	18
0	5	6
1	9	4
2	16	4
done	16	4
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	6	9
1	12	7
2	16	7
3	26	7
4	28	7
done	28	7
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	5	6
1	9	4
2	11	4
3	15	4
done	15	4
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	3	5
1	7	1
done	7	1
0	12	16
1	24	16
2	52	16
3	88	16
4	98	16
5	101	16
done	101	16
0	5	7
1	9	7
done	9	7
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	4	4
1	6	4
done	6	4
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	2	3
1	4	1
done	4	1
0	12	16
1	24	16
2	52	16
3	88	16
4	98	16
5	101	16
done	101	16
0	13	18
1	26	18
2	51	18
3	81	18
4	86	18
done	86	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	12	16
1	25	16
2	47	16
3	76	16
4	85	16
5	88	16
6	90	16
done	90	16
0	14	20
1	29	20
2	64	20
3	116	20
4	139	20
5	150	20
6	151	20
done	151	20
0	13	17
1	26	17
2	55	17
3	91	17
4	99	17
5	102	17
done	102	17
0	13	16
1	28	14
2	58	14
3	90	14
4	97	14
done	97	14
0	13	17
1	24	17
2	44	17
3	71	17
4	75	17
done	75	17
0	13	17
1	24	17
2	44	17
3	71	17
4	75	17
done	75	17
0	14	18
1	24	18
2	45	18
3	71	18
4	75	18
5	77	18
6	78	18
done	78	18
0	14	18
1	24	18
2	45	18
3	71	18
4	75	18
5	77	18
6	78	18
done	78	18
0	13	17
1	23	17
2	43	17
3	70	17
4	76	17
5	77	17
done	77	17
0	14	18
1	24	18
2	45	18
3	71	18
4	75	18
5	77	18
6	78	18
done	78	18
0	14	18
1	24	18
2	45	18
3	71	18
4	75	18
5	77	18
6	78	18
done	78	18
0	13	17
1	23	17
2	43	17
3	70	17
4	76	17
5	77	17
done	77	17
0	13	17
1	26	17
2	49	17
3	77	17
4	81	17
5	86	17
6	89	17
7	91	17
done	91	17
0	13	17
1	26	17
2	49	17
3	77	17
4	81	17
5	86	17
6	89	17
7	91	17
done	91	17
0	12	16
1	25	16
2	47	16
3	76	16
4	85	16
5	88	16
6	90	16
done	90	16
0	15	19
1	28	19
2	51	19
3	79	19
4	83	19
5	88	19
6	91	19
7	93	19
done	93	19
0	15	19
1	28	19
2	51	19
3	79	19
4	83	19
5	88	19
6	91	19
7	93	19
done	93	19
0	14	18
1	27	18
2	49	18
3	78	18
4	85	18
5	88	18
6	90	18
done	90	18
0	15	19
1	28	19
2	51	19
3	79	19
4	83	19
5	88	19
6	91	19
7	93	19
done	93	19
0	15	19
1	28	19
2	51	19
3	79	19
4	83	19
5	88	19
6	91	19
7	93	19
done	93	19
0	14	18
1	27	18
2	49	18
3	78	18
4	85	18
5	88	18
6	90	18
done	90	18
0	13	17
1	26	17
2	49	17
3	77	17
4	81	17
5	86	17
6	89	17
7	91	17
done	91	17
0	13	17
1	26	17
2	49	17
3	77	17
4	81	17
5	86	17
6	89	17
7	91	17
done	91	17
0	12	16
1	25	16
2	47	16
3	76	16
4	85	16
5	88	16
6	90	16
done	90	16
0	12	16
1	25	16
2	47	16
3	76	16
4	85	16
5	88	16
6	90	16
done	90	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	10	11
1	18	11
2	33	11
3	50	11
4	62	11
5	65	11
done	65	11

prune320.0ms

Filtered

114 candidates to 161 candidates (-41.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	160	11	171

Merged error: 6.0b

Counts

171 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
0.8b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b	(- (* b b) (* (* 3.0 a) c))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

12.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
8.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
17.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
10.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4min

Counts

83 → 83

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	63	23
done	63	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	214	12
5	263	12
6	288	12
7	346	12
8	555	12
9	1480	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	628	12
4	3225	12
done	5000	12
0	13	30
1	39	24
2	128	22
3	370	20
4	531	20
5	558	20
6	660	20
7	1001	20
8	2339	20
done	5001	20
0	11	20
1	31	20
2	99	18
3	379	16
4	1027	16
5	1481	16
6	1979	16
7	3146	16
done	5001	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	42	10
3	96	10
4	254	10
5	834	10
6	4965	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	103	10
4	210	10
5	652	10
6	2953	10
done	5001	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	920	11
5	4638	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	621	11
4	3194	11
done	5001	11
0	12	29
1	38	23
2	127	21
3	376	19
4	530	19
5	557	19
6	663	19
7	1006	19
8	2362	19
done	5000	19
0	6	6
1	14	6
2	35	6
3	53	6
done	53	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1029	15
5	1449	15
6	1950	15
7	3164	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
done	53	6
0	12	14
1	20	13
2	39	13
3	67	13
4	74	13
5	80	13
6	84	13
7	100	13
8	104	13
9	109	13
10	116	13
11	134	13
12	155	13
13	172	13
14	175	13
done	175	13
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	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	67	27
done	67	27
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	12	38
1	21	38
2	53	14
3	121	14
4	231	14
5	605	14
6	2448	14
done	5000	14
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	11	13
1	19	13
2	37	13
3	62	13
4	66	13
done	66	13
0	13	16
1	33	16
2	72	16
3	140	16
4	304	16
5	745	16
6	2570	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	638	22
9	694	22
10	766	22
done	766	22
0	2	2
done	2	2
0	11	25
1	22	13
2	55	13
3	112	13
4	162	7
5	246	6
6	979	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	63	14
done	63	14
0	12	14
1	20	14
2	38	14
3	63	14
4	67	14
done	67	14
0	12	14
1	19	14
2	36	14
3	61	14
4	63	14
done	63	14
0	12	14
1	20	14
2	38	14
3	63	14
4	67	14
done	67	14
0	10	12
1	18	12
2	36	12
3	61	12
4	65	12
done	65	12
0	2	2
done	2	2
0	15	19
1	28	19
2	53	19
3	86	19
4	96	19
5	105	19
6	118	19
7	136	19
8	152	19
9	159	19
10	176	19
11	178	19
done	178	19
0	13	18
1	26	18
2	50	18
3	84	18
4	89	18
5	95	18
6	104	18
7	117	18
8	135	18
9	151	18
10	158	18
11	175	18
12	177	18
done	177	18
0	12	17
1	25	17
2	58	17
3	107	17
4	131	17
5	141	17
6	153	17
7	171	17
8	187	17
9	194	17
10	211	17
11	213	17
done	213	17
0	12	17
1	22	17
2	47	17
3	82	17
4	99	17
5	114	17
6	147	17
7	238	17
8	458	17
9	1131	17
10	4292	17
done	5000	17
0	18	50
1	41	50
2	166	22
3	669	22
4	2631	20
done	5000	20
0	15	50
1	41	50
2	172	20
3	810	18
4	3016	18
done	5000	18
0	13	35
1	23	35
2	48	35
3	81	35
4	90	35
5	92	35
done	92	35
0	12	17
1	22	17
2	47	17
3	80	17
4	89	17
5	91	17
done	91	17
0	13	50
1	30	50
2	92	18
3	309	18
4	1168	18
5	4033	18
done	5000	18
0	12	17
1	22	17
2	47	17
3	80	17
4	89	17
5	91	17
done	91	17
0	12	17
1	22	17
2	47	17
3	80	17
4	89	17
5	91	17
done	91	17
0	4	4
1	9	4
2	11	4
done	11	4
0	11	13
1	19	13
2	40	13
3	67	13
4	72	12
done	72	12
0	13	29
1	23	29
2	41	29
3	66	29
4	68	29
done	68	29
0	12	15
1	20	15
2	38	15
3	63	15
4	65	15
done	65	15
0	12	15
1	20	15
2	38	15
3	63	15
4	67	15
done	67	15
0	12	15
1	20	15
2	38	15
3	63	15
4	65	15
done	65	15
0	3	3
1	5	1
done	5	1
0	11	14
1	19	14
2	37	14
3	62	14
4	64	14
done	64	14
0	13	16
1	20	16
2	37	16
3	62	16
4	64	16
done	64	16
0	13	16
1	21	16
2	39	16
3	64	16
4	68	16
done	68	16
0	13	16
1	20	16
2	37	16
3	62	16
4	64	16
done	64	16
0	13	16
1	21	16
2	39	16
3	64	16
4	68	16
done	68	16
0	3	3
1	5	1
done	5	1
0	11	14
1	19	14
2	37	14
3	62	14
4	64	14
done	64	14
0	12	14
1	22	14
2	40	14
3	65	14
4	67	14
done	67	14
0	11	16
1	24	16
2	55	16
3	88	16
4	96	16
5	97	16
done	97	16
0	13	31
1	28	31
2	60	31
3	100	31
4	106	31
done	106	31
0	12	17
1	22	17
2	44	17
3	72	17
4	75	17
done	75	17
0	5	5
1	10	3
2	18	3
3	27	3
4	32	3
done	32	3
0	13	18
1	22	18
2	43	18
3	71	18
4	74	18
done	74	18
0	13	18
1	22	18
2	43	18
3	71	18
4	74	18
done	74	18
0	5	5
1	10	3
2	18	3
3	27	3
4	32	3
done	32	3
0	11	14
1	22	14
2	42	14
3	69	14
4	73	14
done	73	14
0	14	20
1	36	20
2	82	20
3	181	20
4	442	20
5	1302	20
done	5000	20
0	12	29
1	25	17
2	74	17
3	175	17
4	303	11
5	528	8
6	1807	6
done	5001	4
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	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	691	16
5	2579	16
done	5000	16
0	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5

prune170.0ms

Filtered

65 candidates to 83 candidates (-27.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	83	11	94

Merged error: 5.9b

Counts

94 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ 1 (neg c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)))
0.2b	(* (/ 1 (neg c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
1.4b	(- (* b b) (* (* 3.0 a) c))
22.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
36×	`add-sqr-sqrt`
35×	`times-frac`
34×	`associate-l`
31×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`div-exp` `add-cbrt-cube`
16×	`prod-exp`
10×	`pow1`
9×	`distribute-lft-neg-in` `rec-exp` `distribute-rgt-neg-in` `1-exp`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/r/`
4×	`frac-times` `flip3-+` `associate-r/` `associate-r*` `cbrt-unprod` `flip-+`
3×	`neg-mul-1` `sqrt-prod` `associate-/l*` `unswap-sqr`
2×	`flip3--` `pow-flip` `sqrt-div` `pow-prod-down` `associate-*l/` `flip--` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `associate-/r` `-commutative` `distribute-lft-out` `inv-pow`

Counts

4 → 133

Calls

4 calls:

16.0ms	(/ 1 (* (/ 1 (neg c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)))
18.0ms	(* (/ 1 (neg c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (* (/ 1 (neg c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)))
39.0ms	(* (/ 1 (neg c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
10.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.7min

Counts

145 → 145

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	63	23
done	63	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	214	12
5	263	12
6	288	12
7	346	12
8	555	12
9	1480	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	628	12
4	3225	12
done	5000	12
0	13	30
1	39	24
2	128	22
3	370	20
4	531	20
5	558	20
6	660	20
7	1001	20
8	2339	20
done	5001	20
0	11	20
1	31	20
2	99	18
3	379	16
4	1027	16
5	1481	16
6	1979	16
7	3146	16
done	5001	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	42	10
3	96	10
4	254	10
5	834	10
6	4965	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	103	10
4	210	10
5	652	10
6	2953	10
done	5001	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	920	11
5	4638	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	621	11
4	3194	11
done	5001	11
0	12	29
1	38	23
2	127	21
3	376	19
4	530	19
5	557	19
6	663	19
7	1006	19
8	2362	19
done	5000	19
0	6	6
1	14	6
2	35	6
3	53	6
done	53	6
0	10	19
1	30	19
2	98	17
3	378	15
4	1029	15
5	1449	15
6	1950	15
7	3164	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
done	53	6
0	14	17
1	32	17
2	64	15
3	126	15
4	151	15
5	173	15
6	210	15
7	358	15
8	645	15
done	645	15
0	15	18
1	23	18
2	40	17
3	67	17
4	69	17
done	69	17
0	16	19
1	28	18
2	57	17
3	97	17
4	126	17
5	142	17
6	147	17
7	155	17
done	155	17
0	17	20
1	31	19
2	57	18
3	104	17
4	133	17
5	149	17
6	154	17
7	161	17
done	161	17
0	16	19
1	30	18
2	52	17
3	88	17
4	102	17
5	134	17
6	155	17
7	162	17
8	174	17
done	174	17
0	15	18
1	36	18
2	74	16
3	147	16
4	190	16
5	229	16
6	291	16
7	444	16
8	740	16
9	756	16
done	756	16
0	15	18
1	35	18
2	76	16
3	164	16
4	241	16
5	439	16
6	1015	16
7	3425	16
done	5000	16
0	20	53
1	62	47
2	195	19
3	838	19
4	3450	19
done	5000	19
0	18	53
1	52	53
2	172	21
3	599	21
4	2306	17
done	5000	17
0	16	37
1	34	37
2	66	33
3	128	33
4	153	33
5	175	33
6	212	33
7	360	33
8	647	33
done	647	33
0	15	18
1	33	18
2	65	16
3	129	16
4	154	16
5	176	16
6	213	16
7	361	16
8	646	16
done	646	16
0	16	53
1	44	53
2	169	17
3	714	17
4	1798	17
5	4808	17
done	5000	17
0	15	18
1	33	18
2	65	16
3	129	16
4	154	16
5	176	16
6	213	16
7	361	16
8	646	16
done	646	16
0	15	18
1	33	18
2	65	16
3	129	16
4	154	16
5	176	16
6	213	16
7	361	16
8	646	16
done	646	16
0	15	18
1	43	16
2	103	16
3	224	16
4	461	16
5	1008	16
6	1674	16
7	4012	16
done	5000	16
0	15	41
1	38	27
2	113	27
3	316	25
4	787	25
5	1529	24
6	1770	24
7	1886	24
8	1945	24
done	1945	24
0	13	27
1	27	13
2	73	13
3	184	13
4	415	7
5	768	6
6	1608	6
done	5000	6
0	12	15
1	23	15
2	55	15
3	98	15
4	123	14
5	128	14
done	128	14
0	16	19
1	26	19
2	42	19
3	67	19
4	69	19
done	69	19
0	16	19
1	26	19
2	42	19
3	67	19
4	69	19
done	69	19
0	17	20
1	29	19
2	48	19
3	75	17
4	91	17
5	93	17
done	93	17
0	17	20
1	29	19
2	48	19
3	75	17
4	91	17
5	93	17
done	93	17
0	16	19
1	28	19
2	47	17
3	85	17
4	94	17
done	94	17
0	16	19
1	28	19
2	47	17
3	85	17
4	94	17
done	94	17
0	13	15
1	24	15
2	43	13
3	83	13
4	94	13
5	112	13
6	149	13
7	297	13
8	582	13
done	582	13
0	6	6
1	11	6
2	14	4
3	16	4
done	16	4
0	13	15
1	24	15
2	43	13
3	85	13
4	111	13
5	149	13
6	297	13
7	584	13
done	584	13
0	6	6
1	11	6
2	14	4
3	17	4
4	24	4
5	25	4
done	25	4
0	16	32
1	30	32
2	54	30
3	111	30
4	135	30
5	155	30
6	192	30
7	340	30
8	625	30
done	625	30
0	15	18
1	27	18
2	46	16
3	88	16
4	101	16
5	119	16
6	156	16
7	304	16
8	589	16
done	589	16
0	5	6
1	10	4
done	10	4
0	5	6
1	10	4
done	10	4
0	15	18
1	31	18
2	48	18
3	73	18
4	75	18
done	75	18
0	15	18
1	31	18
2	48	18
3	73	18
4	75	18
done	75	18
0	16	19
1	34	18
2	66	18
3	99	16
4	126	16
5	129	16
done	129	16
0	16	19
1	34	18
2	66	18
3	99	16
4	126	16
5	129	16
done	129	16
0	15	18
1	33	17
2	65	17
3	100	15
4	135	15
5	158	15
6	195	15
7	343	15
8	628	15
done	628	15
0	14	17
1	32	16
2	65	16
3	98	14
4	125	14
5	128	14
done	128	14
0	15	18
1	33	17
2	66	17
3	99	15
4	126	15
5	129	15
done	129	15
0	15	18
1	33	17
2	66	17
3	99	15
4	126	15
5	129	15
done	129	15
0	14	17
1	32	16
2	65	16
3	98	14
4	125	14
5	128	14
done	128	14
0	16	19
1	34	18
2	67	18
3	102	16
4	137	16
5	145	16
done	145	16
0	16	19
1	34	18
2	67	18
3	102	16
4	137	16
5	145	16
done	145	16
0	15	18
1	33	17
2	65	17
3	100	15
4	135	15
5	158	15
6	195	15
7	343	15
8	628	15
done	628	15
0	16	19
1	34	18
2	66	18
3	99	16
4	126	16
5	129	16
done	129	16
0	16	19
1	34	18
2	66	18
3	99	16
4	126	16
5	129	16
done	129	16
0	15	18
1	33	17
2	65	17
3	100	15
4	135	15
5	158	15
6	195	15
7	343	15
8	628	15
done	628	15
0	14	17
1	32	16
2	65	16
3	98	14
4	125	14
5	128	14
done	128	14
0	15	18
1	33	17
2	66	17
3	99	15
4	126	15
5	129	15
done	129	15
0	15	18
1	33	17
2	66	17
3	99	15
4	126	15
5	129	15
done	129	15
0	14	17
1	32	16
2	65	16
3	98	14
4	125	14
5	128	14
done	128	14
0	16	19
1	34	18
2	67	18
3	102	16
4	137	16
5	145	16
done	145	16
0	16	19
1	34	18
2	67	18
3	102	16
4	137	16
5	145	16
done	145	16
0	15	18
1	33	17
2	65	17
3	100	15
4	135	15
5	158	15
6	195	15
7	343	15
8	628	15
done	628	15
0	15	18
1	33	18
2	65	16
3	125	16
4	142	16
done	142	16
0	15	18
1	33	18
2	65	16
3	125	16
4	142	16
done	142	16
0	14	17
1	32	17
2	64	15
3	126	15
4	151	15
5	173	15
6	210	15
7	358	15
8	645	15
done	645	15
0	13	16
1	31	16
2	64	14
3	126	14
4	143	14
done	143	14
0	14	17
1	32	17
2	65	15
3	125	15
4	142	15
done	142	15
0	14	17
1	32	17
2	65	15
3	125	15
4	142	15
done	142	15
0	13	16
1	31	16
2	64	14
3	126	14
4	143	14
done	143	14
0	15	18
1	33	18
2	66	16
3	128	16
4	153	16
5	160	16
done	160	16
0	15	18
1	33	18
2	66	16
3	128	16
4	153	16
5	160	16
done	160	16
0	14	17
1	32	17
2	64	15
3	126	15
4	151	15
5	173	15
6	210	15
7	358	15
8	645	15
done	645	15
0	14	17
1	32	17
2	64	15
3	126	15
4	151	15
5	173	15
6	210	15
7	358	15
8	645	15
done	645	15
0	14	17
1	32	17
2	64	15
3	126	15
4	151	15
5	173	15
6	210	15
7	358	15
8	645	15
done	645	15
0	17	21
1	47	21
2	112	19
3	283	19
4	870	19
5	2402	19
done	5000	19
0	15	30
1	31	18
2	84	16
3	279	16
4	853	10
5	1703	9
6	4067	3
done	5000	3
0	12	14
1	28	12
2	55	12
3	80	12
4	84	12
done	84	12
0	2	2
1	5	1
done	5	1
0	2	2
1	5	1
done	5	1
0	16	19
1	27	19
2	46	17
3	74	17
4	76	17
done	76	17
0	17	20
1	32	19
2	64	17
3	120	17
4	166	17
5	170	17
done	170	17
0	18	21
1	35	20
2	65	19
3	121	17
4	173	17
5	176	17
done	176	17
0	17	20
1	34	19
2	58	17
3	98	17
4	128	17
5	144	17
done	144	17
0	16	19
1	37	19
2	78	17
3	153	17
4	201	16
5	252	16
6	291	16
7	439	16
8	726	16
done	726	16
0	17	20
1	29	19
2	60	18
3	104	17
4	138	17
5	168	17
6	170	17
done	170	17
0	17	21
1	33	19
2	78	18
3	152	17
4	176	17
done	176	17
0	19	22
1	36	20
2	79	19
3	153	17
4	175	17
done	175	17
0	18	21
1	35	19
2	73	18
3	134	17
4	158	17
5	177	17
done	177	17
0	17	20
1	39	19
2	86	17
3	174	17
4	249	16
5	283	16
6	320	16
7	468	16
8	755	16
done	755	16
0	18	21
1	32	20
2	58	18
3	108	17
4	144	17
5	174	17
6	176	17
done	176	17
0	19	22
1	36	20
2	77	18
3	151	17
4	171	17
done	171	17
0	18	23
1	36	21
2	74	19
3	161	17
4	183	17
done	183	17
0	18	22
1	35	20
2	68	18
3	138	17
4	159	17
5	176	17
done	176	17
0	17	21
1	40	20
2	83	17
3	175	17
4	252	16
5	285	16
6	322	16
7	470	16
8	755	16
done	755	16
0	16	20
1	40	19
2	86	16
3	210	16
4	458	16
5	778	16
6	1244	16
7	2176	16
8	2627	16
9	2629	16
done	2629	16
0	16	20
1	36	20
2	74	16
3	174	16
4	365	16
5	699	16
6	1230	16
7	2372	16
8	4354	16
done	5000	16
0	21	59
1	69	49
2	232	19
3	1096	19
done	5000	19
0	21	59
1	62	55
2	203	23
3	820	23
4	3276	19
done	5000	19
0	19	59
1	54	55
2	209	19
3	976	19
4	2598	17
done	5000	17
0	17	41
1	37	41
2	75	33
3	171	33
4	351	33
5	639	33
6	1061	33
7	1815	33
8	2174	33
done	2174	33
0	16	20
1	36	20
2	74	16
3	172	16
4	353	16
5	646	16
6	1069	16
7	1778	16
8	2138	16
done	2138	16
0	17	59
1	44	59
2	126	17
3	461	17
4	1630	17
5	3778	17
done	5001	17
0	16	20
1	36	20
2	74	16
3	172	16
4	353	16
5	646	16
6	1069	16
7	1778	16
8	2138	16
done	2138	16
0	16	20
1	36	20
2	74	16
3	172	16
4	353	16
5	646	16
6	1069	16
7	1778	16
8	2138	16
done	2138	16
0	2	2
1	5	1
done	5	1
0	15	18
1	37	18
2	93	16
3	211	16
4	318	16
5	365	16
6	417	16
7	570	16
8	857	16
done	857	16
0	7	10
1	13	8
2	24	4
3	39	2
4	57	2
5	68	2
6	75	2
7	77	2
done	77	2
0	13	15
1	22	14
2	39	14
3	64	14
4	68	14
done	68	14
0	6	7
1	10	6
2	15	4
3	26	2
4	50	2
5	61	2
6	68	2
7	70	2
done	70	2
0	13	15
1	22	14
2	39	14
3	64	14
4	68	14
done	68	14
0	5	6
1	9	2
2	16	2
3	26	2
4	32	2
5	41	2
6	58	2
7	65	2
8	67	2
done	67	2
0	12	14
1	21	14
2	38	14
3	63	14
4	65	14
done	65	14
0	15	19
1	35	19
2	73	15
3	169	15
4	343	15
5	636	15
6	1057	15
7	1770	15
8	2157	15
done	2157	15
0	15	19
1	35	17
2	79	15
3	198	15
4	309	15
5	616	15
6	1021	15
7	1623	15
8	2343	15
done	2343	15
0	5	6
1	9	2
2	16	2
3	26	2
4	32	2
5	41	2
6	58	2
7	65	2
8	67	2
done	67	2
0	16	20
1	36	19
2	76	17
3	187	15
4	312	15
5	619	15
6	1032	15
7	1647	15
8	2357	15
done	2357	15
0	16	20
1	36	19
2	76	17
3	187	15
4	312	15
5	619	15
6	1032	15
7	1647	15
8	2357	15
done	2357	15
0	15	19
1	35	17
2	79	15
3	198	15
4	309	15
5	616	15
6	1021	15
7	1623	15
8	2343	15
done	2343	15
0	16	20
1	46	18
2	107	18
3	232	18
4	469	18
5	1025	18
6	1688	18
7	4043	18
done	5000	18
0	14	29
1	30	15
2	79	15
3	193	15
4	424	9
5	729	8
6	1595	7
done	5000	7
0	18	23
1	50	23
2	121	19
3	320	19
4	1189	19
5	4562	19
done	5000	19
0	16	32
1	34	20
2	95	16
3	334	16
4	1087	10
5	2620	5
done	5000	5
0	13	16
1	31	14
2	59	14
3	86	14
4	90	14
done	90	14
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	5	5
1	8	5
2	11	5
3	15	5
4	16	5
done	16	5
0	9	10
1	16	10
2	28	10
3	43	10
4	56	10
5	59	10
done	59	10
0	8	9
1	13	9
2	20	9
3	23	9
4	24	9
done	24	9
0	1	1
done	1	1
0	5	5
1	9	4
2	14	4
3	18	4
4	19	4
done	19	4
0	11	14
1	25	14
2	65	14
3	133	14
4	303	14
5	1080	14
6	4925	14
done	5000	14

prune214.0ms

Filtered

104 candidates to 145 candidates (-39.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	2	6	8
Picked	1	0	1
Done	1	1	2
Total	145	11	156

Merged error: 5.9b

Counts

156 → 11

regimes608.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.9b

bsearch74.0ms

Steps

Iters	Range	Point
6	8.452635886898758e+130	9.412684251322846e+131	6.642975441552496e+131
2	-4.573495307394448e-219	-4.034898188869506e-219	-4.1022228286851245e-219
8	-6.425427201686376e+146	-2.2501015214505646e+142	-4.228989945007081e+143

Iters

Range

Point

8.452635886898758e+130

9.412684251322846e+131

6.642975441552496e+131

-4.573495307394448e-219

-4.034898188869506e-219

-4.1022228286851245e-219

-6.425427201686376e+146

-2.2501015214505646e+142

-4.228989945007081e+143

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	61
1	44	61
done	44	61

end0.0ms

sample1.8s

Algorithm

intervals

Results

345.0ms	5927×	body	80	valid
338.0ms	1001×	body	2560	valid
266.0ms	948×	body	1280	valid
171.0ms	2954×	body	80	nan
89.0ms	422×	body	640	valid
43.0ms	101×	body	5120	valid
38.0ms	234×	body	320	valid
11.0ms	101×	body	160	valid

Details

sample59.0ms

simplify58.0ms

prune8.0ms

localize16.0ms

rewrite31.0ms

series79.0ms

simplify1.3min

prune201.0ms

localize12.0ms

rewrite44.0ms

series74.0ms

simplify1.3min

prune320.0ms

localize12.0ms

rewrite30.0ms

series108.0ms

simplify1.4min

prune170.0ms

localize14.0ms

rewrite53.0ms

series118.0ms

simplify2.7min

prune214.0ms

regimes608.0ms

bsearch74.0ms

simplify4.0ms

end0.0ms

sample1.8s

Profiling